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Luis Caffarelli obtained his Ph.D. at the University of Buenos Aires. His Ph.D. advisor was Calixto Calderón. He currently holds the Sid Richardson Chair at the University of Texas at Austin. He also has been a professor at the University of Minnesota, the University of Chicago, and the Courant Institute of Mathematical Sciences at New York University. From 1986 to 1996 he was a professor at the Institute for Advanced Study in Princeton. 


In 1991 he was elected to the National Academy of Sciences. He has been awarded Doctor Honoris Causa from l'École Normale Supérieure, Paris; University of Notre Dame; Universidad Autónoma de Madrid, and Universidad de La Plata, Argentina. He received the Bôcher Memorial Prize in 1984. Caffarelli is listed as an ISI highly cited researcher. 


He has been considered one of the world leading experts in free boundary problems and nonlinear partial differential equations. He has developed relevant contributions to the study of the regularity of the Navier-Stokes equations, quasi-geostrophic fluids, the theory of homogenization, the optimal transport theory, as well as to the field of fractional diffusion of Lévy type. 


In 2003 Konex Foundation from Argentina granted him the Diamond Konex Award, one of the most prestigious awards in Argentina, as the most important Scientist of his country in the last decade. In 2005, he received the prestigious Rolf Schock Prize of the Royal Swedish Academy of Sciences "for his important contributions to the theory of nonlinear partial differential equations". He also received the Leroy P. Steele Prize for Lifetime Achievement in Mathematics in 2009. In 2012 he was awarded the Wolf Prize in Mathematics. He is and has been a member of editorial committees of many prestigious journals.