https://hilbert.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Kemeny&feedformat=atomUW-Math Wiki - User contributions [en]2021-08-01T04:18:18ZUser contributionsMediaWiki 1.30.1https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21170Algebra and Algebraic Geometry Seminar Spring 20212021-04-23T17:03:54Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| The QR decomposition for radial neural networks]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
===Eyal Subag===<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras'''<br />
<br />
Abstract: The affine W-algebras are a family of algebras whose representation theory plays an important role in conformal field theory and the geometric Langlands program. In the original paper which introduced W-algebras into mathematics, Feigin and Frenkel conclude with a striking conjecture, joint with Kac and Wakimoto, relating certain irreducible representations of affine Lie algebras and affine W-algebras via a functor since called the `plus' Drinfeld--Sokolov reduction. We have proven this conjecture in forthcoming work. The primary goal of the talk will be to give a motivated introduction to the conjecture, its history, and the objects appearing in it for non-specialists.<br />
<br />
<br />
===Iordan Ganev===<br />
The QR decomposition for radial neural networks<br />
<br />
Abstract: We present a perspective on neural networks stemming from quiver representation theory. This point of view emphasizes the symmetries inherent in neural networks, interacts nicely with gradient descent, and has the potential to improve training algorithms. As an application, we establish an analogue of the QR decomposition for radial neural networks, which leads to a dimensional reduction result. This talk is intended for a broad mathematical audience, and we explain all concepts relating to neural networks and machine learning from first principles. It is based on joint work-in-progress with Robin Walters.</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21099Algebra and Algebraic Geometry Seminar Spring 20212021-04-02T17:24:09Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21098Algebra and Algebraic Geometry Seminar Spring 20212021-04-02T17:23:10Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21097Algebra and Algebraic Geometry Seminar Spring 20212021-04-02T17:22:53Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21015Algebra and Algebraic Geometry Seminar Spring 20212021-03-18T16:41:29Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21014Algebra and Algebraic Geometry Seminar Spring 20212021-03-18T16:39:59Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20984Algebra and Algebraic Geometry Seminar Spring 20212021-03-10T16:30:49Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20983Algebra and Algebraic Geometry Seminar Spring 20212021-03-10T16:29:34Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20966Algebra and Algebraic Geometry Seminar Spring 20212021-03-09T17:46:42Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20950Algebra and Algebraic Geometry Seminar Spring 20212021-03-07T02:45:40Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20861Algebra and Algebraic Geometry Seminar Spring 20212021-02-21T19:02:44Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20860Algebra and Algebraic Geometry Seminar Spring 20212021-02-21T19:01:25Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20829Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:25:21Z<p>Kemeny: /* Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20828Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:25:05Z<p>Kemeny: /* Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20827Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:23:47Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20826Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:22:41Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]][https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20825Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:22:22Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20824Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:21:55Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[#Marian Aprodu| Koszul modules, resonance varieties and applications]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20823Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:18:28Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[#Marian Aprodu| Koszul modules, resonance varieties and applications][https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20822Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:17:45Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[#Marian Aprodu| Koszul modules, resonance varieties and applications. ] [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20821Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:16:49Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications. [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk] ]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20806Algebra and Algebraic Geometry Seminar Spring 20212021-02-09T23:00:34Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20792Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:27:31Z<p>Kemeny: /* February 26: Philip Engel */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20791Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:27:19Z<p>Kemeny: /* February 19: Dhruv Ranganathan */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20790Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:27:05Z<p>Kemeny: /* February 12: Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20789Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:26:52Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===February 12: Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20788Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:25:19Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===February 12: Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20787Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:24:16Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===February 12: Marian Aprodu===<br />
'''TBA'''<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20711Algebra and Algebraic Geometry Seminar Spring 20212021-01-31T19:33:14Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===February 12: Marian Aprodu===<br />
'''TBA'''<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20552Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:39:59Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20551Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:39:37Z<p>Kemeny: /* =Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20550Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:39:15Z<p>Kemeny: /* =Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Marian Aprodu==<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20549Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:38:52Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Marian Aprodu==<br />
'''TBA'''<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20548Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:38:31Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&diff=20525Algebra and Algebraic Geometry Seminar2021-01-17T00:33:52Z<p>Kemeny: Redirected page to Algebra and Algebraic Geometry Seminar Spring 2021</p>
<hr />
<div>#REDIRECT [[Algebra and Algebraic Geometry Seminar Spring 2021]]</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2020&diff=20524Algebra and Algebraic Geometry Seminar Fall 20202021-01-17T00:26:14Z<p>Kemeny: </p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar. The link to the Spring 2021 seminar is here: [https://www.math.wisc.edu/wiki/index.php/Algebra_and_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021 Seminar]<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2020 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|September 14 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 1/4 in lecture series at Imperial College - Register here to get the link to the talk!]<br />
|-<br />
|September 18 <br />
|[https://www.math.wisc.edu/~arinkin/ Dima Arinkin (Madison)]<br />
|[[#Dima Arinkin|Singular support of categories]]<br />
|[https://uwmadison.zoom.us/j/91919237303?pwd=SzhtYVpwSHhoVVFmQWx1NFpBVVNBQT09 Zoom link]<br />
|-<br />
|September 21 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 2/4 in lecture series at Imperial College]<br />
|-<br />
|September 25<br />
|[https://www.math.tamu.edu/~ola/ Aleksandra Sobieska (Madison)]<br />
|[[#Aleksandra Sobieska|Toward Free Resolutions Over Scrolls]]<br />
|<br />
|-<br />
|September 28 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 3/4 in lecture series at Imperial College]<br />
|-<br />
|October 2<br />
|Robert Scherer (UC Davis)<br />
|[[#Robert Scherer|A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 5 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 4/4 in lecture series at Imperial College]<br />
|-<br />
|October 7 @ 7pm<br />
|[https://www.math.wisc.edu/~shamgar// Shamgar Gurevich (Madison)]<br />
|[[#Shamgar Gurevich|Harmonic Analysis on GLn over Finite Fields]]<br />
| [https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ Register here to get link to talk at University of Sydney]<br />
|-<br />
|October 9<br />
|[https://math.berkeley.edu/~germans/ German Stefanich (Berkeley) ]<br />
|[[#German Stefanich|Categorified sheaf theory and the spectral Langlands TQFT]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 16<br />
|[https://sites.google.com/view/ruijie-yang/ Ruijie Yang (Stony Brook)]<br />
|[[#Ruijie Yang|Decomposition theorem for semisimple local systems]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 23 <br />
|[http://www-users.math.umn.edu/~ottxx141/ Nadia Ott (Mittag-Leffler Institute)]<br />
|[[#Nadia Ott|The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|October 30<br />
|[http://w3.impa.br/~heluani/ Reimundo Heluani (IMPA, Rio de Janeiro)]<br />
|[[#Reimundo Heluani|Rogers Ramanujan type identities coming from representation theory]]<br />
| <br />
|-<br />
|November 6<br />
|[https://bakker.people.uic.edu/ Ben Bakker (UIC)]<br />
|[[#Ben Bakker|Quasiprojectivity of images of mixed period maps]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|November 13<br />
|[https://pages.uoregon.edu/honigs/ Katrina Honigs (Oregon)]<br />
|[[#Katrina Honigs|An obstruction to weak approximation on some Calabi-Yau threefolds]]<br />
|<br />
|-<br />
|December 4<br />
|[https://www.iag.uni-hannover.de/de/institut/personenverzeichnis/stefan-schreieder/?&L=1 Stefan Schreieder (Hannover)]<br />
|[[#Stefan Schreieder|Refined unramified cohomology and algebraic cycles]]<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Andrei Căldăraru===<br />
'''Categorical Enumerative Invariants'''<br />
