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'''.
 
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/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .
+
For more information, contact Shaosai Huang.
  
 
[[Image:Hawk.jpg|thumb|300px]]
 
[[Image:Hawk.jpg|thumb|300px]]
  
  
 
+
== Spring 2020 ==
== Fall 2017 ==
 
  
 
{| cellpadding="8"
 
{| cellpadding="8"
Line 15: Line 14:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|September 8
+
|Feb. 7
|TBA
+
|Xiangdong Xie  (Bowling Green University)
|TBA
+
| Minicourse 1
|TBA
+
|(Dymarz)
 
|-
 
|-
|September 15
+
|Feb. 14
|TBA
+
|Xiangdong Xie  (Bowling Green University)
|TBA
+
| Minicourse 2
|TBA
+
|(Dymarz)
 
|-
 
|-
|September 22
+
|Feb. 21
|TBA
+
|Xiangdong Xie  (Bowling Green University)
|TBA
+
| Minicourse 3
|TBA
+
|(Dymarz)
 
|-
 
|-
|September 29
+
|Feb. 28
|Ke Zhu(Minnesota State University)
+
|Kuang-Ru Wu (Purdue University)
|[[#Ke Zhu| ""]]
+
|Griffiths extremality, interpolation of norms, and Kahler quantization
|Bing Wang
+
|(Huang)
 +
|}
 +
 
 +
== Fall 2019 ==
 +
 
 +
{| cellpadding="8"
 +
!align="left" | date
 +
!align="left" | speaker
 +
!align="left" | title
 +
!align="left" | host(s)
 
|-
 
|-
|October 6
+
|Oct. 4
|Shaosai Huang(Stony Brook)
+
|Ruobing Zhang (Stony Brook University)
|TBA
+
| Geometric analysis of collapsing Calabi-Yau spaces
|Bing Wang
+
|(Chen)
 
|-
 
|-
|October 13
 
|(reserved)
 
|TBA
 
|Kjuchukova
 
 
|-
 
|-
|October 20
+
|Oct. 25
|Shengwen Wang (Johns Hopkins)
+
|Emily Stark (Utah)
|TBA
+
| Action rigidity for free products of hyperbolic manifold groups
|Lu Wang
+
|(Dymarz)
 
|-
 
|-
|October 27
+
|Nov. 8
|Marco Mendez-Guaraco (Chicago)
+
|Max Forester (University of Oklahoma)
|TBA
+
|Spectral gaps for stable commutator length in some cubulated groups
|Lu Wang
+
|(Dymarz)
 
|-
 
|-
|November 3
+
|Nov. 22
|TBA
+
|Yu Li (Stony Brook University)
|TBA
+
|On the structure of Ricci shrinkers
|TBA
+
|(Huang)
|-
 
|November 10
 
|TBA
 
|TBA
 
|TBA
 
|-
 
|November 17
 
|Ovidiu Munteanu (University of Connecticut)
 
|TBA
 
|Bing Wang
 
|-
 
|<b>Thanksgiving Recess</b>
 
|
 
|
 
|
 
|-
 
|December 1
 
|TBA
 
|TBA
 
|TBA
 
|-
 
|December 8
 
|TBA
 
|TBA
 
|TBA
 
 
|-
 
|-
 
|}
 
|}
  
== Fall Abstracts ==
+
==Spring Abstracts==
 +
 
 +
===Kuang-Ru Wu===
 +
 
 +
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.
 +
 
 +
==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.
  
=== Marco Mendez-Guaraco ===
+
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"
 
  
=== Ke Zhu===
+
===Emily Stark===
"Isometric Embedding via Heat Kernel"
 
  
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding.   In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.
+
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.
  
=== Shaosai Huang ===
+
===Max Forester===
"TBA"
 
  
=== Ovidiu Munteanu ===
+
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.
"TBA"
 
  
=== Shengwen Wang ===
+
===Yu Li===
"TBA"
+
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]]
 
2016-2017  [[Geometry_and_Topology_Seminar_2016-2017]]
 
<br><br>
 
<br><br>

Latest revision as of 23:41, 28 December 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


Spring 2020

date speaker title host(s)
Feb. 7 Xiangdong Xie (Bowling Green University) Minicourse 1 (Dymarz)
Feb. 14 Xiangdong Xie (Bowling Green University) Minicourse 2 (Dymarz)
Feb. 21 Xiangdong Xie (Bowling Green University) Minicourse 3 (Dymarz)
Feb. 28 Kuang-Ru Wu (Purdue University) Griffiths extremality, interpolation of norms, and Kahler quantization (Huang)

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)

Spring Abstracts

Kuang-Ru Wu

Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.

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