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]]
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== Spring 2017 ==
+
 
 +
== Fall 2019 ==
  
 
{| cellpadding="8"
 
{| cellpadding="8"
Line 15: Line 16:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|Jan 20
+
|Oct. 4
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)
+
|Ruobing Zhang (Stony Brook University)
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]
+
| Geometric analysis of collapsing Calabi-Yau spaces
| Maxim
+
|(Chen)
|-
 
|Jan 27
 
 
|
 
|
 
|-
 
|Feb 3
 
| Rafael Montezuma (University of Chicago)  
 
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]
 
| Lu Wang
 
|-
 
|Feb 10
 
 
|
 
|
 
|-
 
|Feb 17
 
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University)  
 
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]
 
| [http://www.math.wisc.edu/~dymarz Dymarz]
 
|-
 
|Feb 24
 
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)
 
| [[#Lucas Ambrozio| "Free boundary minimal hypersurfaces of Euclidean domains"]]
 
| Lu Wang
 
 
|-
 
|-
|March 3
 
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)
 
| [[#Mark Powell| "Stable classification of 4-manifolds"]]
 
| Kjuchukova
 
 
|-
 
|-
|March 10
+
|Oct. 25
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)
+
|Emily Stark (Utah)
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]
+
| Action rigidity for free products of hyperbolic manifold groups
| local
+
|(Dymarz)
 
|-
 
|-
|March 17
+
|Nov. 8
|  
+
|Max Forester (University of Oklahoma)
|  
+
| TBA
|  
+
|(Dymarz)
 
|-
 
|-
|March 24
+
|Nov. 22
| Spring Break
+
|Yu Li (Stony Brook University)
|  
+
|On the structure of Ricci shrinkers
|  
+
|(Huang)
 
|-
 
|-
|March 31
 
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)
 
| [[#Xiangwen Zhang| "The Anomaly Flow and Strominger systems"]]
 
| Lu Wang
 
|
 
|-
 
|April 7
 
| [https://www.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)
 
|[[#Paul Feehan| "TBA"]]
 
| Lu Wang
 
|-
 
|April 14
 
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin)
 
| [[#Xianghong Gong| "TBA"]]
 
| local
 
|-
 
|April 21
 
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) 
 
| [[#Joseph Maher|"TBA"]]
 
| [http://www.math.wisc.edu/~dymarz Dymarz]
 
|-
 
|April 28
 
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)
 
| [[#Bena Tshishiku| "TBA"]]
 
| [http://www.math.wisc.edu/~dymarz Dymarz]
 
|-
 
|
 
 
|}
 
|}
  
== Spring Abstracts ==
+
==Fall Abstracts==
 
 
===Lucas Ambrozio===
 
"Free boundary minimal hypersurfaces of Euclidean domains"
 
 
 
We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes).
 
 
 
===Paul Feehan===
 
"TBA"
 
 
 
===Rafael Montezuma===
 
"Metrics of positive scalar curvature and unbounded min-max widths"
 
 
 
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.
 
 
 
===Carmen Rovi===
 
''The mod 8 signature of a fiber bundle''
 
 
 
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and  representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.
 
 
 
===Yair Hartman===
 
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."
 
  
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.
+
===Ruobing Zhang===
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.
 
  
===Bena Tshishiku===
+
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.
"TBA"
 
  
===Mark Powell===
+
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.
''Stable classification of 4-manifolds''
 
  
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2.
+
===Emily Stark===
Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations.
 
Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group.  I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. 
 
As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.
 
  
===Autumn Kent===
+
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.
''Analytic functions from hyperbolic manifolds''
 
  
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps."  These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior.  The ideas involved form a mix of geometry, algebra, and analysis.
+
===Max Forester===
  
===Xiangwen Zhang===
+
“TBA”
"The Anomaly Flow and Strominger systems"
 
  
The anomaly flow is a geometric flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced condition of Hermitian metrics. I will discuss criteria for long time existence and convergence of the flow on toric fibrations with the Fu-Yau ansatz. This is joint work with D.H. Phong and S. Picard.
+
===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]]
 
2016-2017  [[Geometry_and_Topology_Seminar_2016-2017]]
 
<br><br>
 
<br><br>

Latest revision as of 08:14, 20 October 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) TBA (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

“TBA”

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