##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry Seminar

## Song Sun

#### UC Berkeley

## Metric collapsing of Calabi-Yau manifolds and complex structure degenerations

##### Abstract:

A Calabi-Yau manifold is a Ricci-flat Kahler manifold. It is a longstanding question to understand how the Ricci-flat metrics develop singularities when the complex structure degenerates. An especially intriguing phenomenon is that these metrics can collapse to lower dimensions and exhibit very non-algebraic features, and it is challenging to describe the corresponding geometric behavior. In this talk I will discuss an answer to this question for a special class of degenerations. Based on joint works with H. Hein-J. Viaclovsky-R. Zhang 2018 and with R. Zhang 2019.

Host: Lei Ni

### May 13, 2020

### 2:00 PM

### Zoom ID: 747-181-629

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