##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry

## Junliang Shen

#### MIT

## Hitchin systems, hyper-Kaehler geometry, and the P=W conjecture

##### Abstract:

The P=W conjecture by de Cataldo, Hausel, and Migliorini suggests a surprising connection between the topology of Hitchin systems and Hodge theory of character varieties. In this talk, we will focus on interactions between compact and noncompact hyper-Kaehler geometries. Such connections, together with symmetries coming from the moduli of compact hyper-Kaehler manifolds, lead to new progress on the P=W conjecture. I will discuss the results we obtained and the difficulties we met. Based on joint work with Mark de Cataldo and Davesh Maulik.

Host: Prof. Dragos Oprea

### April 17, 2020

### 2:00 PM

### Zoom (Contact Prof. James McKernan)

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