Geometry and Topology Seminar: Difference between revisions

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The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''. For more information, contact Shaosai Huang.
The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1pm - 2:20pm'''. For more information, contact Alex Waldron.
 
In the fall of 2020, we will hold '''online meetings''' on
[https://uwmadison.zoom.us/j/94578957620 Zoom platform] 
(available every '''Friday 1:00pm - 2:30pm''').
<br>




Line 10: Line 5:




== Fall 2020 ==
== Fall 2021 ==


{| cellpadding="8"
{| cellpadding="8"
Line 16: Line 11:
!align="left" | speaker
!align="left" | speaker
!align="left" | title
!align="left" | title
!align="left" | host(s)
|-
|-
|Oct. 23
|Sep. 10
|Yu Li (Stony Brook)
|
| On the ancient solutions to the Ricci flow
|Organizational meeting
|(Huang)
|-
|Sep. 17
|Alex Waldron
|Harmonic map flow for almost-holomorphic maps
|-
|Sep. 24
|Sean Paul
|Geometric Invariant Theory, Stable Pairs, Canonical Kähler metrics & Heights
|-
|Oct. 1
|Andrew Zimmer
|Entropy rigidity old and new
|-
|-
|Oct. 30
|Oct. 8
|Yi Lai (Berkeley)
|Laurentiu Maxim
| A family of 3d steady gradient solitons that are flying wings
|Topology of complex projective hypersurfaces
|(Huang)
|-
|-
|Nov. 6
|Oct. 15
|Jiyuan Han (Purdue)
|Gavin Ball
| On the Yau-Tian-Donaldson conjecture for generalized Kähler-Ricci soliton equations
|Introduction to G2 Geometry
|(Chen)
|-
|-
|Nov. 13
|Oct. 22
|Ilyas Khan (Madison)
|Chenxi Wu
|Rigidity Properties of Mean Curvature Flow Translators with Curvature Conditions
|Stable translation lengths on sphere graphs
|(Local)
|-
|-
|Nov. 20
|Oct. 29
|Max Hallgren (Cornell)
|Brian Hepler
|The Entropy of Ricci Flows with a Type-I Scalar Curvature Bound
|
|(Huang)
|-
|Nov. 5
|Botong Wang
|
|-
|Nov. 12
|Nate Fisher
|
|-
|Nov. 19
|Sigurd Angenent
|
|-
|-
|Dec. 4
|Yang Li (IAS)
| Metric SYZ conjecture
|(Chen)
|}
|}


== Fall Abstracts ==
== Fall Abstracts ==


===Yu Li===
===Alex Waldron===
Ancient solutions model the singularity formation of the Ricci flow.  In two and three dimensions, we currently have complete classifications for κ-noncollapsed ancient solutions, while the higher dimensional problem remains open. This talk will survey some recent developments of κ-noncollapsed ancient solutions with nonnegative curvature in higher dimensions.
 
I'll describe some history, recent results, and open problems about harmonic map flow, particularly in the 2-dimensional case.
 
===Sean Paul===
 
An interesting problem in complex differential geometry seeks to characterize the existence of a constant scalar curvature metric on a Hodge manifold in terms of the algebraic geometry of the underlying variety. The speaker has recently solved this problem for varieties with finite automorphism group. The talk aims to explain why the problem is interesting (and quite rich) and to describe in non-technical language the ideas in the title and how they all fit together.
 
Note: this talk will provide some background for Sean's colloquium later in the afternoon.
 
===Andrew Zimmer===
 
Informally, an "entropy rigidity" result characterizes some special geometric object (e.g. a constant curvature metric on a manifold) as a maximizer/minimizer of some function of the objects asymptotic complexity. In this talk I will survey some classical entropy rigidity results in hyperbolic and Riemannian geometry. Then, if time allows, I will discuss some recent joint work with Canary and Zhang. The talk should be accessible to first year graduate students.
 
===Laurentiu Maxim===
 
I will overview old and new results which show how the presence of singularities affects the topology of complex projective hypersurfaces.
 
===Gavin Ball===
 
I will give an introduction to the theory of manifolds with holonomy group G2. I will begin by describing the exceptional Lie group G2 using some special linear algebra in dimension 7. Then I will give an overview of the holonomy group of a Riemannian manifold and describe Berger's classification theorem. The group G2 is one of two exceptional members of Berger's list, and I will explain the interesting properties manifolds with holonomy G2 have and sketch the construction of examples. If time permits, I will describe some of my recent work on manifolds with closed G2-structure.
 


===Yi Lai===
===Chenxi Wu===
We found a family of $\mathbb{Z}_2\times O(2)$-symmetric 3d steady gradient Ricci solitons. We show that these solitons are all flying wings. This confirms a conjecture of Hamilton.


===Jiyuan Han===
I will discuss some of my prior works in collaboration with Harry Baik, Dongryul Kim, Hyunshik Shin and Eiko Kin on stable translation lengths on sphere graphs for maps in a fibered cone, and discuss the applications on maps on surfaces, finite graphs and handlebody groups.
Let (X,D) be a log variety with an effective holomorphic torus action, and Θ be a closed positive (1,1)-current. For any smooth positive function g defined on the moment polytope of the torus action, we study the Monge-Ampere equations that correspond to generalized and twisted Kahler-Ricci g-solitons. We prove a version of Yau-Tian-Donaldson (YTD) conjecture for these general equations, showing that the existence of solutions is always equivalent to an equivariantly uniform Θ-twisted g-Ding-stability. When Θ is a current associated to a torus invariant linear system, we further show
that equivariant special test configurations suffice for testing the stability. Our results allow arbitrary klt singularities and generalize most of previous results on (uniform) YTD conjecture for (twisted) Kahler-Ricci/Mabuchi solitons or Kahler-Einstein metrics. This is a joint work with Chi Li.


