Xavier Ros Oton

Xavier Ros Oton

Universitat de Barcelona

Experimental Sciences & Mathematics

Xavier is an ICREA Research Professor since 2020. He is a mathematician who works on PDE. He has been the PI of an ERC Starting Grant (2019-2024) and an ERC Consolidator Grant (2024-2029), and has received several awards for young mathematicians in Spain, including the 'Premio Nacional de Investigación' for researchers under 40 in Mathematics and Computer Science. He also received the Scientific Research Award from the Fundación Princesa de Girona, as well as the Stampacchia Gold Medal, an international prize awarded every three years in recognition of outstanding contributions to the Calculus of Variations. In 2022, he was elected member of the Spanish Royal Academy of Sciences.

Research interests

My research interests are on Partial Differential Equations (PDE), a vast and very active field of research in both pure and applied mathematics. PDE are used in essentially all sciences and engineering, and have important connections with several branches of pure mathematics. I work mainly on topics related to the regularity of solutions to nonlinear elliptic/parabolic PDE. This is one of the most basic and important question in PDE theory: to understand whether all solutions to a given PDE are smooth or if, instead, they may have singularities. Some of my main contributions have been in the context of free boundary problems. These are PDE problems that involve unknown/moving interfaces, such as ice melting to water (phase transitions). From the mathematical point of view, they give rise to extremely challenging questions, and their study is closely connected to geometric measure theory. In particular, the study of free boundary problems has a strong geometrical flavor.

Selected publications

– Figalli A, Ros-Oton X & Serra J 2024, ‘The singular set in the Stefan problem‘, Journal Of The American Mathematical Society,  37 (2024), 305-389.
– Ros-Oton X & Torres-Latorre C 2024, ‘Optimal regularity for supercritical parabolic obstacle problems‘, Communications On Pure And Applied Mathematics, 77, 1724-1765

Jin TL, Ros-Oton X, Xiong JA 2024, ‘– Optimal regularity and fine asymptotics for the porous medium equation in bounded domains‘, Journal fur die reine und angewandte mathematik, 2024 – 809 – 269 – 300 – .

– Fernández-Real X & Ros-Oton X 2024, ‘Stable cones in the thin one-phase problem‘, American journal of mathematics, 146 – 3.
– Albalate D, Bel G, Mazaira-Font FA & Ros-Oton X 2024, ‘Paying for protection: bilateral trade with an alliance leader and defense spending of minor partners‘, Journal of economic behavior & organization, 223 – 234 – 247.
– Fernandez-Real X & Ros-Oton X 2024, ‘Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels‘, Proceedings of the london mathematical society, 129 – 3 – e12629.

Selected research activities

-PI of an ERC Consolidator Grant (2024-2029)
-PI of an ERC Starting Grant (2019-2024)
-Editor for Rev. Mat. Iberoam.
-Editor for Disc. Cont. Dyn. Syst. A
-Editor for Collect. Math.
-Plenary talk at the 14th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Abu Dhabi 2024)
-Invited speaker at the 13th Oxbridge PDE Conference (University of Oxford 2024)
-Colloquium at ICFO 2024
-Academic Committee member to design the new Bachelor Degree in Mathematics at UB, 2024.
-Evaluator for the Ramón y Cajal program, April 2024.