**Luis Caffarelli** is an Argentine mathematician who has won several major prizes for his work in the field of partial differential equations and their applications.

- After schooling in Buenos Aires, Caffarelli entered the University of Buenos Aires and was awarded his Master of Science degree in 1968.
- He was awarded his doctorate in 1969 from the University of Buenos Aires, only two years before Luis Caffarelli who was his first Ph.D. student.
- In 1971 Caffarelli submitted his thesis Sobre conjugación y sumabilidad de series de Jacobi Ⓣ(On conjugation and summability of Jacobi series) to the University of Buenos Aires and he was awarded a Ph.D. in 1972.
- Caffarelli's paper Surfaces of minimum capacity for a knot was published in 1975 but it was the following years that proved a remarkable one for Caffarelli in terms of publications for in that year six of his papers were published: Certain multiple valued harmonic function; On the Hölder continuity of multiple valued harmonic functions; The regularity of elliptic and parabolic free boundaries; (with Néstor M Rivière) On the rectifiability of domains with finite perimeter; (with Néstor M Rivière) Smoothness and analyticity of free boundaries in variational inequalities; and The smoothness of the free surface in a filtration problem.
- Although Caffarelli continued to hold his professorship at the University of Minnesota until 1983, he spent the two years 1980-82 as a Professor at the Courant Institute.
- In 1982 Caffarelli was awarded the Guido Stampacchia Prize by the Scuola Normale Superiore di Pisa.
- In 1986 Caffarelli left Chicago when he was appointed Professor at the Institute for Advanced Study in Princeton.
- We have quoted several times above from the speech that Caffarelli delivered on that occasion.
- For ten years Caffarelli worked at the Institute for Advanced Study, then in 1994 he returned to the Courant Institute when he spent three years.
- In a series of pioneering papers, Caffarelli put forward a novel methodology which eventually leads, after several truly amazing technical estimates that step by step improve the regularity of the solutions and the boundary, to full regularity under very mild assumptions.
- A second fundamental contribution by Caffarelli is the study of fully nonlinear elliptic partial differential equations (including the famous Monge-Ampère equation), which he revolutionised.
- Another fundamental contribution by Caffarelli is his joint work with Kohn and Nirenberg on partial regularity of solutions of the incompressible Navier-Stokes equation in 3 space dimensions.
- Although the full regularity of solutions is still unknown and likely very hard, Caffarelli-Kohn-Nirenberg showed that the singular set must have parabolic Hausdorff dimension strictly less than one.
- Caffarelli has also produced deep work on homogenisation and on equations with nonlocal dissipation.
- Caffarelli is the world's leading expert on regularity of solutions of partial differential equations.
- Caffarelli has received many honours in addition to those mentioned above.

Born 8 December 1948, Buenos Aires, Argentina.

View full biography at MacTutor

Origin Argentina, Prize Shaw, Prize Wolf

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive