##### Department of Mathematics,

University of California San Diego

****************************

### Math 295 - Mathematics Colloquium

## Georg Oberdieck

#### MIT

## Enumerative geometry of hyper-Kaehler varieties and modular forms

##### Abstract:

The enumerative geometry of curves on K3 surfaces is governed by modular forms. I will discuss a parallel connection between the enumerative geometry of hyper-Kaehler varieties and Jacobi forms. The case of genus 1 curves is particularly interested and leads to the Igusa cusp form conjecture. In the last part I will explain recent work with Junliang Shen and Aaron Pixton which yields a proof of this conjecture.

Host: Dragos Oprea

### November 28, 2017

### 3:00 PM

### AP&M 6402

****************************