# Hayden Howard Lecture: How do Partial Differential Equations detect Geometry in Euclidean space?

**How do Partial Differential Equations detect Geometry in Euclidean space?**

In this talk we will present an area of analysis that is concerned with the relationship between differential operators, the properties of their solutions, and the geometry of the domain on which they are considered. The goal is to highlight how analytic properties of solutions to PDEs determine the geometry of the domain where they are considered. The tools used in this area come from analysis of partial differential equations, harmonic analysis and geometric measure theory.

A native of Colombia, Tatiana Toro received her Ph.D. in Mathematics from Stanford University in 1992. She is well known for her seminal work on the interplay between the geometry of the domains and regularity properties of solutions of elliptic partial differential equations. She was an invited speaker for the Analysis session at the ICM 2010 in Hyderabad, India, and delivered the first annual AMS Mirzakhani Lecture at the Joint Mathematical Meeting in Denver in January 2020. Her list of honors includes Fellow of AMS, Guggenheim Foundation Fellowship, Simons Foundation Fellowship, and Alfred Sloan Fellowship. She currently holds the Craig McKibben and Sarah Merner Professorship in Mathematics at University of Washington.