UT Math Professor Luis Caffarelli Wins Wolf Prize For Something That Has To Be Explained To Us
The Buenos Aires-born Luis Caffarelli, a math professor at UT, will share this year's Wolf Prize in mathematics with Michael Aschbacher. Caffarelli's work includes "nonlinear analysis, partial differential equations and their applications, calculus of variations and optimization."
Before we jump into all that, let's start with what we do know - the Wolf Awards were founded in 1976, in Israel, and the organization gives out awards not just to mathematicians but also to sculptors, physicists, etc. The prize itself includes 100,000 bucks and a certificate [Note: not actual photographs of said certificate or cash prizes].
Despite being in the awards business for some time, this is only the third Wolf prize that has been awarded to a member of the University of Texas faculty. Previous UT winners were John Tate (mathematics) and Allen Bard (chemistry).
Austinist staffer and Assistant Professor of Mathematics at St. Edward's Dr. Jason Callahan explained the significance of Caffarelli's work:
"Caffarelli studies partial differential equations. Most people first encounter differential equations in calculus after they've learned how to take derivatives of functions of a single variable. Differential equations are simply equations involving the derivatives of an unknown function. To solve differential equations, one must find the function (or functions) whose derivatives make all the equations true (sometimes additional conditions on the unknown function are given so that it can be determined uniquely).
In partial differential equations, the unknown is a function of more than one variable, so the equations involve the partial derivatives of this unknown function with respect to these different variables. Again, to solve partial differential equations, one must find the function (or functions) whose partial derivatives make all the equations true (again, sometimes additional conditions on the unknown function are given so that it can be determined uniquely).
Partial differential equations (PDEs) can be used to describe, model, and solve a variety of real-world phenomena and problems; the PDEs that describe fluid motion (air, water, etc.) are called the Navier-Stokes equations and have been used in the design of aircraft and cars, the study of blood flow, the analysis of pollution, etc. Despite the wide range of practical applications and importance in mathematics, no one has yet proven that solutions to the Navier-Stokes equations always exist in three dimensions (or found a counterexample, i.e., a case in three dimensions where solutions to the Navier-Stokes equations fail to exist). The Clay Math Institute has thus named this as one of the seven Millennium Prize Problems, each of which carries a $1,000,000 prize for a solution or a counterexample. Grigori Perelman recently solved one of these problems (the Poincaré Conjecture) but declined the prize and the money in 2010 (he also declined the Fields Medal for this work in 2006). Caffarelli's work in PDEs could someday lead to an answer to whether solutions always exist to the Navier-Stokes equations in three dimensions (along with the $1,000,000 prize from the Clay Math Institute)."
Thanks to Dr. Callahan for his explanation, and congrats to Dr. Caffarelli.
Filed in News and tagged claymathinstitute, jasoncallahan, mathematics, navierstokes, partialdifferentialequations, wolfprize