Xavier Cabré

Xavier Cabré

Universitat Politècnica de Catalunya

Experimental Sciences & Mathematics

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, 2020.

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

- Cabre X, Ros-Oton X, Figalli A & Serra J 2020, 'Stable solutions to semilinear elliptic equations are smooth up to dimension 9', Acta Mathematica, 224, 2, 187 - 252.

- Cabre X, Cinti E & Serra J 2020, 'Stable s-minimal cones in R-3 are flat for s similar to 1', Journal Fur Die Reine Und Angewandte Mathematik, 764, 157 - 180.

- Cabre X 2020, 'Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory', Annali Di Matematica Pura Ed Applicata (4), 199, no. 5, 1979-1995.

Selected research activities

Editor of ‘Calculus of Variations and Partial Differential Equations’ and of ‘Publicacions Matemàtiques’.

Plenary speaker at the 2020 Fields Medal Symposium. Online, The Fields Institute (Toronto).

Former Ph.D. student Joaquim Serra (graduated 2014): holder of a 2020 EMS Prize (European Math Society) and PI of an ERC Starting Grant.