Born in 1966 in Barcelona. PhD in Mathematics (area: Partial Differential Equations), Courant Institute, New York University, 1994. Kurt Friedrichs Prize, New York University, 1995. Member of the Institute for Advanced Study, Princeton, 1994-95. Habilitation à diriger des recherches, Université Pierre et Marie Curie-Paris VI, 1998. Harrington Faculty Fellow, The University of Texas at Austin, 2001-02. Tenure Associate Professor, The University of Texas at Austin, 2002-03. ICREA Research Professor at the Universitat Politècnica de Catalunya, since 2003. Fellow of the American Mathematical Society, inaugural class, 2013. Plenary speaker at the 8th European Congress of Mathematics, 2021. Frontiers of Science Award, first edition, 2023. Academician (membre numerari) of the l'Institut d'Estudis Catalans, 2025. Invited speaker at the International Congress of Mathematicians, 2026.
Research interests
My research field is the mathematical analysis of Partial Differential Equations. These equations arise in mathematical physics, differential geometry, finance, and biology. My focus is on elliptic and parabolic equations, and on the analytical understanding of the regularity, symmetry, and other qualitative properties of their solutions. This often involves the use of geometric tools such as isoperimetric inequalities, whose study is an important part of my research. My main current project concerns a recently flourishing area: reaction problems for fractional diffusions associated to jump or Lévy processes. These are the so called 'anomalous diffusions', well noticed in the last decades in some reaction and biological fronts, as well as in mathematical finance.
Selected publications
- Cabré X, Csató G & Mas A 2025, 'Periodic solutions to integro-differential equations: variational formulation, symmetry, and regularity', Communications in partial differential equations, 50, 162-210.
- Cabré X, Erneta IU & Felipe-Navarro JC 2025, 'Null-Lagrangians and calibrations for general nonlocal functionals and an application to the viscosity theory', Journal of functional analysis, 289 - 9 -111086.
- Cabré X, Cinti E & Serra J 2025, 'Stable solutions to the fractional Allen-Cahn equation in the nonlocal perimeter regime', American journal of mathematics, 147, 957-1024.
Selected research activities
Nominated as Academician (Membre Numerari) of the Institut d'Estudis Catalans, 2025.
Interviewed at the "TV3 Telenotícies", July 27 (2025): "Four Catalan mathematicians present their research at the 2026 International Congress of Mathematics in Philadelphia".
Moderator and chairman of the CosmoCaixa talk "Matemáticas para anticipar el mañana" by Fields medalist Pierre-Louis Lions, April 8, 2025.