The Milliman Lectures

Our 2004-2005 Milliman Lecturer, Professor Luis Caffarelli, is scheduled to visit our department and deliver three lectures during the week of February 7-11, 2005.

Professor Caffarelli holds one of the four Sid W. Richardson Foundation Regents Chairs in the Department of Mathematics at the University of Texas in Austin. He is also affiliated with the Texas Institute for Computational Engineering and Sciences. Professor Caffarelli is a leader in the field of partial differential equations and their applications. He is one of the most original mathematicians working in this area; his deep insights and absolutely unique intuition have transformed the field. His ideas have become the foundation upon which the fields of fully nonlinear partial differential equations and free boundary problems are based.

Luis Caffarelli received his Ph.D. from the University of Buenos Aires in 1972. He came to the States as a Postdoctoral fellow at the University of Minnesota in 1973, where he became a Full Professor in 1979. Over the last 25 years, he has been a Professor at the Courant Institute at NYU, at the University of Chicago, and at the University of Texas in Austin. From 1986 to 1996 he was a permanent faculty at the Institute for Advanced Study in Princeton.

Over the last 30 years his mathematical activity has been centered around two very broad questions: existence and regularity (i.e. the degree of smoothness) of solutions for nonlinear partial differential equations, and free boundary regularity for elliptic and parabolic problems. Among his major contributions to the first question are deep results concerning fluid flows and the introduction and successful implementation of convexity methods, as well as the more recent use of homogenization techniques to study fully nonlinear differential equations. Caffarelli's work in free boundary problems constitutes the foundation upon which the field was built. Free boundary problems arise naturally in physics and engineering: the free boundary may appear as the interface between a fluid and the air, or water and ice. For example, in the filtration problem, which studies how water filtrates from a dam made of a porous medium (say earth), the free boundary separates the wet part from the dry part. Caffarelli often proceeds by modeling physical problems to show that mathematically sound solutions exist, then proving the regularity of such solutions.

As a recognition for his leading role in the field, Caffarelli was elected to the American Academy of Arts and Sciences in 1986 and to the National Academy of Sciences in 1991. Among the many honors and awards he has received are Doctorate Honoris Causa from École Normale Superieure in Paris, from Universidad Autónoma de Madrid and from Universidad de la Plata, Argentina. He received the Stampacchia Prize in 1982, the Bocher Prize in 1984, and the Gold XI Plus Medal in 1988. He was a plenary lecturer at the International Congress of Mathematicians in Beijing, China in 2002. He delivered the Fermi Lectures at the Scuola Normale de Pisa in 1998, and the Morse Lectures at the Institute for Advanced Study. He was also an invited lecturer to the American Mathematical Society Centennial Celebration.

The main characteristics that make Caffarelli such a unique member of the mathematical community are his intuition, his originality, and his generosity both with his time and his ideas. By sharing his ideas in a one-on-one basis with the younger generations, he has planted the seeds of a booming field.

Tatiana Toro