Xavier Tolsa

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At the meeting of the Scientific Commission of the GMF , 2016 (2nd from left)

Xavier Tolsa (* 1966 ) is a Catalan mathematician who deals with analysis.

Tolsa is Professor at the University of Barcelona and at the Institució Catalana de Recerca i Estudis Avançats (ICREA), the Catalan Institute for Advanced Scientific Studies.

Tolsa deals with harmonic analysis (Calderon-Zygmund theory) and complex analysis, geometric measure theory, potential theory. In particular, he dealt with Lars Ahlfors ' concept of analytical capacity , which is an obstruction to the fact that a compact set is "removable" in the complex plane. He solved the problem of AG Vitushkin (1967, Russian Math. Surveys) about the semi-additivity of the analytical capacity. This enabled him to solve Paul Painlevé's even older problem of the geometric characterization of removable sets, which he did with that of Mark MelnikovThe concept of so-called curvature of dimensions introduced in 1995 succeeded. Cauchy transform estimates are important in the proofs.

In 2002 he received the Salem Prize . He was invited speaker at the ICM 2006 in Madrid (Analytic capacity, rectifiability, and the Cauchy integral). In 2004 he received the EMS Prize and was an Invited Lecturer at the ECM 2004 (Painleve's problem, analytic capacity and curvature of measures). In 2013 he received the Ferran-Sunyer-i-Balaguer-Preis for his monograph Analytic capacity, the Cauchy Transform, and non-homogeneous Calderón-Zygmund theory , which is to be published by Birkhäuser Verlag.

Fonts

  • Principal values ​​of the Cauchy Integral and rectifiability. Proc. AMS, Vol. 128, 2000, p. 2111
  • Painleve's problem and semi-additivity of analytic capacity. Acta Mathematica, Vol. 190, 2003, pp. 105-149

Web links

Individual evidence

  1. ↑ A compact set E in the complex plane is called removable, if for every open set U that contains E, which in the complement of E in U analytic bounded functions can be analytically continued to all U. E is removable if and only if the analytical capacity vanishes.
  2. ↑ In the 1950s and 1960s he recognized the importance of analytical capacity for problems of rational approximation
  3. ^ "Premi Salem" (PDF; 775 kB), Societat Catalana de Matemàtiques Notícies , July 2002, n ° 17, page 9
personal data
SURNAME Tolsa, Xavier
BRIEF DESCRIPTION Spanish mathematician
DATE OF BIRTH 1966