Number Theory Seminar: Equivariant Morse theory in algebraic geometry

Seminar | January 13 | 4:10-5 p.m. | 740 Evans Hall

 Daniel Halpern-Leistner, Columbia University

 Department of Mathematics

Developments in high energy physics, specifically in 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.