<br />
I will talk about recent papers with Junwu Tu, Si Li, and Kevin Costello where we give a computable definition of Costello's 2005 invariants and compute some of them. These invariants are associated to a pair (A,s) consisting of a cyclic A∞-algebra and a choice of splitting s of its non-commutative Hodge filtration. They are expected to recover classical Gromov-Witten invariants when A is obtained from the Fukaya category of a symplectic manifold, as well as extend various B-model invariants (solutions of Picard-Fuchs equations, BCOV invariants, B-model FJRW invariants) when A is obtained from the derived category of a manifold or a matrix factorization category.<br />
<br />
===Dima Arinkin===<br />
<br />
'''Singular support of categories'''<br />
<br />
In many situations, geometric objects on a space have some kind of singular support, which refines the usual support.<br />
For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset<br />
of the cotangent bundle; there is also a version of this notion for coherent sheaves on local complete intersections.<br />
I would like to describe a higher categorical version of this notion.<br />
<br />
Let X be a smooth variety, and let Z be a closed conical isotropic subset of the cotangent bundle of X. I will define a<br />
2-category associated with Z; its objects may be viewed as `categories over X with singular support in Z'. In particular, if Z is<br />
the zero section, this gives the notion of categories over Z in the usual sense.<br />
<br />
The project is motivated by the local geometric Langlands correspondence; I will sketch the relation with the Langlands correspondence without <br />
going into details.<br />
<br />
===Aleksandra Sobieska===<br />
'''Toward Free Resolutions Over Scrolls'''<br />
<br />
Free resolutions over the polynomial ring have a storied and active record of study. However, resolutions over other rings are much more mysterious; even simple examples can be infinite! In these cases, we look to any combinatorics of the ring to glean information. This talk will present a minimal free resolution of the ground field over the semigroup ring arising from rational normal $2$-scrolls, and (if time permits) a computation of the Betti numbers of the ground field for all rational normal $k$-scrolls.<br />
<br />
===Robert Scherer===<br />
'''A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees'''<br />
<br />
We study the identity $y(x)=xA(y(x))$, from the theory of rooted trees, for appropriate generating functions $y(x)$ and $A(x)$ with non-negative integer coefficients. A problem that has been studied extensively is to determine the asymptotics of the coefficients of $y(x)$ from analytic properties of the complex function $z\mapsto A(z)$, assumed to have a positive radius of convergence $R$. It is well-known that the vanishing of $A(x)-xA'(x)$ on $(0,R)$ is sufficient to ensure that $y(r)<R$, where $r$ is the radius of convergence of $y(x)$. This result has been generalized in the literature to account for more general functional equations than the one above, and used to determine asymptotics for the Taylor coefficients of $y(x)$. What has not been shown is whether that sufficient condition is also necessary. We show here that it is, thus establishing a criterion for sharpness of the inequality $y(r)\leq R$. As an application, we prove, and significantly extend, a 1996 conjecture of Kuperberg regarding the asymptotic growth rate of an integer sequence arising in the study of Lie algebra representations. <br />
<br />
===Shamgar Gurevich===<br />
'''Harmonic Analysis on GLn over Finite Fields'''<br />
<br />
There are many formulas that express interesting properties of a finite group G in terms of sums over<br />
its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
Trace(ρ(g)) / dim(ρ), for an irreducible representation ρ of G and an element g of G. For example, Diaconis<br />
and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G. Recently,<br />
we discovered that for classical groups G over finite fields there is a natural invariant of representations that<br />
provides strong information on the character ratio. We call this invariant rank. Rank suggests a new<br />
organization of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s<br />
“philosophy of cusp forms”, which is (since the 60s) the main organization principle, and is based on the (huge<br />
collection) of “Large” representations. This talk will discuss the notion of rank for the group GLn over finite<br />
fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify<br />
mixing time and rate for random walks. This is joint work with Roger Howe (Yale and Texas A&M). The<br />
numerics for this work was carried with Steve Goldstein (Madison) and John Cannon (Sydney).<br />
<br />
===German Stefanich===<br />
'''Categorified sheaf theory and the spectral Langlands TQFT'''<br />
<br />
It is expected that the Betti version of the geometric Langlands program should ultimately be about the equivalence of two 4-dimensional topological field theories. In this talk I will give an overview of ongoing work in categorified sheaf theory and explain how one can use it to describe the categories of boundary conditions arising on the spectral side.<br />
<br />
===Ruijie Yang===<br />
'''Decomposition theorem for semisimple local systems<br />
'''<br />
<br />
In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved by Mochizuki and Sabbah in a series of very long papers via harmonic analysis and $D$-modules. In this talk, I would like to explain a simpler proof in the case of semisimple local systems using a more geometric approach. This is joint work in progress with Chuanhao Wei. <br />
<br />
===Nadia Ott===<br />
'''The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures<br />
<br />
Super Riemann surfaces (SUSY curves) arise in the formulation of superstring theory, and their moduli spaces, called supermoduli space, are the integration spaces for superstring scattering amplitudes. I will focus specifically on genus zero SUSY curves. As with ordinary curves, genus zero SUSY curves present a certain challenge, as they have an infinitesimal group of automorphisms, and so in order for the moduli problem to be representable by a Deligne-Mumford superstack, we must introduce punctures. In fact, there are two kinds of punctures on a SUSY curve of Neveu-Schwarz or Ramond type. Neveu-Schwarz punctures are entirely analogous to the marked points in ordinary moduli theory. By contrast, the Ramond punctures are more subtle and have no ordinary analog. I will give a construction of the moduli space M_{0,n}^R of genus zero SUSY curves with Ramond punctures as a Deligne-Mumford superstack by an explicit quotient presentation (rather than by an abstract existence argument).<br />
<br />
===Reimundo Heluani===<br />
'''A Rogers-Ramanujan-Slater type identity related to the Ising model'''<br />
<br />
We prove three new q-series identities of the Rogers-Ramanujan-Slater<br />
type. We find a PBW basis for the Ising model as a consequence of one of these<br />
identities. If time permits it will be shown that the singular support of the<br />
Ising model is a hyper-surface (in the differential sense) on the arc space of<br />
it's associated scheme. This is joint work with G. E. Andrews and J. van Ekeren<br />
and is available online at https://arxiv.org/abs/2005.10769<br />
<br />
===Ben Bakker===<br />
'''Quasiprojectivity of images of mixed period maps'''<br />
<br />
Families of smooth proper algebraic varieties give rise to variations of pure Hodge structures; general algebraic families yield variations of mixed Hodge structures. It was conjectured by Griffiths and proven in joint work with Y. Brunebarbe and J. Tsimerman that the closure of the image of the classifying map to the moduli space of Hodge structures is a quasiprojective algebraic variety in the pure case. In this talk I will explain how to extend this result to the mixed setting. As in the pure case, the proof heavily uses techniques from o-minimal geometry, and we will also discuss some related applications. <br />
<br />
===Katrina Honigs===<br />
'''An obstruction to weak approximation on some Calabi-Yau threefolds'''<br />
<br />
The study of Q-rational points on algebraic varieties is fundamental to arithmetic geometry. One of the few methods available to show that a variety does not have any Q-points is to give a Brauer-Manin obstruction. Hosono and Takagi have constructed a class of Calabi-Yau threefolds that occur as a linear section of a double quintic symmetroid and given a detailed analysis of them as complex varieties in the context of mirror symmetry. This construction can be used to produce varieties over Q as well, and these threefolds come tantalizingly equipped with a natural Brauer class. In work with Hashimoto, Lamarche and Vogt, we analyze these threefolds and their Brauer class over Q and give a condition under which the Brauer class obstructs weak approximation, though it cannot obstruct the existence of Q-rational points.<br />
<br />
===Stefan Schreieder===<br />
'''Refined unramified cohomology and algebraic cycles'''<br />
<br />
We introduce refined unramified cohomology groups, explain their relation to classical unramified cohomology, and prove some general comparison theorems to certain cycle groups. This generalizes and simplifies work of Bloch—Ogus, Colliot-Thélène—Voisin, Voisin, and Ma who dealt with cycles of low (co-)dimension. Our approach has several applications. Most notably, it allows to construct the first example of a variety with infinite torsion in its Griffiths group.</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2020&diff=20523Algebra and Algebraic Geometry Seminar Fall 20202021-01-17T00:26:01Z<p>Kemeny: </p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar. The link to the Spring 2021 seminar is here [https://www.math.wisc.edu/wiki/index.php/Algebra_and_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021 Seminar]<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2020 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|September 14 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 1/4 in lecture series at Imperial College - Register here to get the link to the talk!]<br />
|-<br />
|September 18 <br />
|[https://www.math.wisc.edu/~arinkin/ Dima Arinkin (Madison)]<br />
|[[#Dima Arinkin|Singular support of categories]]<br />
|[https://uwmadison.zoom.us/j/91919237303?pwd=SzhtYVpwSHhoVVFmQWx1NFpBVVNBQT09 Zoom link]<br />
|-<br />
|September 21 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 2/4 in lecture series at Imperial College]<br />
|-<br />
|September 25<br />
|[https://www.math.tamu.edu/~ola/ Aleksandra Sobieska (Madison)]<br />
|[[#Aleksandra Sobieska|Toward Free Resolutions Over Scrolls]]<br />
