The 2023 ICIAM Collatz Prize is awarded to Maria Colombo (EPFL Lausanne, Switzerland) for her fundamental contributions to the regularity theory and the analysis of singularities in elliptic PDEs, geometric variational problems, transport equations, and incompressible fluid dynamics.
Maria Colombo was born in 1989 in Luino, Italy. She received her Bachelor and Master degrees in Mathematics from University of Pisa, and PhD degree from Scuola Normale Superiore of Pisa in 2015. After holding positions at the University of Zurich and ETH Zurich, she joined EPFL Lausanne as an Assistant Professor in 2018, where she is now a Full Professor of Mathematics. Maria Colombo has received several prizes and awards that include the 2022 Peter Lax award, the 2019 Bartolozzi Prize from the Italian Mathematical Union, and the 2015 Michele Cuozzo Prize for her PhD thesis.
Maria Colombo has made substantial contributions to the regularity theory and the analysis of singularities in elliptic PDEs, transport equations, and incompressible fluid dynamics. In particular, she has made significant advances in the understanding of the long-time behavior of solutions to fundamental equations in fluids such as Euler and Navier-Stokes equations. In her joint work with Buckmaster and Vicol, they showed the existence of badly behaved weak solutions of the Navier-Stokes equations which are smooth except for a singular set of times of Hausdorff dimension less than 1. Very recently, her joint work with Albritton and Brue’ constructed for the first time nonunique Leray-Hopf solutions of the forced Navier-Stokes equations. Together with her student Haffter, they also proved that the singular set of Leray-Hopf weak solutions of the supercritical SQG (surface quasi-geostrophic) equation is contained in a compact set in spacetime whose Hausdorff dimension is also estimated. Maria Colombo has several works (with Spolaor, Edelen and Velichkov) on the structure of singularities for solutions to the obstacle problem and minimal surfaces. Their work on the log-epiperimetric inequality in GAFA is a beautiful discovery that has sparked subsequent major developments in the area.
Subcommittee for the 2023 ICIAM Collatz Prize
- Kim-Chuan Toh (National University of Singapore, Singapore), Chair;
- Gregoire Allaire (Ecole Polytechnique, France);
- Ricardo Cortez (Tulane University, USA);
- Hiroshi Suito (Tohoku University, Japan).