### Wednesday, January 7, 2009

## Math prizes add up

The Steele Prize is actually three awards. Caffarelli’s was for lifetime achievement, the award that John Tate, a math professor, won in 1995. The university’s Karen Uhlenbeck received the prize for seminal research contribution in 2007.

The other Steele Prize is for mathematical exposition. If someone at the university wins it, the Math Department could declare a Steel Prize hat trick.

Caffarelli’s award was announced barely a month after colleagues gathered in Austin to mark his 60th birthday with a symposium, “Future Directions in Nonlinear Partial Differential Equations: A meeting in honor of Luis A. Caffarelli on the occasion of his 60th birthday.”

And, the Steele Prize comes four years after Caffarelli won the Rolf Schock Prize, another major math award.

As one can tell from the name of Caffarelli’s field of math, which features the words nonlinear, partial and differential, it is difficult.

Here is how the AMS booklet with information about the 2009 award winners puts it: “This is a difficult field: there are rarely exact formulas for solutions of nonlinear PDEs, and rarely will exact algebraic calculations yield useful expressions.”

It goes on to say that, “Luis Caffarelli’s vast work totally dominates this field, starting with his early papers on the obstacle problem. In estimate after estimate, lemma after lemma, he shows that the generalized solution and the free boundary have a bit more regularity than is obvious, then a bit more, and then more; until finally he proves under a mild geometric condition that the solution is smooth and the free boundary is a smooth hypersurface. The arguments are intricate, but completely elementary.”

Uhlenbeck’s Steele Prize was for her foundational contributions in analytic aspects of mathematical gauge theory. According to the AMS, the theorems she developed and the techniques she introduced to prove them “are the analytic foundation underlying the many applications of gauge theory to geometry and topology.”Tate was cited for scientific accomplishments that “span four and a half decades. He has been deeply influential in many of the important developments in algebra, algebraic geometry, and number theory

during this time.”