|<br />
|-<br />
|September 28 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 3/4 in lecture series at Imperial College]<br />
|-<br />
|October 2<br />
|Robert Scherer (UC Davis)<br />
|[[#Robert Scherer|A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 5 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 4/4 in lecture series at Imperial College]<br />
|-<br />
|October 7 @ 7pm<br />
|[https://www.math.wisc.edu/~shamgar// Shamgar Gurevich (Madison)]<br />
|[[#Shamgar Gurevich|Harmonic Analysis on GLn over Finite Fields]]<br />
| [https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ Register here to get link to talk at University of Sydney]<br />
|-<br />
|October 9<br />
|[https://math.berkeley.edu/~germans/ German Stefanich (Berkeley) ]<br />
|[[#German Stefanich|Categorified sheaf theory and the spectral Langlands TQFT]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 16<br />
|[https://sites.google.com/view/ruijie-yang/ Ruijie Yang (Stony Brook)]<br />
|[[#Ruijie Yang|Decomposition theorem for semisimple local systems]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 23 <br />
|[http://www-users.math.umn.edu/~ottxx141/ Nadia Ott (Mittag-Leffler Institute)]<br />
|[[#Nadia Ott|The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|October 30<br />
|[http://w3.impa.br/~heluani/ Reimundo Heluani (IMPA, Rio de Janeiro)]<br />
|[[#Reimundo Heluani|Rogers Ramanujan type identities coming from representation theory]]<br />
| <br />
|-<br />
|November 6<br />
|[https://bakker.people.uic.edu/ Ben Bakker (UIC)]<br />
|[[#Ben Bakker|Quasiprojectivity of images of mixed period maps]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|November 13<br />
|[https://pages.uoregon.edu/honigs/ Katrina Honigs (Oregon)]<br />
|[[#Katrina Honigs|An obstruction to weak approximation on some Calabi-Yau threefolds]]<br />
|<br />
|-<br />
|December 4<br />
|[https://www.iag.uni-hannover.de/de/institut/personenverzeichnis/stefan-schreieder/?&L=1 Stefan Schreieder (Hannover)]<br />
|[[#Stefan Schreieder|Refined unramified cohomology and algebraic cycles]]<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Andrei Căldăraru===<br />
'''Categorical Enumerative Invariants'''<br />
<br />
I will talk about recent papers with Junwu Tu, Si Li, and Kevin Costello where we give a computable definition of Costello's 2005 invariants and compute some of them. These invariants are associated to a pair (A,s) consisting of a cyclic A∞-algebra and a choice of splitting s of its non-commutative Hodge filtration. They are expected to recover classical Gromov-Witten invariants when A is obtained from the Fukaya category of a symplectic manifold, as well as extend various B-model invariants (solutions of Picard-Fuchs equations, BCOV invariants, B-model FJRW invariants) when A is obtained from the derived category of a manifold or a matrix factorization category.<br />
<br />
===Dima Arinkin===<br />
<br />
'''Singular support of categories'''<br />
<br />
In many situations, geometric objects on a space have some kind of singular support, which refines the usual support.<br />
For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset<br />
of the cotangent bundle; there is also a version of this notion for coherent sheaves on local complete intersections.<br />
I would like to describe a higher categorical version of this notion.<br />
<br />
Let X be a smooth variety, and let Z be a closed conical isotropic subset of the cotangent bundle of X. I will define a<br />
2-category associated with Z; its objects may be viewed as `categories over X with singular support in Z'. In particular, if Z is<br />
the zero section, this gives the notion of categories over Z in the usual sense.<br />
<br />
The project is motivated by the local geometric Langlands correspondence; I will sketch the relation with the Langlands correspondence without <br />
going into details.<br />
<br />
===Aleksandra Sobieska===<br />
'''Toward Free Resolutions Over Scrolls'''<br />
<br />
Free resolutions over the polynomial ring have a storied and active record of study. However, resolutions over other rings are much more mysterious; even simple examples can be infinite! In these cases, we look to any combinatorics of the ring to glean information. This talk will present a minimal free resolution of the ground field over the semigroup ring arising from rational normal $2$-scrolls, and (if time permits) a computation of the Betti numbers of the ground field for all rational normal $k$-scrolls.<br />
<br />
===Robert Scherer===<br />
'''A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees'''<br />
<br />
We study the identity $y(x)=xA(y(x))$, from the theory of rooted trees, for appropriate generating functions $y(x)$ and $A(x)$ with non-negative integer coefficients. A problem that has been studied extensively is to determine the asymptotics of the coefficients of $y(x)$ from analytic properties of the complex function $z\mapsto A(z)$, assumed to have a positive radius of convergence $R$. It is well-known that the vanishing of $A(x)-xA'(x)$ on $(0,R)$ is sufficient to ensure that $y(r)<R$, where $r$ is the radius of convergence of $y(x)$. This result has been generalized in the literature to account for more general functional equations than the one above, and used to determine asymptotics for the Taylor coefficients of $y(x)$. What has not been shown is whether that sufficient condition is also necessary. We show here that it is, thus establishing a criterion for sharpness of the inequality $y(r)\leq R$. As an application, we prove, and significantly extend, a 1996 conjecture of Kuperberg regarding the asymptotic growth rate of an integer sequence arising in the study of Lie algebra representations. <br />
<br />
===Shamgar Gurevich===<br />
'''Harmonic Analysis on GLn over Finite Fields'''<br />
<br />
There are many formulas that express interesting properties of a finite group G in terms of sums over<br />
its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
Trace(ρ(g)) / dim(ρ), for an irreducible representation ρ of G and an element g of G. For example, Diaconis<br />
and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G. Recently,<br />
we discovered that for classical groups G over finite fields there is a natural invariant of representations that<br />
provides strong information on the character ratio. We call this invariant rank. Rank suggests a new<br />
organization of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s<br />
“philosophy of cusp forms”, which is (since the 60s) the main organization principle, and is based on the (huge<br />
collection) of “Large” representations. This talk will discuss the notion of rank for the group GLn over finite<br />
fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify<br />
mixing time and rate for random walks. This is joint work with Roger Howe (Yale and Texas A&M). The<br />
numerics for this work was carried with Steve Goldstein (Madison) and John Cannon (Sydney).<br />
<br />
===German Stefanich===<br />
'''Categorified sheaf theory and the spectral Langlands TQFT'''<br />
<br />
It is expected that the Betti version of the geometric Langlands program should ultimately be about the equivalence of two 4-dimensional topological field theories. In this talk I will give an overview of ongoing work in categorified sheaf theory and explain how one can use it to describe the categories of boundary conditions arising on the spectral side.<br />
<br />
===Ruijie Yang===<br />
'''Decomposition theorem for semisimple local systems<br />
'''<br />
<br />
In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved by Mochizuki and Sabbah in a series of very long papers via harmonic analysis and $D$-modules. In this talk, I would like to explain a simpler proof in the case of semisimple local systems using a more geometric approach. This is joint work in progress with Chuanhao Wei. <br />
<br />
===Nadia Ott===<br />
'''The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures<br />
<br />
Super Riemann surfaces (SUSY curves) arise in the formulation of superstring theory, and their moduli spaces, called supermoduli space, are the integration spaces for superstring scattering amplitudes. I will focus specifically on genus zero SUSY curves. As with ordinary curves, genus zero SUSY curves present a certain challenge, as they have an infinitesimal group of automorphisms, and so in order for the moduli problem to be representable by a Deligne-Mumford superstack, we must introduce punctures. In fact, there are two kinds of punctures on a SUSY curve of Neveu-Schwarz or Ramond type. Neveu-Schwarz punctures are entirely analogous to the marked points in ordinary moduli theory. By contrast, the Ramond punctures are more subtle and have no ordinary analog. I will give a construction of the moduli space M_{0,n}^R of genus zero SUSY curves with Ramond punctures as a Deligne-Mumford superstack by an explicit quotient presentation (rather than by an abstract existence argument).<br />
<br />
===Reimundo Heluani===<br />
'''A Rogers-Ramanujan-Slater type identity related to the Ising model'''<br />
<br />
We prove three new q-series identities of the Rogers-Ramanujan-Slater<br />
type. We find a PBW basis for the Ising model as a consequence of one of these<br />
identities. If time permits it will be shown that the singular support of the<br />
Ising model is a hyper-surface (in the differential sense) on the arc space of<br />
it's associated scheme. This is joint work with G. E. Andrews and J. van Ekeren<br />
and is available online at https://arxiv.org/abs/2005.10769<br />
<br />
===Ben Bakker===<br />
'''Quasiprojectivity of images of mixed period maps'''<br />
<br />
Families of smooth proper algebraic varieties give rise to variations of pure Hodge structures; general algebraic families yield variations of mixed Hodge structures. It was conjectured by Griffiths and proven in joint work with Y. Brunebarbe and J. Tsimerman that the closure of the image of the classifying map to the moduli space of Hodge structures is a quasiprojective algebraic variety in the pure case. In this talk I will explain how to extend this result to the mixed setting. As in the pure case, the proof heavily uses techniques from o-minimal geometry, and we will also discuss some related applications. <br />
<br />
===Katrina Honigs===<br />
'''An obstruction to weak approximation on some Calabi-Yau threefolds'''<br />
<br />
