Carlos E. Kenig

The University of Chicago


Election Year: 2014
Primary Section: 11, Mathematics
Membership Type: Member

Biosketch

Carlos Kenig is the Louis Block Distinguished Service Professor in the Department of Mathematics at the University of Chicago. Kenig is recognized for his applications of tools and techniques of harmonic analysis to a number of different areas of partial differential equations. In particular, in the last 25 years Kenig has made pioneering contributions to the study of nonlinear dispersive equations, including his recent research on the classification of the long-time behavior of large solutions. Kenig was born in Buenos Aires, Argentina in 1953. He obtained his PhD at the University of Chicago in 1978. After being an instructor at Princeton University and a professor at the University of Minnesota, Kenig returned to the University of Chicago in 1985. Kenig was awarded the Salem Prize in 1984 and the Bocher Prize of the American Mathematical Society in 2008. He was an invited speaker at the International Congress of Mathematicians in 1986 and 2002 and a plenary speaker in 2010. Kenig is a Fellow of the American Academy of Arts and Sciences and of the American Mathematical Society. He is a member of the National Academy of Sciences and a vice-president elect of the American Mathematical Society.

Research Interests

Kenig (with his collaborators, postdocs and students) have been interested in obtaining optimal estimates for solutions of elliptic boundary value problems under minimal regularity assumptions. They have been interested in free boundary problems. For example: how do regularity properties of harmonic measure give geometric information on the boundary? They have been interested in qualitative and quantitative uniqueness properties of solutions of partial differential equations (unique continuation) in connection with mathematical physics, control theory and spectral geometry. They have also been interested in inverse problems. Here one knows the solutions of a partial differential equation on a subset of the boundary, and one seeks to determine the equation. (Such problems arise in geophysical prospection and medical imaging). For the last 25 years, they have been studying non-linear dispersive equations (which model various wave propagation phenomena). The initial emphasis was on the development of a satisfactory well-posedness theory. This was achieved through a systematic use of the methods of modern harmonic analysis. Subsequently interest shifted to the study of the long-time behavior of large solutions. Issues like blow-up, scattering and soliton resolution have come to the forefront and are currently vigorously researched.

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