#### 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

*Communications On Pure And Applied Mathematics*, Volume77, Issue3

- Audrito A, Felipe-Navarro JC & **Ros-Oton X** 2023, 'The Neumann problem for the fractional Laplacian: regularity up to the boundary', *Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze*, 24, 2, 1155 - 1222.

**Ros-Oton X**& Serra J 2023, 'The singular set in the Stefan problem',

*Journal Of The American Mathematical Society*, .

#### Selected research activities

- ERC Consolidator Grant, 2024 - 2029
- Premio Nacional de Investigación para Jóvenes en Matemáticas y Tecnologías de la Información y las Comunicaciones 2023
- Frontiers of Science Awards 2023
- Ferran Sunyer i Balaguer Prize 2023 for the book ``Integro-Differential Elliptic Equations''