The study of Q-rational points on algebraic varieties is fundamental to arithmetic geometry. One of the few methods available to show that a variety does not have any Q-points is to give a Brauer-Manin obstruction. Hosono and Takagi have constructed a class of Calabi-Yau threefolds that occur as a linear section of a double quintic symmetroid and given a detailed analysis of them as complex varieties in the context of mirror symmetry. This construction can be used to produce varieties over Q as well, and these threefolds come tantalizingly equipped with a natural Brauer class. In work with Hashimoto, Lamarche and Vogt, we analyze these threefolds and their Brauer class over Q and give a condition under which the Brauer class obstructs weak approximation, though it cannot obstruct the existence of Q-rational points.<br />
<br />
===Stefan Schreieder===<br />
'''Refined unramified cohomology and algebraic cycles'''<br />
<br />
We introduce refined unramified cohomology groups, explain their relation to classical unramified cohomology, and prove some general comparison theorems to certain cycle groups. This generalizes and simplifies work of Bloch—Ogus, Colliot-Thélène—Voisin, Voisin, and Ma who dealt with cycles of low (co-)dimension. Our approach has several applications. Most notably, it allows to construct the first example of a variety with infinite torsion in its Griffiths group.</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20522Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:17:14Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA (Feb)<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA (April)<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20521Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:17:00Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA (Feb)<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA (April)<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20519Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:14:56Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA (Feb)<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA (April)<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20518Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:14:31Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA (Feb)<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA (April)<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20516Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:12:56Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA (Feb)<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20515Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:12:25Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20514Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:11:54Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20513Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:11:18Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA @<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20512Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:10:59Z<p>Kemeny: Created page with "The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar. ==Algebra and Algebraic Ge..."</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA @ <br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2020&diff=20408Algebra and Algebraic Geometry Seminar Fall 20202020-12-01T00:36:16Z<p>Kemeny: /* Fall 2020 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2020 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|September 14 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 1/4 in lecture series at Imperial College - Register here to get the link to the talk!]<br />
|-<br />
|September 18 <br />
|[https://www.math.wisc.edu/~arinkin/ Dima Arinkin (Madison)]<br />
|[[#Dima Arinkin|Singular support of categories]]<br />
|[https://uwmadison.zoom.us/j/91919237303?pwd=SzhtYVpwSHhoVVFmQWx1NFpBVVNBQT09 Zoom link]<br />
|-<br />
|September 21 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 2/4 in lecture series at Imperial College]<br />
|-<br />
|September 25<br />
|[https://www.math.tamu.edu/~ola/ Aleksandra Sobieska (Madison)]<br />
|[[#Aleksandra Sobieska|Toward Free Resolutions Over Scrolls]]<br />
|<br />
|-<br />
|September 28 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 3/4 in lecture series at Imperial College]<br />
|-<br />
|October 2<br />
|Robert Scherer (UC Davis)<br />
|[[#Robert Scherer|A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 5 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 4/4 in lecture series at Imperial College]<br />
|-<br />
|October 7 @ 7pm<br />
|[https://www.math.wisc.edu/~shamgar// Shamgar Gurevich (Madison)]<br />
|[[#Shamgar Gurevich|Harmonic Analysis on GLn over Finite Fields]]<br />
| [https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ Register here to get link to talk at University of Sydney]<br />
|-<br />
|October 9<br />
|[https://math.berkeley.edu/~germans/ German Stefanich (Berkeley) ]<br />
|[[#German Stefanich|Categorified sheaf theory and the spectral Langlands TQFT]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 16<br />
|[https://sites.google.com/view/ruijie-yang/ Ruijie Yang (Stony Brook)]<br />
|[[#Ruijie Yang|Decomposition theorem for semisimple local systems]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 23 <br />
|[http://www-users.math.umn.edu/~ottxx141/ Nadia Ott (Mittag-Leffler Institute)]<br />
|[[#Nadia Ott|The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|October 30<br />
|[http://w3.impa.br/~heluani/ Reimundo Heluani (IMPA, Rio de Janeiro)]<br />
|[[#Reimundo Heluani|Rogers Ramanujan type identities coming from representation theory]]<br />
| <br />
|-<br />
|November 6<br />
|[https://bakker.people.uic.edu/ Ben Bakker (UIC)]<br />
|[[#Ben Bakker|Quasiprojectivity of images of mixed period maps]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|November 13<br />
|[https://pages.uoregon.edu/honigs/ Katrina Honigs (Oregon)]<br />
|[[#Katrina Honigs|An obstruction to weak approximation on some Calabi-Yau threefolds]]<br />
|<br />
|-<br />
|December 4<br />
|[https://www.iag.uni-hannover.de/de/institut/personenverzeichnis/stefan-schreieder/?&L=1 Stefan Schreieder (Hannover)]<br />
|[[#Stefan Schreieder|Refined unramified cohomology and algebraic cycles]]<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Andrei Căldăraru===<br />
'''Categorical Enumerative Invariants'''<br />
<br />
I will talk about recent papers with Junwu Tu, Si Li, and Kevin Costello where we give a computable definition of Costello's 2005 invariants and compute some of them. These invariants are associated to a pair (A,s) consisting of a cyclic A∞-algebra and a choice of splitting s of its non-commutative Hodge filtration. They are expected to recover classical Gromov-Witten invariants when A is obtained from the Fukaya category of a symplectic manifold, as well as extend various B-model invariants (solutions of Picard-Fuchs equations, BCOV invariants, B-model FJRW invariants) when A is obtained from the derived category of a manifold or a matrix factorization category.<br />
<br />
===Dima Arinkin===<br />
<br />
'''Singular support of categories'''<br />
<br />
In many situations, geometric objects on a space have some kind of singular support, which refines the usual support.<br />
For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset<br />
of the cotangent bundle; there is also a version of this notion for coherent sheaves on local complete intersections.<br />
I would like to describe a higher categorical version of this notion.<br />
<br />
Let X be a smooth variety, and let Z be a closed conical isotropic subset of the cotangent bundle of X. I will define a<br />
2-category associated with Z; its objects may be viewed as `categories over X with singular support in Z'. In particular, if Z is<br />
the zero section, this gives the notion of categories over Z in the usual sense.<br />
<br />
The project is motivated by the local geometric Langlands correspondence; I will sketch the relation with the Langlands correspondence without <br />
going into details.<br />
<br />
===Aleksandra Sobieska===<br />
'''Toward Free Resolutions Over Scrolls'''<br />
<br />
Free resolutions over the polynomial ring have a storied and active record of study. However, resolutions over other rings are much more mysterious; even simple examples can be infinite! In these cases, we look to any combinatorics of the ring to glean information. This talk will present a minimal free resolution of the ground field over the semigroup ring arising from rational normal $2$-scrolls, and (if time permits) a computation of the Betti numbers of the ground field for all rational normal $k$-scrolls.<br />
<br />
===Robert Scherer===<br />
'''A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees'''<br />
<br />
We study the identity $y(x)=xA(y(x))$, from the theory of rooted trees, for appropriate generating functions $y(x)$ and $A(x)$ with non-negative integer coefficients. A problem that has been studied extensively is to determine the asymptotics of the coefficients of $y(x)$ from analytic properties of the complex function $z\mapsto A(z)$, assumed to have a positive radius of convergence $R$. It is well-known that the vanishing of $A(x)-xA'(x)$ on $(0,R)$ is sufficient to ensure that $y(r)<R$, where $r$ is the radius of convergence of $y(x)$. This result has been generalized in the literature to account for more general functional equations than the one above, and used to determine asymptotics for the Taylor coefficients of $y(x)$. What has not been shown is whether that sufficient condition is also necessary. We show here that it is, thus establishing a criterion for sharpness of the inequality $y(r)\leq R$. As an application, we prove, and significantly extend, a 1996 conjecture of Kuperberg regarding the asymptotic growth rate of an integer sequence arising in the study of Lie algebra representations. <br />
<br />
===Shamgar Gurevich===<br />
'''Harmonic Analysis on GLn over Finite Fields'''<br />
<br />
There are many formulas that express interesting properties of a finite group G in terms of sums over<br />
its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
Trace(ρ(g)) / dim(ρ), for an irreducible representation ρ of G and an element g of G. For example, Diaconis<br />
and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G. Recently,<br />
we discovered that for classical groups G over finite fields there is a natural invariant of representations that<br />
provides strong information on the character ratio. We call this invariant rank. Rank suggests a new<br />
organization of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s<br />
“philosophy of cusp forms”, which is (since the 60s) the main organization principle, and is based on the (huge<br />
collection) of “Large” representations. This talk will discuss the notion of rank for the group GLn over finite<br />
fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify<br />
mixing time and rate for random walks. This is joint work with Roger Howe (Yale and Texas A&M). The<br />
numerics for this work was carried with Steve Goldstein (Madison) and John Cannon (Sydney).<br />
