We would like to congratulate the 2023 Abel Prize recipient Luis A. Caffarelli, who has been recognized for his "seminal contributions to regularity theory for nonlinear partial differential equations including free-boundary problems and the Monge–Ampère equation."

Luis Caffarelli has made significant contributions to regularity theory, which characterizes the qualitative features of solutions of nonlinear partial differential equations beyond their original functional analytic set-up. His work has ruled out or characterized singularities and has applications in a variety of areas, including modeling, discretization strategies and numerical simulations. A significant part of Caffarelli's work concerns free-boundary problems, including obstacle problems, which have applications in solid-liquid interfaces, financial mathematics and fluid flow.

Caffarelli's regularity theorems have had a major impact on our understanding of the Monge-Ampère equation and singularities. He has also made significant contributions to homogenization theory. Caffarelli's geometric insight and analytical tools have made him an exceptionally prolific mathematician with an enormous impact on the field, having worked with over 130 collaborators and more than 30 PhD students over 50 years.

Caffarelli will be formally presented with the award at the Abel Prize award ceremony on May 23.

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