Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Abstract

In 1990 Tian-Yau proved that if Y is a Fano manifold and D is a smooth anti-canonical divisor, the complement X=Y\D admits a complete Calabi-Yau metric. A long standing problem has been to understand the existence of Calabi-Yau metrics when D is singular. I will discuss the resolution of this problem when D=D_1+D_2 has two components and simple normal crossings. I will also explain a general picture which suggests the case of general SNC divisors should be inductive on the number of components. This is joint work with Y. Li.

Speaker

Tristan Collins is the Class of 1948 Career Development Assistant Professor in the Mathematics Department at MIT. He has produced important results at the intersection of geometric analysis, partial differential equations and algebraic geometry. In joint work with Valentino Tosatti, Collins described the singularity formation of the Ricci flow on Kahler manifolds in terms of algebraic data. In recent work with Gabor Szekelyhidi, he gave a necessary and sufficient algebraic condition for existence of Ricci-flat metrics, which play an important role in String Theory and mathematical physics. This result lead to the discovery of infinitely many new Einstein metrics on the five dimensional sphere. With Shing-Tung Yau and Adam Jacob, Collins is studying the relationship between categorical stability conditions and existence of solutions to differential equations arising from mirror symmetry.

Collins received the 2018 Sloan Research Fellowship; and in 2021, the André Aisenstadt Prize in Mathematics, awarded to a young outstanding Canadian mathematician.

Web page:

https://math.mit.edu/directory/profile?pid=2063