Northwestern-Notre Dame-UIC Complex Geometry Seminar
Spring 2022
Spring 2022
Our next meeting will be held in-person at UIC SEO636 on Tuesday April 5th.
Tuesday April 5th, 3pm Central Time
Tristan Collins (MIT) Complete Calabi-Yau metrics on the complement of two divisors
Tuesday April 5th, 3pm Central Time
Tristan Collins (MIT) Complete Calabi-Yau metrics on the complement of two divisors
I will discuss the existence of a complete Calabi-Yau metric on the complement of a simple normal crossings anti-canonical divisor with two components, as well as possible extensions to more general situations. This is joint work with Yang Li.
Tuesday April 5th, 4.30pm Central Time
Jakob Hultgren (University of Maryland) Singular affine structures, real Monge-Ampère equations and unit simplices
Tuesday April 5th, 4.30pm Central Time
Jakob Hultgren (University of Maryland) Singular affine structures, real Monge-Ampère equations and unit simplices
Recent developments in complex geometry have highlighted the importance of real Monge-Ampère equations on singular affine manifolds, in particular for the SYZ conjecture concerning collapsing families of Calabi-Yau manifolds. We show that for symmetric data, the real Monge-Ampère equation on the unit simplex admits a unique Aleksandrov solution. This is concluded as a special case of a result giving necessary and sufficient conditions in terms of optimal transport for existence of solutions. I will outline the proof and explain a built in phenomena reminiscent of free boundary problems. Time permitting, I will discuss an application to the SYZ conjecture related to recent work by Y. Li.
Recent developments in complex geometry have highlighted the importance of real Monge-Ampère equations on singular affine manifolds, in particular for the SYZ conjecture concerning collapsing families of Calabi-Yau manifolds. We show that for symmetric data, the real Monge-Ampère equation on the unit simplex admits a unique Aleksandrov solution. This is concluded as a special case of a result giving necessary and sufficient conditions in terms of optimal transport for existence of solutions. I will outline the proof and explain a built in phenomena reminiscent of free boundary problems. Time permitting, I will discuss an application to the SYZ conjecture related to recent work by Y. Li.