Difference between revisions of "Geometry and Topology Seminar"

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The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
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The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.
<br>
+
<br>  
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].
+
For more information, contact Shaosai Huang.
  
 
[[Image:Hawk.jpg|thumb|300px]]
 
[[Image:Hawk.jpg|thumb|300px]]
  
  
== Fall 2014==
 
  
  
 +
== Fall 2019 ==
  
 
{| cellpadding="8"
 
{| cellpadding="8"
Line 16: Line 16:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|August 29
+
|Oct. 4
| Yuanqi Wang
+
|Ruobing Zhang (Stony Brook University)
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]
+
| Geometric analysis of collapsing Calabi-Yau spaces
| [http://www.math.wisc.edu/~bwang Wang]
+
|(Chen)
 
|-
 
|-
|September 5
 
|
 
|
 
|
 
 
|-
 
|-
|September 12
+
|Oct. 25
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)
+
|Emily Stark (Utah)
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]
+
| Action rigidity for free products of hyperbolic manifold groups
| [http://www.math.wisc.edu/~maxim/ Maxim]
+
|(Dymarz)
 
|-
 
|-
|September 19
+
|Nov. 8
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)
+
|Max Forester (University of Oklahoma)
| [[#Ben Knudsen (Northwestern)|''TBA'']]
+
|Spectral gaps for stable commutator length in some cubulated groups
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]
+
|(Dymarz)
 
|-
 
|-
|September 26
+
|Nov. 22
|  
+
|Yu Li (Stony Brook University)
|
+
|On the structure of Ricci shrinkers
|
+
|(Huang)
 
|-
 
|-
|October 3
 
|
 
|
 
|
 
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|October 10
 
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|
 
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|October 17
 
|
 
|
 
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|October 24
 
|
 
|
 
|
 
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|October 31
 
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)
 
| [[#Jing Tao (Oklahoma)|''TBA'']]
 
| [http://www.math.wisc.edu/~rkent/ Kent]
 
|-
 
|November 7
 
|
 
|
 
|
 
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|November 14
 
|
 
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|November 21
 
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|Thanksgiving Recess
 
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|December 5
 
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|December 12
 
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|}
 
|}
  
== Fall Abstracts ==
+
==Fall Abstracts==
  
===Yuanqi Wang===
+
===Ruobing Zhang===
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''
 
  
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,
+
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.
 
  
===Chris Davis (UW-Eau Claire)===
+
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.
''TBA''
 
  
===Ben Knudsen (Northwestern)===
+
===Emily Stark===
''TBA''
 
  
===Jing Tao (Oklahoma)===
+
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.
''TBA''
 
 
 
== Spring 2015 ==
 
 
 
 
 
{| cellpadding="8"
 
!align="left" | date
 
!align="left" | speaker
 
!align="left" | title
 
!align="left" | host(s)
 
|-
 
|January 23
 
|
 
|
 
|
 
|-
 
|January 30
 
|
 
|
 
|
 
|-
 
|February 6
 
|
 
|
 
|
 
|-
 
|February 13
 
|
 
|
 
|
 
|-
 
|February 20
 
|
 
|
 
|
 
|-
 
|February 27
 
|
 
|
 
|
 
|-
 
|March 6
 
|
 
|
 
|
 
|-
 
|March 13
 
|
 
|
 
|
 
|-
 
|March 20
 
|
 
|
 
|
 
|-
 
|March 27
 
|
 
|
 
|
 
|-
 
| Spring Break
 
|
 
|
 
|
 
|-
 
|April 10
 
|
 
|
 
|
 
|-
 
| April 17
 
|
 
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|April 24
 
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|May 1
 
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|May 8
 
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|-
 
|}
 
  
== Spring Abstracts ==
+
===Max Forester===
  
 +
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.
  
 +
===Yu Li===
 +
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.
  
 
== Archive of past Geometry seminars ==
 
== Archive of past Geometry seminars ==
 
+
2018-2019  [[Geometry_and_Topology_Seminar_2018-2019]]
 +
<br><br>
 +
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]
 +
<br><br>
 +
2016-2017  [[Geometry_and_Topology_Seminar_2016-2017]]
 +
<br><br>
 +
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]
 +
<br><br>
 +
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]
 +
<br><br>
 
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]
 
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]
 
<br><br>
 
<br><br>

Latest revision as of 08:44, 4 November 2019

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.

Hawk.jpg



Fall 2019

date speaker title host(s)
Oct. 4 Ruobing Zhang (Stony Brook University) Geometric analysis of collapsing Calabi-Yau spaces (Chen)
Oct. 25 Emily Stark (Utah) Action rigidity for free products of hyperbolic manifold groups (Dymarz)
Nov. 8 Max Forester (University of Oklahoma) Spectral gaps for stable commutator length in some cubulated groups (Dymarz)
Nov. 22 Yu Li (Stony Brook University) On the structure of Ricci shrinkers (Huang)

Fall Abstracts

Ruobing Zhang

This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.

First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.

Emily Stark

The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.

Max Forester

I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.

Yu Li

We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.

Archive of past Geometry seminars

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

2010: Fall-2010-Geometry-Topology