Tolsa is a professor at the Autonomous University of Barcelona and at the Institució Catalana de Recerca i Estudis Avançats (ICREA), the Catalan Institute for Advanced Scientific Studies.
This enabled him to solve an even older problem of Paul 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 by Mark Melnikov in 1995.
He received in 2004 the EMS Prize[5] and was an Invited Lecturer at the 2004 ECM with talk Painlevé's problem, analytic capacity and curvature of measures.
In 2013 he received the Ferran Sunyer i Balaguer Prize for his monograph Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory (Birkhäuser Verlag, 2013}.