Singular Affine Structures, Monge-Ampère Equations and Unit Simplices
Time: 2022-02-24
Published By: Wenqiong Li
Speaker(s): Jakob Hultgren(University of Maryland)
Time: 09:00-10:00 March 2, 2022
Venue: Online
Abstract:
Recent developments in complex geometry have highlighted the importance of real Monge-Ampère equations on singular affine manifolds, in particular for the well known 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 solution. This is the first general existence result for Monge-Ampère equations on a singular affine manifold. I will outline the proof, which uses tools from optimal transport 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.
Link: https://us02web.zoom.us/j/87349722554?pwd=MTBhYXVpa2lUSlorVk1GYTIzQkRmUT09
Recent developments in complex geometry have highlighted the importance of real Monge-Ampère equations on singular affine manifolds, in particular for the well known 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 solution. This is the first general existence result for Monge-Ampère equations on a singular affine manifold. I will outline the proof, which uses tools from optimal transport 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.
Speaker:
Jakob Hultgren is currently a Novikov Postdoctoral Fellow at University of Maryland and a Knut and Alice Wallenberg postdoctoral scholar. He completed his PhD at Chalmers University of Technology in 2018 under the supervision of Robert Berman and David Witt Nyström after which he spent a year as a postdoc at University of Oslo. His research interests lie in complex differential geometry and PDE. In particular, he is interested in real and complex Monge-Ampère equations, optimal transport and their applications to geometry.
Link: https://us02web.zoom.us/j/87349722554?pwd=MTBhYXVpa2lUSlorVk1GYTIzQkRmUT09
ID: 873 4972 2554
Password: 728406