<br />
===German Stefanich===<br />
'''Categorified sheaf theory and the spectral Langlands TQFT'''<br />
<br />
It is expected that the Betti version of the geometric Langlands program should ultimately be about the equivalence of two 4-dimensional topological field theories. In this talk I will give an overview of ongoing work in categorified sheaf theory and explain how one can use it to describe the categories of boundary conditions arising on the spectral side.<br />
<br />
===Ruijie Yang===<br />
'''Decomposition theorem for semisimple local systems<br />
'''<br />
<br />
In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved by Mochizuki and Sabbah in a series of very long papers via harmonic analysis and $D$-modules. In this talk, I would like to explain a simpler proof in the case of semisimple local systems using a more geometric approach. This is joint work in progress with Chuanhao Wei. <br />
<br />
===Nadia Ott===<br />
'''The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures<br />
<br />
Super Riemann surfaces (SUSY curves) arise in the formulation of superstring theory, and their moduli spaces, called supermoduli space, are the integration spaces for superstring scattering amplitudes. I will focus specifically on genus zero SUSY curves. As with ordinary curves, genus zero SUSY curves present a certain challenge, as they have an infinitesimal group of automorphisms, and so in order for the moduli problem to be representable by a Deligne-Mumford superstack, we must introduce punctures. In fact, there are two kinds of punctures on a SUSY curve of Neveu-Schwarz or Ramond type. Neveu-Schwarz punctures are entirely analogous to the marked points in ordinary moduli theory. By contrast, the Ramond punctures are more subtle and have no ordinary analog. I will give a construction of the moduli space M_{0,n}^R of genus zero SUSY curves with Ramond punctures as a Deligne-Mumford superstack by an explicit quotient presentation (rather than by an abstract existence argument).<br />
<br />
===Reimundo Heluani===<br />
'''A Rogers-Ramanujan-Slater type identity related to the Ising model'''<br />
<br />
We prove three new q-series identities of the Rogers-Ramanujan-Slater<br />
type. We find a PBW basis for the Ising model as a consequence of one of these<br />
identities. If time permits it will be shown that the singular support of the<br />
Ising model is a hyper-surface (in the differential sense) on the arc space of<br />
it's associated scheme. This is joint work with G. E. Andrews and J. van Ekeren<br />
and is available online at https://arxiv.org/abs/2005.10769<br />
<br />
===Ben Bakker===<br />
'''Quasiprojectivity of images of mixed period maps'''<br />
<br />
Families of smooth proper algebraic varieties give rise to variations of pure Hodge structures; general algebraic families yield variations of mixed Hodge structures. It was conjectured by Griffiths and proven in joint work with Y. Brunebarbe and J. Tsimerman that the closure of the image of the classifying map to the moduli space of Hodge structures is a quasiprojective algebraic variety in the pure case. In this talk I will explain how to extend this result to the mixed setting. As in the pure case, the proof heavily uses techniques from o-minimal geometry, and we will also discuss some related applications. <br />
<br />
===Katrina Honigs===<br />
'''An obstruction to weak approximation on some Calabi-Yau threefolds'''<br />
<br />
The study of Q-rational points on algebraic varieties is fundamental to arithmetic geometry. One of the few methods available to show that a variety does not have any Q-points is to give a Brauer-Manin obstruction. Hosono and Takagi have constructed a class of Calabi-Yau threefolds that occur as a linear section of a double quintic symmetroid and given a detailed analysis of them as complex varieties in the context of mirror symmetry. This construction can be used to produce varieties over Q as well, and these threefolds come tantalizingly equipped with a natural Brauer class. In work with Hashimoto, Lamarche and Vogt, we analyze these threefolds and their Brauer class over Q and give a condition under which the Brauer class obstructs weak approximation, though it cannot obstruct the existence of Q-rational points.<br />
<br />
===Stefan Schreieder===<br />
'''Refined unramified cohomology and algebraic cycles'''<br />
<br />
We introduce refined unramified cohomology groups, explain their relation to classical unramified cohomology, and prove some general comparison theorems to certain cycle groups. This generalizes and simplifies work of Bloch—Ogus, Colliot-Thélène—Voisin, Voisin, and Ma who dealt with cycles of low (co-)dimension. Our approach has several applications. Most notably, it allows to construct the first example of a variety with infinite torsion in its Griffiths group.</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2020&diff=20407Algebra and Algebraic Geometry Seminar Fall 20202020-12-01T00:35:39Z<p>Kemeny: /* Fall 2020 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2020 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|September 14 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 1/4 in lecture series at Imperial College - Register here to get the link to the talk!]<br />
|-<br />
|September 18 <br />
|[https://www.math.wisc.edu/~arinkin/ Dima Arinkin (Madison)]<br />
|[[#Dima Arinkin|Singular support of categories]]<br />
|[https://uwmadison.zoom.us/j/91919237303?pwd=SzhtYVpwSHhoVVFmQWx1NFpBVVNBQT09 Zoom link]<br />
|-<br />
|September 21 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 2/4 in lecture series at Imperial College]<br />
|-<br />
|September 25<br />
|[https://www.math.tamu.edu/~ola/ Aleksandra Sobieska (Madison)]<br />
|[[#Aleksandra Sobieska|Toward Free Resolutions Over Scrolls]]<br />
|<br />
|-<br />
|September 28 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 3/4 in lecture series at Imperial College]<br />
|-<br />
|October 2<br />
|Robert Scherer (UC Davis)<br />
|[[#Robert Scherer|A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 5 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 4/4 in lecture series at Imperial College]<br />
|-<br />
|October 7 @ 7pm<br />
|[https://www.math.wisc.edu/~shamgar// Shamgar Gurevich (Madison)]<br />
|[[#Shamgar Gurevich|Harmonic Analysis on GLn over Finite Fields]]<br />
| [https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ Register here to get link to talk at University of Sydney]<br />
|-<br />
|October 9<br />
|[https://math.berkeley.edu/~germans/ German Stefanich (Berkeley) ]<br />
|[[#German Stefanich|Categorified sheaf theory and the spectral Langlands TQFT]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 16<br />
|[https://sites.google.com/view/ruijie-yang/ Ruijie Yang (Stony Brook)]<br />
|[[#Ruijie Yang|Decomposition theorem for semisimple local systems]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 23 <br />
|[http://www-users.math.umn.edu/~ottxx141/ Nadia Ott (Mittag-Leffler Institute)]<br />
|[[#Nadia Ott|The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|October 30<br />
|[http://w3.impa.br/~heluani/ Reimundo Heluani (IMPA, Rio de Janeiro)]<br />
|[[#Reimundo Heluani|Rogers Ramanujan type identities coming from representation theory]]<br />
| <br />
|-<br />
|November 6<br />
|[https://bakker.people.uic.edu/ Ben Bakker (UIC)]<br />
|[[#Ben Bakker|Quasiprojectivity of images of mixed period maps]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|November 13<br />
|[https://pages.uoregon.edu/honigs/ Katrina Honigs (Oregon)]<br />
|[[#Katrina Honigs|An obstruction to weak approximation on some Calabi-Yau threefolds]]<br />
|<br />
|-<br />
|December 4<br />
|[https://www.iag.uni-hannover.de/de/institut/personenverzeichnis/stefan-schreieder/?&L=1 Stefan Schreieder (Hannover)]<br />
|[[#Refined unramified cohomology and algebraic cycles]]<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Andrei Căldăraru===<br />
'''Categorical Enumerative Invariants'''<br />
<br />
I will talk about recent papers with Junwu Tu, Si Li, and Kevin Costello where we give a computable definition of Costello's 2005 invariants and compute some of them. These invariants are associated to a pair (A,s) consisting of a cyclic A∞-algebra and a choice of splitting s of its non-commutative Hodge filtration. They are expected to recover classical Gromov-Witten invariants when A is obtained from the Fukaya category of a symplectic manifold, as well as extend various B-model invariants (solutions of Picard-Fuchs equations, BCOV invariants, B-model FJRW invariants) when A is obtained from the derived category of a manifold or a matrix factorization category.<br />
<br />
===Dima Arinkin===<br />
<br />
'''Singular support of categories'''<br />
<br />
In many situations, geometric objects on a space have some kind of singular support, which refines the usual support.<br />
For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset<br />
of the cotangent bundle; there is also a version of this notion for coherent sheaves on local complete intersections.<br />
I would like to describe a higher categorical version of this notion.<br />
<br />
Let X be a smooth variety, and let Z be a closed conical isotropic subset of the cotangent bundle of X. I will define a<br />
2-category associated with Z; its objects may be viewed as `categories over X with singular support in Z'. In particular, if Z is<br />
the zero section, this gives the notion of categories over Z in the usual sense.<br />
<br />
The project is motivated by the local geometric Langlands correspondence; I will sketch the relation with the Langlands correspondence without <br />
going into details.<br />
<br />
===Aleksandra Sobieska===<br />
'''Toward Free Resolutions Over Scrolls'''<br />
<br />
Free resolutions over the polynomial ring have a storied and active record of study. However, resolutions over other rings are much more mysterious; even simple examples can be infinite! In these cases, we look to any combinatorics of the ring to glean information. This talk will present a minimal free resolution of the ground field over the semigroup ring arising from rational normal $2$-scrolls, and (if time permits) a computation of the Betti numbers of the ground field for all rational normal $k$-scrolls.<br />
<br />
===Robert Scherer===<br />
'''A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees'''<br />
<br />
