He learnt the obstacle problem from scratch after a lecture series, and went on to prove how smooth free boundaries are, then how regular solutions of the Monge–Ampère equation are. The second of those is the regularity theory that optimal transport leans on.
He was born in Buenos Aires in 1948 and studied mathematics there. His 1972 doctorate, under Calixto Calderón, was on polynomials: Sobre conjugación y sumabilidad de series de Jacobi. The next year he went to the University of Minnesota as a postdoctoral fellow, where Calderón had taken a permanent post.
At Minnesota the direction changed. He attended a lecture series on harmonic analysis by Hans Lewy, asked Lewy for problems, and was given the obstacle problem: how an elastic membrane rests on a given obstacle. He had to learn the subject from nothing and, in the biography's phrase, was hooked. The region where the membrane touches the obstacle has a boundary that is not given in advance — a free boundary — and the question is how regular it is. He published six papers in 1976, and in 1977 his first paper in Acta Mathematica, The regularity of free boundaries in higher dimensions.
| Year | Where | What |
|---|---|---|
| 1972 | Buenos Aires | PhD, Calderón |
| 1973 | Minnesota | postdoctoral position; Lewy's lectures, the obstacle problem |
| 1977 | Acta Mathematica | regularity of free boundaries in higher dimensions |
| 1980 | Courant Institute, NYU | moves; later the Chinatown walk with Kohn and Nirenberg |
| 1982 | — | Navier–Stokes paper with Kohn and Nirenberg; Stampacchia Prize |
| 1983–86 | Chicago | professor; speaker at the Warsaw ICM in 1983; Bôcher Prize 1984 |
| 1986–94 | Institute for Advanced Study | Monge–Ampère regularity (the biography says “a decade”) |
| 1994 | Courant Institute | returns, missing graduate students |
| 1997– | Texas at Austin | Sid Richardson Chair; homogenization |
On a walk in Chinatown, after the move to the Courant Institute, he, Robert Kohn and Louis Nirenberg decided to write together about the Navier–Stokes equations. The result, Partial regularity of suitable weak solutions of the Navier–Stokes equations (1982), won the American Mathematical Society's 2014 Steele Prize for Seminal Contribution to Research. Nirenberg, asked about him, is quoted as saying he had a hard time keeping up and that Caffarelli “immediately sees things that other people don't see.”
In the Institute years a major focus was the Monge–Ampère equation, and what is now called Caffarelli's regularity theory comes from that work. The biography says it has important applications elsewhere, optimal transportation among them. ch-optimal-transport is the companion chapter: what the transport problem is, why it becomes a Monge–Ampère equation, and checks of the pieces that can be checked on a computer.
He has published 320 papers and, at 74, still publishes several a year. He has co-written with more than 130 people, most often with Avner Friedman; his papers have about 19,000 citations (the biography's source: MathSciNet); and he has advised more than thirty PhD students, among them Alessio Figalli, who won the Fields Medal in 2018.
| Year | Honour |
|---|---|
| 1982 | Guido Stampacchia Prize |
| 1984 | Bôcher Prize |
| 1991 | National Academy of Sciences, US |
| 2005 | Rolf Schock Prize |
| 2009 | AMS Steele Prize for Lifetime Achievement |
| 2012 | Wolf Prize |
| 2013 | Solomon Lefschetz Medal |
| 2014 | AMS Steele Prize for Seminal Contribution (the 1982 paper) |
| 2018 | Shaw Prize |
He is married to the mathematician Irene Martínez Gamba, who holds the W. A. Tex Moncrief, Jr. Chair in Computational Engineering and Sciences at Texas; they have three sons. The Abel Prize 2023 also went to him, but that is not in the biography this page was checked against: the biography gives his age as 74, so it predates the prize, and the prize is here from search results only, whose titles but not full text were seen.
It does not assess any of the theorems. The biography is a short popular piece; the page repeats its dates and names and no more, and the verify script checks that they are in the source and consistent with each other, not that the source is right. Two soft spots are worth naming. The biography says he spent “a decade” at the Institute for Advanced Study, yet its own dates (1986 to 1994) give eight years. And the age, 74, fixes the biography at 2022 or the start of 2023, so every present-tense claim in it is as of then.
Luis A. Caffarelli: a biography (short English biography, supplied as a PDF;
photo credit there to Nolan Zunk, University of Texas at Austin; its own source for the
paper and citation counts is MathSciNet). · Abel Prize 2023: search-result titles
only, not read. · Checks: book7/ch-caffarelli-verify.py.
This chapter makes no claim about his present circumstances.