# Data depths meet Hamilton-Jacobi equations

Ryan Murray (North Carolina State University)

Widespread application of modern machine learning has increased the need for robust statistical algorithms. One fundamental geometric quantity in robust statistics is known as a data depth, which generalizes the notion of quantiles and medians to multiple dimensions. This talk will discuss recent work (in collaboration with Martin Molina-Fructuoso) which connects certain types of data depths with Hamilton-Jacobi equations, a first-order partial differential equation that is fundamental to control theory. Computational considerations, connections to convex geometry and a number of related open problems will all be discussed.

Ryan Murray received his PhD in mathematics from Carnegie Mellon University in 2016, and was a Chowla Assistant Professor at Penn State University from 2016-2019. Since 2019 he is an assistant professor at North Carolina State University, department of mathematics.