Difference between revisions of "Geometry and Topology Seminar"

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== Fall 2010 ==
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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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<br>
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For more information, contact Shaosai Huang.
  
The seminar will be held  in room B901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm
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[[Image:Hawk.jpg|thumb|300px]]
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== Fall 2019 ==
  
 
{| cellpadding="8"
 
{| cellpadding="8"
Line 9: Line 16:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|September 10
+
|Oct. 4
|[http://www.math.wisc.edu/~oh/ Yong-Geun Oh] (UW Madison)
+
|Ruobing Zhang (Stony Brook University)
|[[#Yong-Geun Oh (UW Madison)|
+
| Geometric analysis of collapsing Calabi-Yau spaces
''Counting embedded curves in Calabi-Yau threefolds and Gopakumar-Vafa invariants'']]
+
|(Chen)
|local
 
 
|-
 
|-
|September 17
 
|Leva Buhovsky (U of Chicago)
 
|[[#Leva Buhovsky (U of Chicago)|
 
''On the uniqueness of Hofer's geometry'']]
 
|[http://www.math.wisc.edu/~oh/ Yong-Geun]
 
 
|-
 
|-
|September 24
+
|Oct. 25
|[http://sites.google.com/site/polterov/home/ Leonid Polterovich] (Tel Aviv U and U of Chicago)
+
|Emily Stark (Utah)
|[[#Leonid Polterovich (Tel Aviv U and U of Chicago)|
+
| TBA
''Poisson brackets and symplectic invariants'']]
+
|(Dymarz)
|[http://www.math.wisc.edu/~oh/ Yong-Geun]
 
 
|-
 
|-
|October 8
+
|Nov. 8
|[http://www.math.wisc.edu/~stpaul/ Sean Paul] (UW Madison)
+
|Max Forester (University of Oklahoma)
|[[#Sean Paul (UW Madison)|
+
| TBA
''Canonical Kahler metrics and the stability of projective varieties'']]
+
|(Dymarz)
|local
 
 
|-
 
|-
|October 15
+
|Nov. 22
|Conan Leung (Chinese U. of Hong Kong)
+
|Yu Li (Stony Brook University)
|[[#Conan Leung (Chinese U. of Hong Kong)|
+
|On the structure of Ricci shrinkers
''TBA'']]
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|(Huang)
|Honorary fellow, local
 
|-
 
|October 22
 
|[http://www.mathi.uni-heidelberg.de/~banagl/ Markus Banagl] (U. Heidelberg)
 
|[[# Markus Banagl (U. Heidelberg)|
 
''Intersection Space Methods and Their Application to Equivariant Cohomology, String Theory, and Mirror Symmetry'']]
 
|[http://www.math.wisc.edu/~maxim/ Maxim]
 
|-
 
|October 29
 
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (U of Minnesota)
 
|[[#Ke Zhu (U of Minnesota)|
 
''TBA'']]
 
|[http://www.math.wisc.edu/~oh/ Yong-Geun]
 
|-
 
|November 5
 
|[http://www.math.psu.edu/tabachni/ Sergei Tabachnikov]  (Penn State)
 
|[[#Sergei Tabachnikov (Penn State)|
 
''TBA'']]
 
|[http://www.math.wisc.edu/~maribeff/ Gloria]
 
|-
 
|January 21
 
|Mohammed Abouzaid (Clay Institute & MIT)
 
|[[#Mohammed Abouzaid (Clay Institute & MIT)|
 
''TBA'']]
 
|[http://www.math.wisc.edu/~oh/ Yong-Geun]
 
 
|-
 
|-
 
|}
 
|}
  
== Abstracts ==
+
==Fall Abstracts==
===Yong-Geun Oh (UW Madison)===
 
''Counting embedded curves in Calabi-Yau threefolds and Gopakumar-Vafa invariants''
 
 
 
Gopakumar-Vafa BPS invariant is some integer counting invariant of the cohomology
 
of D-brane moduli spaces in string theory. In relation to the Gromov-Witten theory,
 
it is expected that the invariant would coincide with the `number' of embedded
 
(pseudo)holomorphic curves (Gopakumar-Vafa conjecture). In this talk, we will explain the speaker's recent
 
result that the latter integer invariants can be defined for a generic choice of
 
compatible almost complex structures. We will also discuss the corresponding
 
wall-crossing phenomena and some open questions towards a complete solution to
 
the Gopakumar-Vafa conjecture.
 
 
 
===Leva Buhovsky (U of Chicago)===
 
''On the uniqueness of Hofer's geometry''
 
 
 
In this talk we address the question whether Hofer's metric is unique among the Finsler-type bi-invariant metrics on the group of Hamiltonian diffeomorphisms. The talk is based on a recent joint work with Yaron Ostrover.
 
  
===Leonid Polterovich (Tel Aviv U and U of Chicago)===
+
===Ruobing Zhang===
''Poisson brackets and symplectic invariants''
 
  
We discuss new invariants associated to collections of closed subsets
+
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.
of a symplectic manifold. These invariants are defined
 
through an elementary variational problem involving Poisson brackets.
 
The proof of non-triviality of these invariants requires methods of modern
 
symplectic topology (Floer theory). We present applications
 
to approximation theory on symplectic manifolds and to Hamiltonian dynamics.
 
The talk is based on a work in progress with Lev Buhovsky and Michael Entov.
 
  
===Sean Paul (UW Madison)===
+
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.
''Canonical Kahler metrics and the stability of projective varieties"
 
  
I will give a survey of my own work on this problem, the basic reference is:
+
===Emily Stark===
http://arxiv.org/pdf/0811.2548v3
 
  
===Conan Leung (Chinese U. of Hong Kong)===
+
"TBA"
''TBA''
 
  
===Markus Banagl (U. Heidelberg)===
+
===Max Forester===
''Intersection Space Methods and Their Application to Equivariant Cohomology, String Theory, and Mirror Symmetry.''
 
Using homotopy theoretic methods, we shall associate to certain classes of
 
singular spaces generalized geometric Poincaré complexes called intersection
 
spaces. Their cohomology is generally not isomorphic to intersection
 
cohomology.
 
In this talk, we shall concentrate on the applications of the new
 
cohomology theory to the equivariant real cohomology of isometric actions of
 
torsionfree discrete groups, to type II string theory and D-branes, and to
 
the relation of the new theory to classical intersection cohomology under
 
mirror symmetry.
 
  
===Ke Zhu (U of Minnesota)===
+
“TBA”
''TBA''
 
  
===Sergei Tabachnikov (Penn State)===
+
===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.
  
===Mohammed Abouzaid (Clay Institute & MIT)===
+
== Archive of past Geometry seminars ==
''TBA''
+
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]]
 +
<br><br>
 +
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]
 +
<br><br>
 +
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]
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<br><br>
 +
2010: [[Fall-2010-Geometry-Topology]]

Latest revision as of 22:01, 24 September 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) TBA (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

"TBA"

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