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.

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 2017, 'Isoperimetric, Sobolev, and Eigenvalue Inequalities via the Alexandroff-Bakelman-Pucci Method: A Survey', Chinese Annals Of Mathematics Series B, vol. 38, no. 1, pp 201-214.

- Cabre X 2017, 'Boundedness of stable solutions to semilinear elliptic equations: a survey', Advanced Nonlinear Studies, vol. 17, no. 2, pp 355-368.

Selected research activities

  • Editor of the 'Journal of the European Mathematical Society' and of 'Publicacions Matemàtiques'.
  • Adviser of three PhD students and four Postdocs. Director of two 2017 Master Theses.
  • Former Ph.D. student Xavier Ros-Oton (graduated 2014): Premio José Luis Rubio de Francia 2017 (RSME), Premio Antonio Valle 2017 (SEMA), and Premio Vicent Caselles 2015 (RSME).
  • Scientific Committee: Llavefest, A broad perspective on finite and infinite dimensional Dynamical Systems. Barcelona, June 2017.
  • Organizer of the Summer School JISD2017 (CRM, Bellaterra, June 2017) and of a thematic session in the BMD2017 (SCM, IEC Barcelona, April 2017).

Plenary Talks

        11 plenary addresses and 4 colloquia and seminars. Most relevant:

  • 'SIAM Conference on Analysis of Partial Differential Equations'. Baltimore, USA. December 9-12, 2017.
  • 'Nonlocal PDEs. Clay Research Conference'. Oxford, UK. September 25-29, 2017.
  • 'Advanced School & Workshop on Nonlocal Partial Differential Equations and Applications to Geometry, Physics and Probability'. International Centre for Theoretical Physics, Trieste, Italy. May 22-June 2, 2017.