We study the identity $y(x)=xA(y(x))$, from the theory of rooted trees, for appropriate generating functions $y(x)$ and $A(x)$ with non-negative integer coefficients. A problem that has been studied extensively is to determine the asymptotics of the coefficients of $y(x)$ from analytic properties of the complex function $z\mapsto A(z)$, assumed to have a positive radius of convergence $R$. It is well-known that the vanishing of $A(x)-xA'(x)$ on $(0,R)$ is sufficient to ensure that $y(r)<R$, where $r$ is the radius of convergence of $y(x)$. This result has been generalized in the literature to account for more general functional equations than the one above, and used to determine asymptotics for the Taylor coefficients of $y(x)$. What has not been shown is whether that sufficient condition is also necessary. We show here that it is, thus establishing a criterion for sharpness of the inequality $y(r)\leq R$. As an application, we prove, and significantly extend, a 1996 conjecture of Kuperberg regarding the asymptotic growth rate of an integer sequence arising in the study of Lie algebra representations. <br />
<br />
===Shamgar Gurevich===<br />
'''Harmonic Analysis on GLn over Finite Fields'''<br />
<br />
There are many formulas that express interesting properties of a finite group G in terms of sums over<br />
its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
Trace(ρ(g)) / dim(ρ), for an irreducible representation ρ of G and an element g of G. For example, Diaconis<br />
and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G. Recently,<br />
we discovered that for classical groups G over finite fields there is a natural invariant of representations that<br />
provides strong information on the character ratio. We call this invariant rank. Rank suggests a new<br />
organization of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s<br />
“philosophy of cusp forms”, which is (since the 60s) the main organization principle, and is based on the (huge<br />
collection) of “Large” representations. This talk will discuss the notion of rank for the group GLn over finite<br />
fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify<br />
mixing time and rate for random walks. This is joint work with Roger Howe (Yale and Texas A&M). The<br />
numerics for this work was carried with Steve Goldstein (Madison) and John Cannon (Sydney).<br />
<br />
===German Stefanich===<br />
'''Categorified sheaf theory and the spectral Langlands TQFT'''<br />
<br />
It is expected that the Betti version of the geometric Langlands program should ultimately be about the equivalence of two 4-dimensional topological field theories. In this talk I will give an overview of ongoing work in categorified sheaf theory and explain how one can use it to describe the categories of boundary conditions arising on the spectral side.<br />
<br />
===Ruijie Yang===<br />
'''Decomposition theorem for semisimple local systems<br />
'''<br />
<br />
In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved by Mochizuki and Sabbah in a series of very long papers via harmonic analysis and $D$-modules. In this talk, I would like to explain a simpler proof in the case of semisimple local systems using a more geometric approach. This is joint work in progress with Chuanhao Wei. <br />
<br />
===Nadia Ott===<br />
'''The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures<br />
<br />
Super Riemann surfaces (SUSY curves) arise in the formulation of superstring theory, and their moduli spaces, called supermoduli space, are the integration spaces for superstring scattering amplitudes. I will focus specifically on genus zero SUSY curves. As with ordinary curves, genus zero SUSY curves present a certain challenge, as they have an infinitesimal group of automorphisms, and so in order for the moduli problem to be representable by a Deligne-Mumford superstack, we must introduce punctures. In fact, there are two kinds of punctures on a SUSY curve of Neveu-Schwarz or Ramond type. Neveu-Schwarz punctures are entirely analogous to the marked points in ordinary moduli theory. By contrast, the Ramond punctures are more subtle and have no ordinary analog. I will give a construction of the moduli space M_{0,n}^R of genus zero SUSY curves with Ramond punctures as a Deligne-Mumford superstack by an explicit quotient presentation (rather than by an abstract existence argument).<br />
<br />
===Reimundo Heluani===<br />
'''A Rogers-Ramanujan-Slater type identity related to the Ising model'''<br />
<br />
We prove three new q-series identities of the Rogers-Ramanujan-Slater<br />
type. We find a PBW basis for the Ising model as a consequence of one of these<br />
identities. If time permits it will be shown that the singular support of the<br />
Ising model is a hyper-surface (in the differential sense) on the arc space of<br />
it's associated scheme. This is joint work with G. E. Andrews and J. van Ekeren<br />
and is available online at https://arxiv.org/abs/2005.10769<br />
<br />
===Ben Bakker===<br />
'''Quasiprojectivity of images of mixed period maps'''<br />
<br />
Families of smooth proper algebraic varieties give rise to variations of pure Hodge structures; general algebraic families yield variations of mixed Hodge structures. It was conjectured by Griffiths and proven in joint work with Y. Brunebarbe and J. Tsimerman that the closure of the image of the classifying map to the moduli space of Hodge structures is a quasiprojective algebraic variety in the pure case. In this talk I will explain how to extend this result to the mixed setting. As in the pure case, the proof heavily uses techniques from o-minimal geometry, and we will also discuss some related applications. <br />
<br />
===Katrina Honigs===<br />
'''An obstruction to weak approximation on some Calabi-Yau threefolds'''<br />
<br />
The study of Q-rational points on algebraic varieties is fundamental to arithmetic geometry. One of the few methods available to show that a variety does not have any Q-points is to give a Brauer-Manin obstruction. Hosono and Takagi have constructed a class of Calabi-Yau threefolds that occur as a linear section of a double quintic symmetroid and given a detailed analysis of them as complex varieties in the context of mirror symmetry. This construction can be used to produce varieties over Q as well, and these threefolds come tantalizingly equipped with a natural Brauer class. In work with Hashimoto, Lamarche and Vogt, we analyze these threefolds and their Brauer class over Q and give a condition under which the Brauer class obstructs weak approximation, though it cannot obstruct the existence of Q-rational points.<br />
<br />
===Stefan Schreieder===<br />
'''Refined unramified cohomology and algebraic cycles'''<br />
<br />
We introduce refined unramified cohomology groups, explain their relation to classical unramified cohomology, and prove some general comparison theorems to certain cycle groups. This generalizes and simplifies work of Bloch—Ogus, Colliot-Thélène—Voisin, Voisin, and Ma who dealt with cycles of low (co-)dimension. Our approach has several applications. Most notably, it allows to construct the first example of a variety with infinite torsion in its Griffiths group.</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2020&diff=20406Algebra and Algebraic Geometry Seminar Fall 20202020-12-01T00:35:05Z<p>Kemeny: /* Fall 2020 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2020 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|September 14 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 1/4 in lecture series at Imperial College - Register here to get the link to the talk!]<br />
|-<br />
|September 18 <br />
|[https://www.math.wisc.edu/~arinkin/ Dima Arinkin (Madison)]<br />
|[[#Dima Arinkin|Singular support of categories]]<br />
|[https://uwmadison.zoom.us/j/91919237303?pwd=SzhtYVpwSHhoVVFmQWx1NFpBVVNBQT09 Zoom link]<br />
|-<br />
|September 21 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 2/4 in lecture series at Imperial College]<br />
|-<br />
|September 25<br />
|[https://www.math.tamu.edu/~ola/ Aleksandra Sobieska (Madison)]<br />
|[[#Aleksandra Sobieska|Toward Free Resolutions Over Scrolls]]<br />
|<br />
|-<br />
|September 28 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 3/4 in lecture series at Imperial College]<br />
|-<br />
|October 2<br />
|Robert Scherer (UC Davis)<br />
|[[#Robert Scherer|A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 5 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 4/4 in lecture series at Imperial College]<br />
|-<br />
|October 7 @ 7pm<br />
|[https://www.math.wisc.edu/~shamgar// Shamgar Gurevich (Madison)]<br />
|[[#Shamgar Gurevich|Harmonic Analysis on GLn over Finite Fields]]<br />
| [https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ Register here to get link to talk at University of Sydney]<br />
|-<br />
|October 9<br />
|[https://math.berkeley.edu/~germans/ German Stefanich (Berkeley) ]<br />
|[[#German Stefanich|Categorified sheaf theory and the spectral Langlands TQFT]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 16<br />
|[https://sites.google.com/view/ruijie-yang/ Ruijie Yang (Stony Brook)]<br />
|[[#Ruijie Yang|Decomposition theorem for semisimple local systems]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 23 <br />
|[http://www-users.math.umn.edu/~ottxx141/ Nadia Ott (Mittag-Leffler Institute)]<br />
|[[#Nadia Ott|The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|October 30<br />
|[http://w3.impa.br/~heluani/ Reimundo Heluani (IMPA, Rio de Janeiro)]<br />
|[[#Reimundo Heluani|Rogers Ramanujan type identities coming from representation theory]]<br />
| <br />
|-<br />
|November 6<br />
|[https://bakker.people.uic.edu/ Ben Bakker (UIC)]<br />
|[[#Ben Bakker|Quasiprojectivity of images of mixed period maps]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|November 13<br />
|[https://pages.uoregon.edu/honigs/ Katrina Honigs (Oregon)]<br />
|[[#Katrina Honigs|An obstruction to weak approximation on some Calabi-Yau threefolds]]<br />
|<br />
|-<br />
|December 4<br />
|[https://www.iag.uni-hannover.de/de/institut/personenverzeichnis/stefan-schreieder/?&L=1 Stefan Schreieder (Hannover)]<br />
|[[Refined unramified cohomology and algebraic cycles]]<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Andrei Căldăraru===<br />
'''Categorical Enumerative Invariants'''<br />
<br />
I will talk about recent papers with Junwu Tu, Si Li, and Kevin Costello where we give a computable definition of Costello's 2005 invariants and compute some of them. These invariants are associated to a pair (A,s) consisting of a cyclic A∞-algebra and a choice of splitting s of its non-commutative Hodge filtration. They are expected to recover classical Gromov-Witten invariants when A is obtained from the Fukaya category of a symplectic manifold, as well as extend various B-model invariants (solutions of Picard-Fuchs equations, BCOV invariants, B-model FJRW invariants) when A is obtained from the derived category of a manifold or a matrix factorization category.<br />
<br />
===Dima Arinkin===<br />
<br />
'''Singular support of categories'''<br />
<br />
