University of Chicago mathematician Carlos Kenig has been named a co-recipient of the 2008 Maxime Bocher Memorial Prize from the American Mathematical Society for his work in the field of analysis. The AMS awarded the prize to Kenig at the Joint Mathematics Meetings in San Diego, Calif., on Jan. 7.
Analysis is a major branch of mathematics that includes calculus and other techniques often applied to scientific problems. The AMS cited Kenig specifically "for his important contributions to harmonic analysis, partial differential equations, and in particular to nonlinear dispersive partial differential equations."
An outgrowth of the research of Joseph Fourier nearly two centuries ago, harmonic analysis can be applied to the study of heat, light and other phenomena involving wave motion. Kenig principally studies partial differential equations and one of their subclasses--nonlinear dispersive equations--which describe various aspects of such phenomena.
The difficulty and beauty of harmonic analysis attracted Kenig to the field. "There were a lot of issues that were not understood," said Kenig, the Louis Block Distinguished Service Professor in Mathematics and the College. When Kenig began working with dispersive equations approximately 20 years ago, he suspected that the field could benefit from the application of sophisticated mathematical techniques from harmonic analysis.
"I found that using techniques from harmonic analysis could get a lot of results that were not conceivable before," Kenig said. "This opened up the field. This approach was successful beyond my wildest dreams."
The interest of mathematicians in the field has grown along with the advances. "When we got started in this area it was rather small, but it has attracted the attention of many, many researchers. I would say from a few dozens to literally hundreds now in the theoretical aspects," Kenig said.
The field has now enjoyed two good cycles of generating good ideas and then reaping their benefits. But many challenges remain. "The more we discover, the more difficult things become," Kenig said. "Now we're entering a really challenging period in the field."
The AMS awards the Bocher Prize every three years. Previous recipients include the late Albert Calderón in 1979 and Frank Merle of France's University of Cergy-Pontoise in 2005. Kenig obtained his Ph.D. in 1978 under the direction of Calderón, the University of Chicago's University Professor Emeritus in Mathematics. Merle co-authored one of three papers with Kenig that are singled out for praise in the latter's Bocher Prize citation.
Co-authoring another of those papers with Kenig were Gustavo Ponce, Professor of Mathematics at the University of California, Santa Barbara, and Luis Vega, a member of the mathematics faculty at the University of the Basque Country in Spain. The third paper was co-authored with Alex Ionescu, Associate Professor of Mathematics at the University of Wisconsin, Madison.
"To be Carlos' collaborator of one of three cited papers for his prize is kind of like having a wink from Mr. Bocher himself," Merle said, referring to Maxime Bocher, who served as AMS president in 1909-10.
Merle characterized Kenig's Bocher Prize as "great news for the field of dispersive equations." He further praised Kenig for his ability "to recognize important breakthroughs very early and to suggest potentially highly promising directions of research" in mathematics. But as a collaborator and friend, Merle also said he valued Kenig's "great human qualities."