##### Department of Mathematics,

University of California San Diego

****************************

### Math 258 - Differential Geometry Seminar

## Connor Mooney

#### UC Irvine

## Solutions to the Monge-Ampere equation with polyhedral and Y-shaped singularities

##### Abstract:

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.

Host: Luca Spolaor

### October 6, 2021

### 11:00 AM

APM 7321

****************************