In many situations, geometric objects on a space have some kind of singular support, which refines the usual support.<br />
For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset<br />
of the cotangent bundle; there is also a version of this notion for coherent sheaves on local complete intersections.<br />
I would like to describe a higher categorical version of this notion.<br />
<br />
Let X be a smooth variety, and let Z be a closed conical isotropic subset of the cotangent bundle of X. I will define a<br />
2-category associated with Z; its objects may be viewed as `categories over X with singular support in Z'. In particular, if Z is<br />
the zero section, this gives the notion of categories over Z in the usual sense.<br />
<br />
The project is motivated by the local geometric Langlands correspondence; I will sketch the relation with the Langlands correspondence without <br />
going into details.<br />
<br />
===Aleksandra Sobieska===<br />
'''Toward Free Resolutions Over Scrolls'''<br />
<br />
Free resolutions over the polynomial ring have a storied and active record of study. However, resolutions over other rings are much more mysterious; even simple examples can be infinite! In these cases, we look to any combinatorics of the ring to glean information. This talk will present a minimal free resolution of the ground field over the semigroup ring arising from rational normal $2$-scrolls, and (if time permits) a computation of the Betti numbers of the ground field for all rational normal $k$-scrolls.<br />
<br />
===Robert Scherer===<br />
'''A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees'''<br />
<br />
We study the identity $y(x)=xA(y(x))$, from the theory of rooted trees, for appropriate generating functions $y(x)$ and $A(x)$ with non-negative integer coefficients. A problem that has been studied extensively is to determine the asymptotics of the coefficients of $y(x)$ from analytic properties of the complex function $z\mapsto A(z)$, assumed to have a positive radius of convergence $R$. It is well-known that the vanishing of $A(x)-xA'(x)$ on $(0,R)$ is sufficient to ensure that $y(r)<R$, where $r$ is the radius of convergence of $y(x)$. This result has been generalized in the literature to account for more general functional equations than the one above, and used to determine asymptotics for the Taylor coefficients of $y(x)$. What has not been shown is whether that sufficient condition is also necessary. We show here that it is, thus establishing a criterion for sharpness of the inequality $y(r)\leq R$. As an application, we prove, and significantly extend, a 1996 conjecture of Kuperberg regarding the asymptotic growth rate of an integer sequence arising in the study of Lie algebra representations. <br />
<br />
===Shamgar Gurevich===<br />
'''Harmonic Analysis on GLn over Finite Fields'''<br />
<br />
There are many formulas that express interesting properties of a finite group G in terms of sums over<br />
its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
Trace(ρ(g)) / dim(ρ), for an irreducible representation ρ of G and an element g of G. For example, Diaconis<br />
and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G. Recently,<br />
we discovered that for classical groups G over finite fields there is a natural invariant of representations that<br />
provides strong information on the character ratio. We call this invariant rank. Rank suggests a new<br />
organization of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s<br />
“philosophy of cusp forms”, which is (since the 60s) the main organization principle, and is based on the (huge<br />
collection) of “Large” representations. This talk will discuss the notion of rank for the group GLn over finite<br />
fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify<br />
mixing time and rate for random walks. This is joint work with Roger Howe (Yale and Texas A&M). The<br />
numerics for this work was carried with Steve Goldstein (Madison) and John Cannon (Sydney).<br />
<br />
===German Stefanich===<br />
'''Categorified sheaf theory and the spectral Langlands TQFT'''<br />
<br />
It is expected that the Betti version of the geometric Langlands program should ultimately be about the equivalence of two 4-dimensional topological field theories. In this talk I will give an overview of ongoing work in categorified sheaf theory and explain how one can use it to describe the categories of boundary conditions arising on the spectral side.<br />
<br />
===Ruijie Yang===<br />
'''Decomposition theorem for semisimple local systems<br />
'''<br />
<br />
In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved by Mochizuki and Sabbah in a series of very long papers via harmonic analysis and $D$-modules. In this talk, I would like to explain a simpler proof in the case of semisimple local systems using a more geometric approach. This is joint work in progress with Chuanhao Wei. <br />
<br />
===Nadia Ott===<br />
'''The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures<br />
<br />
Super Riemann surfaces (SUSY curves) arise in the formulation of superstring theory, and their moduli spaces, called supermoduli space, are the integration spaces for superstring scattering amplitudes. I will focus specifically on genus zero SUSY curves. As with ordinary curves, genus zero SUSY curves present a certain challenge, as they have an infinitesimal group of automorphisms, and so in order for the moduli problem to be representable by a Deligne-Mumford superstack, we must introduce punctures. In fact, there are two kinds of punctures on a SUSY curve of Neveu-Schwarz or Ramond type. Neveu-Schwarz punctures are entirely analogous to the marked points in ordinary moduli theory. By contrast, the Ramond punctures are more subtle and have no ordinary analog. I will give a construction of the moduli space M_{0,n}^R of genus zero SUSY curves with Ramond punctures as a Deligne-Mumford superstack by an explicit quotient presentation (rather than by an abstract existence argument).<br />
<br />
===Reimundo Heluani===<br />
'''A Rogers-Ramanujan-Slater type identity related to the Ising model'''<br />
<br />
We prove three new q-series identities of the Rogers-Ramanujan-Slater<br />
type. We find a PBW basis for the Ising model as a consequence of one of these<br />
identities. If time permits it will be shown that the singular support of the<br />
Ising model is a hyper-surface (in the differential sense) on the arc space of<br />
it's associated scheme. This is joint work with G. E. Andrews and J. van Ekeren<br />
and is available online at https://arxiv.org/abs/2005.10769<br />
<br />
===Ben Bakker===<br />
'''Quasiprojectivity of images of mixed period maps'''<br />
<br />
Families of smooth proper algebraic varieties give rise to variations of pure Hodge structures; general algebraic families yield variations of mixed Hodge structures. It was conjectured by Griffiths and proven in joint work with Y. Brunebarbe and J. Tsimerman that the closure of the image of the classifying map to the moduli space of Hodge structures is a quasiprojective algebraic variety in the pure case. In this talk I will explain how to extend this result to the mixed setting. As in the pure case, the proof heavily uses techniques from o-minimal geometry, and we will also discuss some related applications. <br />
<br />
===Katrina Honigs===<br />
'''An obstruction to weak approximation on some Calabi-Yau threefolds'''<br />
<br />
The study of Q-rational points on algebraic varieties is fundamental to arithmetic geometry. One of the few methods available to show that a variety does not have any Q-points is to give a Brauer-Manin obstruction. Hosono and Takagi have constructed a class of Calabi-Yau threefolds that occur as a linear section of a double quintic symmetroid and given a detailed analysis of them as complex varieties in the context of mirror symmetry. This construction can be used to produce varieties over Q as well, and these threefolds come tantalizingly equipped with a natural Brauer class. In work with Hashimoto, Lamarche and Vogt, we analyze these threefolds and their Brauer class over Q and give a condition under which the Brauer class obstructs weak approximation, though it cannot obstruct the existence of Q-rational points.<br />
<br />
===Stefan Schreieder===<br />
'''Refined unramified cohomology and algebraic cycles'''<br />
<br />
We introduce refined unramified cohomology groups, explain their relation to classical unramified cohomology, and prove some general comparison theorems to certain cycle groups. This generalizes and simplifies work of Bloch—Ogus, Colliot-Thélène—Voisin, Voisin, and Ma who dealt with cycles of low (co-)dimension. Our approach has several applications. Most notably, it allows to construct the first example of a variety with infinite torsion in its Griffiths group.</div>Kemenyhttps://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2020&diff=20405Algebra and Algebraic Geometry Seminar Fall 20202020-12-01T00:34:46Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2020 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|September 14 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 1/4 in lecture series at Imperial College - Register here to get the link to the talk!]<br />
|-<br />
|September 18 <br />
|[https://www.math.wisc.edu/~arinkin/ Dima Arinkin (Madison)]<br />
|[[#Dima Arinkin|Singular support of categories]]<br />
|[https://uwmadison.zoom.us/j/91919237303?pwd=SzhtYVpwSHhoVVFmQWx1NFpBVVNBQT09 Zoom link]<br />
|-<br />
|September 21 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 2/4 in lecture series at Imperial College]<br />
|-<br />
|September 25<br />
|[https://www.math.tamu.edu/~ola/ Aleksandra Sobieska (Madison)]<br />
|[[#Aleksandra Sobieska|Toward Free Resolutions Over Scrolls]]<br />
|<br />
|-<br />
|September 28 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 3/4 in lecture series at Imperial College]<br />
|-<br />
|October 2<br />
|Robert Scherer (UC Davis)<br />
|[[#Robert Scherer|A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 5 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 4/4 in lecture series at Imperial College]<br />
|-<br />
|October 7 @ 7pm<br />
|[https://www.math.wisc.edu/~shamgar// Shamgar Gurevich (Madison)]<br />
|[[#Shamgar Gurevich|Harmonic Analysis on GLn over Finite Fields]]<br />
| [https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ Register here to get link to talk at University of Sydney]<br />
|-<br />
|October 9<br />
|[https://math.berkeley.edu/~germans/ German Stefanich (Berkeley) ]<br />
|[[#German Stefanich|Categorified sheaf theory and the spectral Langlands TQFT]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 16<br />
|[https://sites.google.com/view/ruijie-yang/ Ruijie Yang (Stony Brook)]<br />
