Team members

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 „ElipticPDE” (2019-2024) and has received several awards for young mathematicians in Spain, as well as the Scientific Research Award from the Fundación Princesa de Girona in 2019.

His research interests are on Partial Differential Equations (PDE) and he works 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 his 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.

For further information on Xavier’s previous publications and research career, please refer to his personal website.

Marvin Weidner is a postdoctoral researcher in the ERC project “EllipticPDE” at Universitat de Barcelona. Before coming to Barcelona in September 2022, he did his PhD at Bielefeld University (Germany). His research interests lie in partial differential equations with an emphasis on the regularity theory for nonlocal problems.

Juan Carlos Cantero is a postdoctoral researcher in the “EllipticPDE” ERC group. Previously, he finished his PhD at Universitat Autònoma de Barcelona in July 2021 and was a postdoctoral researcher there until August 2023. His main research interests are Partial Differential Equations, and in particular those arising from Fluid Mechanics and Physics.

Clara joined the ERC project “ElipticPDE” in September 2020 to begin her PhD studies under the supervision of Xavier Ros-Oton in the Department of Mathematics of Universitat de Barcelona and will be focusing on free boundary problems for elliptic operators. She had previously collaborated with the group by doing her masters thesis under the supervision of Ros-Oton on the boundary Harnack inequality and the obstacle problem.

Bruno Vergara is a postdoctoral researcher in the ERC team EllipticPDE at the Universitat de Barcelona. Previously, he was a postdoc at University of Zurich, where he joined the ERC team in September 2019, and a PhD student at Universidad Autónoma de Madrid-ICMAT in Madrid. His research interests lie in partial differential equations, with an emphasis on problems in fluid mechanics, dispersive and elliptic equations, geometric analysis and mathematical physics.

Teo comes from Ljubljana, Slovenia, where he did his undergraduate studies in mathematics. In June 2019 he finished his masters degree with a thesis titled “On the absolutely continuous spectrum of generalised indefinite strings” under supervision of prof. dr. Aleksey Kostenko. In the same year he started his PhD under Xavier Ros-Oton’s supervision. His research interests are elliptic and parabolic PDEs, non-local equations, Free boundary problems, regularity theory.

In his free time, Teo likes to play volleyball, ping pong and card games. His favorite one is Bridge, in which he occasionally competes.

Alessandro was a member of the ERC project from September 2019 to August 2020 at Universität Zürich.

He holds a PhD in Pure and Applied Mathematics from Università degli Studi di Torino (Italy) and Universidad Autónoma de Madrid (Spain). He has been previously involved in the ERC project: “Complex Patterns for Strongly Interacting Dynamical Systems – COMPAT” (PI: Prof. Susanna Terracini).

Currently, he has a postodc position at the ETH Zurich, under the MSC IF 2019 No. 892017 (LNLFB-Problems).

Wiktoria holds a M. Sc. and a B. Sc. degree in Mathematics from the University of Bonn, Germany, where she specialized in Partial Differential Equations and Probability Theory. After her studies she spent 1 year as a researcher at the University of Zurich in the group of Xavier Ros-Oton, where she was supported by the ERC Grant Agreement No 801867. Within the area of Partial Differential Equations her focus was on the regularity of free boundaries.

Since 2021 Wiktoria combines her analytical skills and care for a climate resilient future in her work as an energy and sustainability consultant.

Juan Carlos is a PhD student at BGSMath-Universitat Politècnica de Catalunya in Barcelona under the supervision of Prof. Xavier Cabré. He was visiting the ERC team in Zurich for three months in fall 2019. His research is mainly focused on the study of qualitative and regularity properties of solutions to equations driven by integro-differential operators.