===Ilyas Khan===
In this talk we discuss some uniqueness results for mean curvature flow translators. Under certain curvature conditions, we classify the blow-down limits of translating solutions of the mean curvature flow and employ recent techniques from the theory of ancient MCF solutions to show the uniqueness of translators with these blow-down limits.


===Max Hallgren===
In this talk, we study the singularities of closed Ricci flow solutions which satisfy a Type-I scalar curvature assumption. Bamler's structure theory of Ricci flows with bounded scalar curvature shows that singularities are modeled on shrinking Ricci solitons with singularities of codimension 4. We extend the analysis by characterizing the singular set of the flow in terms of a Gaussian density functional, and also establish entropy uniqueness of dilation limits at a fixed point, generalizing results previously known assuming a Type-I bound on the full curvature tensor.  We also show that in dimension 4, the singular Ricci soliton is smooth away from finitely many points, which are conical smooth orbifold singularities.


===Yang Li===
One possible interpretation of the SYZ conjecture is that for a polarized family of CY manifolds near the large complex structure limit, there is a special Lagrangian fibration on the generic region of the CY manifold. Generic here means a set with a large percentage of the CY measure, and the percentage tends to 100% in the limit. I will discuss my recent progress on this version of the SYZ conjecture.


== Archive of past Geometry seminars ==
== Archive of past Geometry seminars ==

Revision as of 18:45, 14 October 2021

The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1pm - 2:20pm. For more information, contact Alex Waldron.


Hawk.jpg


Fall 2021

date speaker title
Sep. 10 Organizational meeting
Sep. 17 Alex Waldron Harmonic map flow for almost-holomorphic maps
Sep. 24 Sean Paul Geometric Invariant Theory, Stable Pairs, Canonical Kähler metrics & Heights
Oct. 1 Andrew Zimmer Entropy rigidity old and new
Oct. 8 Laurentiu Maxim Topology of complex projective hypersurfaces
Oct. 15 Gavin Ball Introduction to G2 Geometry
Oct. 22 Chenxi Wu Stable translation lengths on sphere graphs
Oct. 29 Brian Hepler
Nov. 5 Botong Wang
Nov. 12 Nate Fisher
Nov. 19 Sigurd Angenent



Fall Abstracts

Alex Waldron

I'll describe some history, recent results, and open problems about harmonic map flow, particularly in the 2-dimensional case.

Sean Paul

An interesting problem in complex differential geometry seeks to characterize the existence of a constant scalar curvature metric on a Hodge manifold in terms of the algebraic geometry of the underlying variety. The speaker has recently solved this problem for varieties with finite automorphism group. The talk aims to explain why the problem is interesting (and quite rich) and to describe in non-technical language the ideas in the title and how they all fit together.

Note: this talk will provide some background for Sean's colloquium later in the afternoon.

Andrew Zimmer

Informally, an "entropy rigidity" result characterizes some special geometric object (e.g. a constant curvature metric on a manifold) as a maximizer/minimizer of some function of the objects asymptotic complexity. In this talk I will survey some classical entropy rigidity results in hyperbolic and Riemannian geometry. Then, if time allows, I will discuss some recent joint work with Canary and Zhang. The talk should be accessible to first year graduate students.

Laurentiu Maxim

I will overview old and new results which show how the presence of singularities affects the topology of complex projective hypersurfaces.

Gavin Ball

I will give an introduction to the theory of manifolds with holonomy group G2. I will begin by describing the exceptional Lie group G2 using some special linear algebra in dimension 7. Then I will give an overview of the holonomy group of a Riemannian manifold and describe Berger's classification theorem. The group G2 is one of two exceptional members of Berger's list, and I will explain the interesting properties manifolds with holonomy G2 have and sketch the construction of examples. If time permits, I will describe some of my recent work on manifolds with closed G2-structure.


Chenxi Wu

I will discuss some of my prior works in collaboration with Harry Baik, Dongryul Kim, Hyunshik Shin and Eiko Kin on stable translation lengths on sphere graphs for maps in a fibered cone, and discuss the applications on maps on surfaces, finite graphs and handlebody groups.



Archive of past Geometry seminars

2020-2021 Geometry_and_Topology_Seminar_2020-2021

2019-2020 Geometry_and_Topology_Seminar_2019-2020

2018-2019 Geometry_and_Topology_Seminar_2018-2019

2017-2018 Geometry_and_Topology_Seminar_2017-2018

2016-2017 Geometry_and_Topology_Seminar_2016-2017

2015-2016: Geometry_and_Topology_Seminar_2015-2016

2014-2015: Geometry_and_Topology_Seminar_2014-2015

2013-2014: Geometry_and_Topology_Seminar_2013-2014

2012-2013: Geometry_and_Topology_Seminar_2012-2013

2011-2012: Geometry_and_Topology_Seminar_2011-2012

Fall-2010-Geometry-Topology

Dynamics_Seminar_2020-2021