Colloquia: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
No edit summary
(32 intermediate revisions by 4 users not shown)
Line 8: Line 8:
=Fall 2021=
=Fall 2021=


== Sep. 17, 2021 , [https://markshus.wixsite.com/math Mark Shusterman] (Harvard) ==
== September 17, 2021, Social Sciences 5208 + [http://128.104.155.144/ClassroomStreams/socsci5208_stream.html Live Stream], [https://markshus.wixsite.com/math Mark Shusterman] (Harvard) ==


(hosted by Gurevich)
(hosted by Gurevich)


== October 8, 2021 , [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==
'''Finitely Presented Groups in Arithmetic Geometry'''


(Wasow lecture; hosted by Thiffeault)
I will report on recent works, in part joint with Esnault—Srinivas, and with Jarden, on the finite presentability of several (profinite) groups arising in algebraic geometry and in number theory. These results build on a cohomological criterion of Lubotzky involving Euler characteristics. I will try to explain the analogy, rooted in arithmetic topology, between these results and classical facts about fundamental groups of three-dimensional manifolds.


== October 11, 13, 15, 2021 '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==
== September 24, 2021, B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom stream], [https://math.wisc.edu/staff/paul-sean/ Sean Paul] (UW-Madison) ==
'''The Tian-Yau-Donaldson conjecture for general polarized manifolds'''
 
According to the Yau-Tian-Donaldson conjecture, the existence of a constant scalar curvature Kähler (cscK) metric in the cohomology class of an ample line bundle L on a compact complex manifold X should be equivalent to an algebro-geometric "stability condition" satisfied by the pair (X,L).  The cscK metrics are the critical points of Mabuchi's K-energy functional M, defined on the space of Kähler potentials, and an important result of Chen-Cheng shows that cscK metrics exist iff M satisfies a standard growth condition (coercivity/properness). Recently the speaker has shown that the K-energy is indeed proper if and only if the polarized manifold is stable. The stability condition is closely related to the classical notion of Hilbert-Mumford stability.  The speaker will give a non-technical general account of the many areas of mathematics that are involved in the proof. In particular, he hopes to discuss the surprising role played by arithmetic geometry​in the spirit of Arakelov, Faltings, and Bismut-Gillet- Soule.
 
== October 1, 2021, B239, [https://people.math.wisc.edu/~andreic/ Andrei Caldararu] (UW-Madison) ==
'''Yet another Moonshine'''
 
The j-function, introduced by Felix Klein in 1879, is an essential ingredient in the study of elliptic curves. It is Z-periodic on the complex upper half-plane, so it admits a Fourier expansion. The original Monstrous Moonshine conjecture, due to McKay and Conway/Norton in the 1980s, relates the Fourier coefficients of the j-function around the cusp to dimensions of irreducible representations of the Monster simple group. It was proved by Borcherds in 1992.
 
In my talk I will try to give a rudimentary introduction to modular forms, explain Monstrous Moonshine, and discuss a new version of it obtained in joint work with Yunfan He and Shengyuan Huang.  Our version involves studying the j-function around CM points (so-called Landau-Ginzburg points in the physics literature) and expanding with respect to a coordinate which arises naturally in string theory.
 
== October 8, 2021, Zoom, [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==
 
('''Wasow lecture'''; hosted by Thiffeault)
 
'''Asymptotics beyond all orders: the devil's invention?'''
 
"Divergent series are the invention of the devil, and it is shameful to base on them any demonstration whatsoever." --- N. H. Abel.
 
The lecture will introduce the concept of an asymptotic series, showing how useful divergent series can be, despite Abel's reservations. We will then discuss Stokes' phenomenon, whereby the coefficients in the series appear to change discontinuously. We will show how understanding Stokes' phenomenon is the key which allows us to determine the qualitative and quantitative behaviour of the solution in many practical problems. Examples will be drawn from the areas of surface waves on fluids, crystal growth, dislocation dynamics, and Hele-Shaw flow.
 
== October 11, 13, 15, 2021, Zoom,  '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==


(Special lecture series; hosted by Gurevich)
(Special lecture series; hosted by Gurevich)
== October 22, 2021, Zoom,  [https://math.berkeley.edu/people/faculty/vera-serganova Vera Serganova] (UC Berkeley) ==
(hosted by Gurevich/Gorin)


== October 29, 2021 , [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton University) ==
== October 29, 2021 , [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton University) ==
Line 24: Line 50:
(hosted by Wainger)
(hosted by Wainger)


== November 5, 2021 , [https://faculty.washington.edu/jathreya/ Jayadev S. Athreya] (University of Washington) ==


(hosted by Uyanik)


== Nov. 19, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==
== November 12, 2021 , [https://sites.tufts.edu/kasso/ Kasso Okoudjou] (Tufts University) ==


(reserved by the hiring committee)
(hosted by Stovall)


== Dec. 3, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==
== November 19, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==


(reserved by the hiring committee)
(reserved by the hiring committee)


== Dec. 10, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==
== December 3, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==


(reserved by the hiring committee)
(reserved by the hiring committee)


== December 10, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==


(reserved by the hiring committee)


== Future ==
== Future ==


[[Colloquia/Spring2021|Spring 2022]]
[[Colloquia/Spring2022|Spring 2022]]


== Past Colloquia ==
== Past Colloquia ==

Revision as of 14:21, 22 September 2021


UW Madison mathematics Colloquium is on Fridays at 4:00 pm.


