# Daniel Halpern-Leistner : Equivariant geometry and Calabi-Yau manifolds

Developments in high energy physics, specifically the theory of mirror symmetry, have 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.

**Category**: Geometry and Topology**Duration**: 01:14:45**Date**: January 25, 2017 at 11:55 AM**Views**: 103-
**Tags:**seminar, Geometry/topology Seminar

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