# Geometry and Topology Seminar 2019-2020

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.

## Contents

## 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

"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