Second Advanced Grant for Xavier Tolsa, a member of the Departament de Matemàtiques.  
26.04.2021
Research

The European Research Council has awarded Xavier Tolsa, ICREA researcher at the Department of Mathematics, an Advanced Grant to fund his project "Geometric Analysis and Potential Theory."
ICREA researcher from the UAB Department of Mathematics Xavier Tolsa was awarded an Advanced Grant for the development of his scientific project Geometric Analysis and Potential Theory (GAPT), which aims to study different mathematical analyses combining harmonic analysis methods, geometric measure theory, and potential theory. Some of these issues deal with harmonic measure, caloric measure, rectifiability, and certain related free border problems. Although in recent years several advances have been made in these fields, there are still many unsolved problems that this project aims to study. Xavier Tolsa received his PhD in Mathematics from the UAB in 1998. After spending a year at the University of Göteborg and another at the Université de ParisSud, in 2001 he became part of the UAB Department of Mathematics under a Ramon y Cajal grant, and in 2003 he became an ICREA researcher and continued on with the UAB. His research focuses on the area of mathematical analysis, and specifically on harmonic analysis, geometric measure theory, potential theory, and other related areas. The results of his research have helped to solve numerous open problems, such as the Painlevé problem for bounded analytical functions (posed at the start of the 20th century), and the demonstration of the semiadditivity of analytical capacity, speculated in the 1960s. In other recent collaboration projects, he has worked on solving the DavidSemmes problem, a twophase problem for harmonic measures, and Carleson's epsylon^2 conjecture. In 2002 he received the prestigious Salem Prize for his work in solving the PainlevéVitushkin problem. In 2004 he was awarded a prize from the European Mathematical Society for his fundamental contributions to harmonic and complex analysis and the Rei Jaume I award in i el Premi Rei Jaume I for basic research 2019. In 2012 he received another ERC Advanced Grant for his project "Geometric analysis in the Euclidean space".






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