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Geometry and Topology Seminar

Friday, October 8, 2021
3:00pm to 4:00pm
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Linde Hall 187
Solutions to the Monge-Ampere equation with polyhedral and Y-shaped singularities
Connor Mooney, Department of Mathematics, UC, Irvine,

The Monge-Ampere equation det(D^2u) = 1 arises in prescribed curvature problems and in optimal transport. An interesting feature of the equation is that it admits singular solutions. We will discuss new examples of convex functions on R^n that solve the Monge-Ampere equation away from finitely many points, but contain polyhedral and Y-shaped singular structures. Along the way we will discuss geometric motivations for constructing such examples, as well as their connection to a certain obstacle problem.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu or visit https://sites.google.com/site/caltechgtseminar/home.