Seminar Event Detail


Complex Analysis, Dynamics and Geometry

Date:  Monday, April 25, 2022
Location:  3096 East Hall (3:00 PM to 4:00 PM)

Title:  Singular affine structures, real Monge-Ampère equations and unit simplices

Abstract:   Recent developments in complex geometry have highlighted the importance of real Monge-Ampere 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-Ampere 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.

Files:


Speaker:  Jakob Hultgren
Institution:  University of Maryland

Event Organizer:     

 

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