# *Special Lecture* Exponential convergence for parabolic optimal transport with boundary

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Jun Kitagawa, Michigan State University
Fine Hall 224

*Special Lecture*

Please note the time and location

A solution of the classical optimal transport (or Monge-Kantorovich problem) can be constructed from the solution of an elliptic Monge-Amp{\`e}re equation. A natural approach is then to consider a parabolic version of this equation and try to find stationary solution as time goes to infinity.

In this talk, I will discuss an exponential convergence result for such solutions on domains with nonempty boundary. This is related to a Li-Yau Harnack type inequality, but differs from the classical case since the boundary is nonempty, our proof utilizes the optimal transport structure, and the pseudo-Riemannian optimal transport metric defined by Kim and McCann.

This talk is based on joint work with Farhan Abedin (MSU).