**Department of Mathematics**

**2014-2015 Distinguished Lecture Series**

**Presents**

Professor Luis Caffarelli

Professor of Mathematics

University of Texas at Austin

**Public Lecture**

Diffusion Processes and Phase Transitions

Tuesday, May 19, 2015

2:00-3:00pm

Natural Sciences II, Room 2201

Reception to Follow in Rowland Hall 408

Abstract

I shall introduce local and integral diffusion processes, free boundary problems with and without memory, and discuss applications to American options and economics.

**Mathematics Colloquium**

The Porous Media Equation

Thursday, May 21, 2015

2:00-3:00pm

Natural Sciences II, Room 1201

Reception to Follow

Abstract

I shall briefly describe the theory from the 1980's for the porous media equation, then discuss a joint work with Vazquez about the case where the pressure is a potential of the density and versions with memory effects.

**About Professor Caffarelli**

Professor Luis Caffarelli is the Sid Richardson Chair at the University of Texas at Austin. He did pioneering work on regularity theory for free boundaries, fully nonlinear elliptic equations including the celebrated Monge-Ampere equation, partial regularity of weak solutions of the Navier-Stokes equation, homogenization, and more recently integral differential equations.

Among the honors he received are: Bôcher Memorial Prize of the American Mathematical Society (1984), Member of the National Academy of Sciences (1991), Diamond Konex Award of Konex Foundation from Argentina (2003), Rolf Schock Prize of the Royal Swedish Academy of Sciences (2005), Leroy P. Steele Prize for Lifetime Achievement in Mathematics (2009), and Wolf Prize in Mathematics (2012).