##### Department of Mathematics,

University of California San Diego

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### Colloquium

## Daniel Halpern-Leistner

#### Columbia University

## Equivariant Morse theory in algebraic geometry

##### Abstract:

The development of the theory of mirror symmetry in high energy physics has led to deep conjectures regarding the geometry of a special class of complex manifolds called Calabi-Yau manifolds. One of the most intriguing of these conjectures states that various geometric invariants, some classical and some more homological in nature, agree for any two Calabi-Yau manifolds which are ``birationally equivalent" to one another. I will discuss how new methods in equivariant geometry have shed light on this conjecture over the past few years, leading to the first substantial progress for compact Calabi-Yau manifolds of dimension greater than three. The key technique is the new theory of ``Theta-stratifications," which allows one to bring ideas from equivariant Morse theory into the setting of algebraic geometry.

Host: James McKernan

### December 6, 2016

### 3:00 PM

### AP&M 6402

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