Fall 2021

September 17, 2021, Social Sciences 5208 + Live Stream, Mark Shusterman (Harvard)

(hosted by Gurevich)

Finitely Presented Groups in Arithmetic Geometry

I will report on recent works, in part joint with Esnault—Srinivas, and with Jarden, on the finite presentability of several (profinite) groups arising in algebraic geometry and in number theory. These results build on a cohomological criterion of Lubotzky involving Euler characteristics. I will try to explain the analogy, rooted in arithmetic topology, between these results and classical facts about fundamental groups of three-dimensional manifolds.

September 24, 2021, B239 + Zoom stream, Sean Paul (UW-Madison)

The Tian-Yau-Donaldson conjecture for general polarized manifolds

According to the Yau-Tian-Donaldson conjecture, the existence of a constant scalar curvature Kähler (cscK) metric in the cohomology class of an ample line bundle L on a compact complex manifold X should be equivalent to an algebro-geometric "stability condition" satisfied by the pair (X,L). The cscK metrics are the critical points of Mabuchi's K-energy functional M, defined on the space of Kähler potentials, and an important result of Chen-Cheng shows that cscK metrics exist iff M satisfies a standard growth condition (coercivity/properness). Recently the speaker has shown that the K-energy is indeed proper if and only if the polarized manifold is stable. The stability condition is closely related to the classical notion of Hilbert-Mumford stability. The speaker will give a non-technical general account of the many areas of mathematics that are involved in the proof. In particular, he hopes to discuss the surprising role played by arithmetic geometry​in the spirit of Arakelov, Faltings, and Bismut-Gillet- Soule.

October 1, 2021, B239, Andrei Caldararu (UW-Madison)

Yet another Moonshine

The j-function, introduced by Felix Klein in 1879, is an essential ingredient in the study of elliptic curves. It is Z-periodic on the complex upper half-plane, so it admits a Fourier expansion. The original Monstrous Moonshine conjecture, due to McKay and Conway/Norton in the 1980s, relates the Fourier coefficients of the j-function around the cusp to dimensions of irreducible representations of the Monster simple group. It was proved by Borcherds in 1992.

In my talk I will try to give a rudimentary introduction to modular forms, explain Monstrous Moonshine, and discuss a new version of it obtained in joint work with Yunfan He and Shengyuan Huang. Our version involves studying the j-function around CM points (so-called Landau-Ginzburg points in the physics literature) and expanding with respect to a coordinate which arises naturally in string theory.

October 8, 2021, Zoom, Jon Chapman (University of Oxford)

(Wasow lecture; hosted by Thiffeault)

Asymptotics beyond all orders: the devil's invention?

"Divergent series are the invention of the devil, and it is shameful to base on them any demonstration whatsoever." --- N. H. Abel.

The lecture will introduce the concept of an asymptotic series, showing how useful divergent series can be, despite Abel's reservations. We will then discuss Stokes' phenomenon, whereby the coefficients in the series appear to change discontinuously. We will show how understanding Stokes' phenomenon is the key which allows us to determine the qualitative and quantitative behaviour of the solution in many practical problems. Examples will be drawn from the areas of surface waves on fluids, crystal growth, dislocation dynamics, and Hele-Shaw flow.

October 11, 13, 15, 2021, Zoom, [Mon, Wed, Fri 4-5pm], Geordie Williamson (University of Sydney)

(Special lecture series; hosted by Gurevich)

October 22, 2021, Zoom, Vera Serganova (UC Berkeley)

(hosted by Gurevich/Gorin)

October 29, 2021 , Alexandru Ionescu (Princeton University)

(hosted by Wainger)

November 5, 2021 , Jayadev S. Athreya (University of Washington)

(hosted by Uyanik)

November 12, 2021 , Kasso Okoudjou (Tufts University)

(hosted by Stovall)

November 19, 2021 , TBA (TBA)

(reserved by the hiring committee)

December 3, 2021 , TBA (TBA)

(reserved by the hiring committee)

December 10, 2021 , TBA (TBA)

(reserved by the hiring committee)

Future

Spring 2022

Past Colloquia

Spring 2021

Fall 2020

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012

WIMAW