Xavier Tolsa | |
|---|---|
 Tolsa atOberwolfach in 2015 | |
| Born | 1966 (age 59–60) |
| Occupation | Mathematician |
| Awards | Salem Prize (2002) EMS Prize (2004) Ferran Sunyer i Balaguer Prize (2013) Rey Jaime I Award (2019) |
Xavier Tolsa (born 1966) is aCatalan mathematician, specializing in analysis.
Tolsa is a professor at theAutonomous University of Barcelona and at theInstitució Catalana de Recerca i Estudis Avançats (ICREA), the Catalan Institute for Advanced Scientific Studies.
Tolsa does research onharmonic analysis (Calderón-Zygmund theory),complex analysis,geometric measure theory, andpotential theory. Specifically, he is known for his research onanalytic capacity andremovable sets. He solved the problem ofA. G. Vitushkin[1][2] about the semi-additivity of analytic capacity. This enabled him to solve an even older problem ofPaul Painlevé on the geometric characterization of removable sets. Tolsa succeeded in solving the Painlevé problem by using the concept of so-called curvatures of measures introduced byMark Melnikov in 1995. Tolsa's proof involves estimates of Cauchy transforms. He has also done research on the so-calledDavid-Semmes problem involvingRiesz transforms and rectifiability.[3]
In 2002 he was awarded theSalem Prize.[4] In 2006 in Madrid he was an Invited Speaker at theICM with talkAnalytic capacity, rectifiability, and the Cauchy integral. He received in 2004 theEMS Prize[5] and was an Invited Lecturer at the 2004ECM with talkPainlevé's problem, analytic capacity and curvature of measures. In 2013 he received theFerran Sunyer i Balaguer Prize for his monographAnalytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory (Birkhäuser Verlag, 2013}.[6] In 2019 he received theRei Jaume I prize for his contributions to Mathematics.
