# 2019-2020 Baylor Lecture Series in Mathematics

### Luis Caffarelli

Dr. Luis Caffarelli was the speaker in the thirteenth annual Baylor Lecture Series in Mathematics when he visits Baylor University on October 17-18, 2019. He is the Sid Richardson Foundation Regents Chair in Mathematics at the University of Texas in Austin and a member of the National Academy of Sciences. He is one of the world's leading experts in the subject of partial differential equations, especially in the areas of free boundary problems and nonlinear partial differential equations. He developed several regularity results for fully nonlinear elliptic equations including the Monge-Ampere equation. He is also well known for his contributions to homogenization. Recently, he has taken an interest in integro-differential equations.

Professor Caffarelli was born and grew up in Buenos Aires. He obtained his Masters of Science (1968) and Ph.D. (1972) at the University of Buenos Aires. His Ph.D. advisor was Calixto Calderón. Prior to his appointment at the University of Texas, he was a professor at the University of Minnesota, the University of Chicago, and the Courant Institute of Mathematical Sciences at New York University. From 1986 to 1996 he was a professor at the Institute for Advanced Study in Princeton.

In 1991 he was elected to the National Academy of Sciences. He has been awarded Doctor Honoris Causa from l'École Normale Supérieure, Paris; University of Notre Dame; Universidad Autónoma de Madrid, and Universidad de La Plata, Argentina. He received the Bôcher Memorial Prize in 1984. In 2003, the Konex Foundation from Argentina granted him the Diamond Konex Award, one of the most prestigious awards in Argentina, as the most important scientist of his country in the last decade. In 2005, he received the prestigious Rolf Schock Prize of the Royal Swedish Academy of Sciences for his important contributions to the theory of nonlinear partial differential equations. He also received the Leroy P. Steele Prize for Lifetime Achievement in Mathematics in 2009. In 2012 he was awarded the Wolf Prize in Mathematics (jointly with Michael Aschbacher) and became a fellow of the American Mathematical Society. In 2018 he was named a SIAM Fellow and he received the Shaw Prize in Mathematics.

For a poster advertising Professor Caffarelli's public lecture, click here.

The titles, and abstracts, for his lectures, with dates and venues are:*Thursday, October 17, 2019 at 4:30 pm - MMSCI 301 *

### COLLOQUIUM LECTURE: **The Interaction of Local and Non-Local Phenomena**

Abstract: Often, infinitesimal and integral diffusion processes interact with each other: solids and gas, bids and calls, elastic membranes involving solids. The interactions may be due to phase transitions, transmission conditions or surface - solid conditions. After a short overview, we will discuss some examples and the mathematics involved.

*Friday, October 18, 2019 at 4:00 pm - BSB D110 *

### PUBLIC LECTURE: **Diffusion-type Equations: From the Heat Equation to Long Distance Interactions**

Abstract: The heat equation (an equation that describes how heat propagates along a solid, for instance along a metal rod) was proposed by Fourier in 1807. It describes how temperature evolves in time given the influx of heat from its infinitesimal surrounding. It was soon realized that the pointwise evolution of other modeled systems (speed of a fluid, density and deformation of an elastic body, price of goods, populations) adjusts and reverts to its surrounding revealing a universality property that made it fundamental to science. On the other hand, in many cases, diffusion processes involve long range interactions including population dynamics, pricing and atmospheric events. We will give an overview of the mathematics involved.