|[[#Ruijie Yang|Decomposition theorem for semisimple local systems]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 23 <br />
|[http://www-users.math.umn.edu/~ottxx141/ Nadia Ott (Mittag-Leffler Institute)]<br />
|[[#Nadia Ott|The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|October 30<br />
|[http://w3.impa.br/~heluani/ Reimundo Heluani (IMPA, Rio de Janeiro)]<br />
|[[#Reimundo Heluani|Rogers Ramanujan type identities coming from representation theory]]<br />
| <br />
|-<br />
|November 6<br />
|[https://bakker.people.uic.edu/ Ben Bakker (UIC)]<br />
|[[#Ben Bakker|Quasiprojectivity of images of mixed period maps]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|November 13<br />
|[https://pages.uoregon.edu/honigs/ Katrina Honigs (Oregon)]<br />
|[[#Katrina Honigs|An obstruction to weak approximation on some Calabi-Yau threefolds]]<br />
|<br />
|-<br />
|December 4<br />
|[https://www.iag.uni-hannover.de/de/institut/personenverzeichnis/stefan-schreieder/?&L=1 Stefan Schreieder (Hannover)]<br />
|Refined unramified cohomology and algebraic cycles<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Andrei Căldăraru===<br />
'''Categorical Enumerative Invariants'''<br />
<br />
I will talk about recent papers with Junwu Tu, Si Li, and Kevin Costello where we give a computable definition of Costello's 2005 invariants and compute some of them. These invariants are associated to a pair (A,s) consisting of a cyclic A∞-algebra and a choice of splitting s of its non-commutative Hodge filtration. They are expected to recover classical Gromov-Witten invariants when A is obtained from the Fukaya category of a symplectic manifold, as well as extend various B-model invariants (solutions of Picard-Fuchs equations, BCOV invariants, B-model FJRW invariants) when A is obtained from the derived category of a manifold or a matrix factorization category.<br />
<br />
===Dima Arinkin===<br />
<br />
'''Singular support of categories'''<br />
<br />
In many situations, geometric objects on a space have some kind of singular support, which refines the usual support.<br />
For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset<br />
of the cotangent bundle; there is also a version of this notion for coherent sheaves on local complete intersections.<br />
I would like to describe a higher categorical version of this notion.<br />
<br />
Let X be a smooth variety, and let Z be a closed conical isotropic subset of the cotangent bundle of X. I will define a<br />
2-category associated with Z; its objects may be viewed as `categories over X with singular support in Z'. In particular, if Z is<br />
the zero section, this gives the notion of categories over Z in the usual sense.<br />
<br />
The project is motivated by the local geometric Langlands correspondence; I will sketch the relation with the Langlands correspondence without <br />
going into details.<br />
<br />
===Aleksandra Sobieska===<br />
'''Toward Free Resolutions Over Scrolls'''<br />
<br />
Free resolutions over the polynomial ring have a storied and active record of study. However, resolutions over other rings are much more mysterious; even simple examples can be infinite! In these cases, we look to any combinatorics of the ring to glean information. This talk will present a minimal free resolution of the ground field over the semigroup ring arising from rational normal $2$-scrolls, and (if time permits) a computation of the Betti numbers of the ground field for all rational normal $k$-scrolls.<br />
<br />
===Robert Scherer===<br />
'''A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees'''<br />
<br />
We study the identity $y(x)=xA(y(x))$, from the theory of rooted trees, for appropriate generating functions $y(x)$ and $A(x)$ with non-negative integer coefficients. A problem that has been studied extensively is to determine the asymptotics of the coefficients of $y(x)$ from analytic properties of the complex function $z\mapsto A(z)$, assumed to have a positive radius of convergence $R$. It is well-known that the vanishing of $A(x)-xA'(x)$ on $(0,R)$ is sufficient to ensure that $y(r)<R$, where $r$ is the radius of convergence of $y(x)$. This result has been generalized in the literature to account for more general functional equations than the one above, and used to determine asymptotics for the Taylor coefficients of $y(x)$. What has not been shown is whether that sufficient condition is also necessary. We show here that it is, thus establishing a criterion for sharpness of the inequality $y(r)\leq R$. As an application, we prove, and significantly extend, a 1996 conjecture of Kuperberg regarding the asymptotic growth rate of an integer sequence arising in the study of Lie algebra representations. <br />
<br />
===Shamgar Gurevich===<br />
'''Harmonic Analysis on GLn over Finite Fields'''<br />
<br />
There are many formulas that express interesting properties of a finite group G in terms of sums over<br />
its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
Trace(ρ(g)) / dim(ρ), for an irreducible representation ρ of G and an element g of G. For example, Diaconis<br />
and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G. Recently,<br />
we discovered that for classical groups G over finite fields there is a natural invariant of representations that<br />
provides strong information on the character ratio. We call this invariant rank. Rank suggests a new<br />
organization of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s<br />
“philosophy of cusp forms”, which is (since the 60s) the main organization principle, and is based on the (huge<br />
collection) of “Large” representations. This talk will discuss the notion of rank for the group GLn over finite<br />
fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify<br />
mixing time and rate for random walks. This is joint work with Roger Howe (Yale and Texas A&M). The<br />
numerics for this work was carried with Steve Goldstein (Madison) and John Cannon (Sydney).<br />
<br />
===German Stefanich===<br />
'''Categorified sheaf theory and the spectral Langlands TQFT'''<br />
<br />
It is expected that the Betti version of the geometric Langlands program should ultimately be about the equivalence of two 4-dimensional topological field theories. In this talk I will give an overview of ongoing work in categorified sheaf theory and explain how one can use it to describe the categories of boundary conditions arising on the spectral side.<br />
<br />
===Ruijie Yang===<br />
'''Decomposition theorem for semisimple local systems<br />
'''<br />
<br />
In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved by Mochizuki and Sabbah in a series of very long papers via harmonic analysis and $D$-modules. In this talk, I would like to explain a simpler proof in the case of semisimple local systems using a more geometric approach. This is joint work in progress with Chuanhao Wei. <br />
<br />
===Nadia Ott===<br />
'''The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures<br />
<br />
Super Riemann surfaces (SUSY curves) arise in the formulation of superstring theory, and their moduli spaces, called supermoduli space, are the integration spaces for superstring scattering amplitudes. I will focus specifically on genus zero SUSY curves. As with ordinary curves, genus zero SUSY curves present a certain challenge, as they have an infinitesimal group of automorphisms, and so in order for the moduli problem to be representable by a Deligne-Mumford superstack, we must introduce punctures. In fact, there are two kinds of punctures on a SUSY curve of Neveu-Schwarz or Ramond type. Neveu-Schwarz punctures are entirely analogous to the marked points in ordinary moduli theory. By contrast, the Ramond punctures are more subtle and have no ordinary analog. I will give a construction of the moduli space M_{0,n}^R of genus zero SUSY curves with Ramond punctures as a Deligne-Mumford superstack by an explicit quotient presentation (rather than by an abstract existence argument).<br />
<br />
===Reimundo Heluani===<br />
'''A Rogers-Ramanujan-Slater type identity related to the Ising model'''<br />
<br />
We prove three new q-series identities of the Rogers-Ramanujan-Slater<br />
type. We find a PBW basis for the Ising model as a consequence of one of these<br />
identities. If time permits it will be shown that the singular support of the<br />
Ising model is a hyper-surface (in the differential sense) on the arc space of<br />
it's associated scheme. This is joint work with G. E. Andrews and J. van Ekeren<br />
and is available online at https://arxiv.org/abs/2005.10769<br />
<br />
===Ben Bakker===<br />
'''Quasiprojectivity of images of mixed period maps'''<br />
<br />
Families of smooth proper algebraic varieties give rise to variations of pure Hodge structures; general algebraic families yield variations of mixed Hodge structures. It was conjectured by Griffiths and proven in joint work with Y. Brunebarbe and J. Tsimerman that the closure of the image of the classifying map to the moduli space of Hodge structures is a quasiprojective algebraic variety in the pure case. In this talk I will explain how to extend this result to the mixed setting. As in the pure case, the proof heavily uses techniques from o-minimal geometry, and we will also discuss some related applications. <br />
<br />
===Katrina Honigs===<br />
'''An obstruction to weak approximation on some Calabi-Yau threefolds'''<br />
<br />
The study of Q-rational points on algebraic varieties is fundamental to arithmetic geometry. One of the few methods available to show that a variety does not have any Q-points is to give a Brauer-Manin obstruction. Hosono and Takagi have constructed a class of Calabi-Yau threefolds that occur as a linear section of a double quintic symmetroid and given a detailed analysis of them as complex varieties in the context of mirror symmetry. This construction can be used to produce varieties over Q as well, and these threefolds come tantalizingly equipped with a natural Brauer class. In work with Hashimoto, Lamarche and Vogt, we analyze these threefolds and their Brauer class over Q and give a condition under which the Brauer class obstructs weak approximation, though it cannot obstruct the existence of Q-rational points.<br />
<br />
===Stefan Schreieder===<br />
'''Refined unramified cohomology and algebraic cycles'''<br />
<br />
We introduce refined unramified cohomology groups, explain their relation to classical unramified cohomology, and prove some general comparison theorems to certain cycle groups. This generalizes and simplifies work of Bloch—Ogus, Colliot-Thélène—Voisin, Voisin, and Ma who dealt with cycles of low (co-)dimension. Our approach has several applications. Most notably, it allows to construct the first example of a variety with infinite torsion in its Griffiths group.</div>Kemeny