Xavier Cabré

Universitat Politècnica de Catalunya (UPC)

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. Editor of the 'Journal of the European Mathematical Society'.

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, Sanchon M & Spruck J 2016, ‘A priori estimates for semistable solutions of semilinear elliptic equations’, Discrete And Continuous Dynamical Systems, 36, 2, 601 – 609.

Cabre X & Serra J 2016, ‘An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions’, Nonlinear Analysis-theory Methods & Applications, 137, 246 – 265.

Cabre X, Ros-Oton X & Serra J 2016, ‘Sharp isoperimetric inequalities via the ABP method’, Journal of the European Mathematical Society, 18, no. 12, 2971 – 2998.

– Sormani C & Cabre X 2016, ‘Recent applications of Nirenberg’s classical ideas’, Notices of the American Mathematical Society, 63, no. 2, 126 – 128.

Selected research activities

Plenary Talks:

– ‘A Mathematical Tribute to Ennio De Giorgi’. Centro De Giorgi, Pisa, Italy. September 19-23, 2016

– ‘Calculus of Variations and Nonlinear Partial Differential Equations’. Columbia University, USA. May 23-27, 2016

Editorial Boards:

– Editor of the ‘Journal of the European Mathematical Society’ and of ‘Publicacions Matemàtiques’