Benjy Firester|Free boundary Monge-Ampère eqns w/applications to optimal transport & C-Y geometry

Workshop on Calabi-Yau metrics and optimal transport 5/21/2026 Speaker: Benjy Firester, MIT Title: Free boundary Monge-Ampère equations with applications to optimal transport and Calabi-Yau geometry Abstract: I will present a variational framework to solve a general class of free-boundary Monge-Ampère equations. This approach combines the classical first and second boundary value problems by imposing both the boundary data and the gradient image of the solution. I will explore applications to the Monge-Ampère eigenvalue problem, convex reconstruction theorems, and geometric problems including a hemispherical Minkowski problem, Calabi-Yau metrics, and free boundary toric Kähler–Einstein/Kähler-Ricci soliton metrics. I will also discuss the connection to the boundary regularity of optimal transport.