Xavier Tolsa

Full professor at UAB
Research area: Analysis / Partial Differential Equations

PhD in Mathematics obtained at UAB


I was born in Barcelona in 1966. First I studied engineering, but later I turned to mathematics. After obtaining my PhD in mathematics in 1998 (UAB), I spent about one year in Goteborg (University of Goteborg – Chalmers) and another year in Paris (Université de Paris-Sud), until I came back to Barcelona (UAB) by means of a “Ramón y Cajal” position. Since 2003 I am an ICREA Research Professor. My current research in mathematics focuses in Fourier analysis, geometric measure theory, and geometric function theory. 

My main scientific achievements are the proof of the semiadditivity of analytic capacity and contribution to the Painlevé problem (2003), and the solution of the David Semmes problem in codimension 1, with F. Nazarov and A. Volberg (2014).

Current and previous  positions
Assistant professor, Universitat de Barcelona – (1994-1999)
Post-doctoral Research. Chalmers University of Technology (1999 – 2000)
Post-doctoral Research. Université Paris-Sud 11 (2000 – 2001)
Ramón y Cajal, Universitat Autònoma de Barcelona – (2001-2003)
ICREA Research Professor, Universitat Autònoma de Barcelona – Matemàtiques (2003 – present)

Salem Prize (2002)
Prize of the European Mathematical Society (2004)
ERC Advanced Grant (2013-2018), to develop the project ”Geometric Analysis in the Euclidean Space”
Ferran Sunyer i Balaguer Prize 2013, for the monograph “Analytic capacity, the Cauchy transform, and non-homogneous Carderón-Zigmund theory” (2013)
Member of the Editorial Board of the “Journal of the European Mathematical Society”. (2014)


Research lines

  • Harmonic analysis
  • Geometric measure theory
  • Harmonic measure
  • Quasiconformal mappings

Selected publications

  • F. Nazarov, X. Tolsa and A. Volberg, ‘On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1’, ActaMathematica, Vol. 213(2) (2014) 237-321
  • X. Tolsa, Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory, Birkhäuser, 2014
  • A. Mas and X. Tolsa, ‘Variation for Riesz transforms and uniform rectifiability’, Journal of the European Mathematical Society, 16(11) (2014), 2267-2321.
  • X. Tolsa, ‘Mass transport and uniform rectifiability’, Geom. Funct. Anal. , 22 (2) (2012), 478-527.
  • X. Tolsa, ‘Bilipschitz maps, analytic capacity, and the Cauchy integral’, Annals of Mathematics, 162 (3) (2005), 1241-1302.
  • X. Tolsa, ‘Painlevé’s problem and the semiadditivity of analytic capacity’, ActaMathematica, Vol. 190(1) (2003),105-149