I was born in Buenos Aires to Luis and Hilda Caffarelli. I have two sisters, Maria Luisa and Alicia, plus a large family of aunts, uncles and cousins, who have all shared good and bad times and remain a very tightly-knit group. Among my most cherished teenage memories is working at the Buenos Aires shipyards in summertime, side by side with my father, while the sun rose over Rio de La Plata.
I am happily married to Irene Martinez Gamba, also a mathematician, and we have three wonderful sons, Alejandro, Nicolas, and Mauro.
I started mathematical studies at the Universidad de Buenos Aires in 1966. Luis Santalo, Manuel Balanzat and Carlos Segovia taught me how to see and think mathematics and gave me support, advice and encouragement. Calixto Calderon became my mentor and, with his help and guidance I completed my PhD thesis by 1972.
Funded by CONICET-Argentina, I left for Minnesota to work with Eugene Fabes and Calixto. From the hot Buenos Aires summer to the Minnesota winter was a dramatic change, but with the generous help of Fabes and Walter Littman I got to love Minneapolis.
Hans Lewy visited a year after my arrival and gave a beautiful course on Potential theory. He also suggested I take a look at his recent work with Stampacchia on the obstacle problem.
The mathematics of numerical simulations was developing and this problem was at the core of variational inequalities modeling in continuum mechanics: the minimization of energy within given convex constraints of staying above the obstacle. I was able to show regularity and stability properties of the solution and transition surface under rather general conditions. The obstacle problem resurfaced in the modeling of porous media flows, game theory, optimal insulations, semi-permeable membranes, involving local and integral diffusion processes. I made several significant contributions, and this problem remains today a source of challenge in diverse areas of mathematics.
At the time, I made several contributions on free boundary problems also related to flows cavitating past an obstacle, opening a new venue to solve challenging fundamental problems in science and engineering concerning fluid solid interactions, flame propagation, optimal insulation and species segregation and phase transition problems that are sources of fundamental areas of beautiful mathematics.
I moved to Courant Institute at NYU, the heart of analysis and applied mathematics, in 1980. It was an exceptional time in my career. With Robert Kohn and Louis Nirenberg, we proved that solutions to Navier Stokes equations for incompressible fluids, sets of singular points couldn’t even be a curve in space-time. I also developed, in collaboration with Nirenberg and Joel Spruck, an extensive theory of existence and regularity for fully nonlinear equations, symmetric functions of the Hessian and the Monge Ampere equation. This beautiful model is a challenging subject due to its geometry and “fragility”, and its role in optimal transportation.
Soon after, in my mid-thirties, Felix Browder invited me to join the University of Chicago faculty. Felix enormously endorsed me then and through the years. I am greatly indebted to him.
Throughout that period, I met some of the best young mathematicians abroad, and between math and family we created a wonderful circle of lasting friendships.
In 1986 we moved to the Institute for Advanced Study at Princeton. I worked on weak regularity theory for the Monge Ampere Equation, optimal transportation, and parabolic phase transition. Yet, I missed having graduate students. Two years after Irene was awarded an NSF fellowship to work with Cathleen Morawetz at Courant, we both joined their faculty in 1994, beginning my second stay at NYU. It proved to be a great time for further advancement.
In 1997, UT Austin offered us an exciting opportunity to contribute to the expansion of graduate programmes in non-linear analysis and computational applied mathematics, bringing together science and engineering through the Institute of Computational Engineering and Sciences where Irene and I became Core Faculty. Many ideas surged in this new setting: modeling for fractional diffusion, stochastics, phase transitions, fully nonlinear models.
Our scientific family of students, postdocs, collaborators and colleagues kept on growing and blooming. Thanksgiving celebrations at our home and picnics at the Oden Ranch remain highlights that have bonded many of us together. Our scientific and personal lives intertwined in a mesh of common objectives and mutual support. We visited Buenos Aires and Mar del Plata, our hometowns, developing further mentoring and collaborations.
The Shaw Foundation recognition is a merit that extends to those who have participated in our passion for the advancement of mathematics. Also, it is to be shared with our children, who have grown up to become a lawyer, a molecular scientist and a medical doctor, brought Elise, Camille and Camila into our family, and given us our grandchildren Isabella and Luca.
I am deeply indebted to my wife Irene for her unwavering love and support in our life’s journey.
26 September 2018 Hong Kong