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Xavier Ros-Oton

Xavier Ros-Oton

Universitat de Barcelona

Experimental Sciences & Mathematics

Xavier is an ICREA Research Professor at the University of Barcelona since 2020. Previously, he has been Assistant Professor at Universität Zürich, as well as R. H. Bing Instructor at the University of Texas at Austin. He is a mathematician who works on Partial Differential Equations (PDEs). Specifically, he studies the regularity of solutions to elliptic and parabolic PDEs, and he is mostly known for his results on free boundary problems and integro-differential equations. He is the PI of an ERC Starting Grant (2019-2024), has received several awards for young mathematicians in Spain, as well as the Scientific Research Award from the Fundación Princesa de Girona in 2019. Furthermore, in 2021 he was awarded the Stampacchia Gold Medal, an international prize awarded every three years in recognition of outstanding contributions to the Calculus of Variations.

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

– Fernandez-Real X & Ros-Oton X 2021, ‘Free Boundary Regularity for Almost Every Solution to the Signorini Problem’, Archive For Rational Mechanics And Analysis, 240(1): 419–466.

Ros-Oton X 2021, ‘Regularity of Free Boundaries in Obstacle Problems’, Geometric Measure Theory And Free Boundary Problems, 2284, 37 – 88.

Ros-Oton X & Torres-Latorre D 2021, ‘New boundary Harnack inequalities with right hand side’, Journal Of Differential Equations, 288, 204 – 249.

Selected research activities

Stampacchia Gold Medal 2021

(International prize awarded every 3 years in recognition of outstanding contributions to the Calculus of Variations)

– Forbes TOP 50 most Awarded Spaniards

(Forbes Spain made a list with the most awarded people from Spain in the last 5 years. The list includes artists, scientists, chefs, athletes, and CEOs.)

– Évariste Galois Prize 2021 from the SCM for my PhD student Damià Torres

– Several interviews and media coverage with local and national press, as well as 2 general public lectures

– Quanta Magazine has written an outreach article for the general public about our work:

ICREA Memoir 2021