The Catalan researchers Xavier Tolsa (UAB), Xavier Cabré (UPC), Joaquim Ortega (UB) and David Asperó (UEA), and the Valencian Gabriel Navarro (UV) have been invited as speakers at the upcoming International Congress of Mathematicians (ICM), which will take place in Philadelphia (United States) between 23 and the 30 of July of the year 2026. It is an honor for the SCM to have them as members.
The International Congress of Mathematicians, organized by the International Mathematical Union (IMU), is the most prestigious event in the field of mathematics. It is held every four years and brings together thousands of mathematicians from around the world to share the most relevant advances in all areas of the discipline. It is at the ICM that the Fields Medals, are awarded, one of the most important recognitions in mathematics, for researchers under 40 years of age.
The distinction of being a speaker at the ICM is only granted to figures of recognized international prestige. In this edition, 21 people have been invited as plenary speakers, among them Xavier Tolsa, who will give a 60-minute lecture. Among the 20 thematic sections of the congress, which include various 45-minute lectures, we highlight David Asperó in the logic section, Gabriel Navarro in algebra, Joaquim Ortega in analysis, and Xavier Cabré in partial differential equations.
Also invited is Núria Planas (UAB), a member of the executive committee of the IMU education commission, who will participate in a round table on mathematics education.
You can find more information about the congress on the website.
Xavier Tolsa Domènech (UAB, ICREA and CRM) is one of the most prominent analysts in the world, recognized for his fundamental contributions to harmonic analysis, geometric measure theory, and potential theory.
He earned his PhD in mathematics in 1998 at the Autonomous University of Barcelona (UAB), and did postdoctoral stays at the universities of Gothenburg and Paris-Sud. Since 2003, he has been an ICREA research professor at the UAB.
He is especially known for proving in 2002 that analytic capacity is semiadditive, solving an open problem from the 1960s. In collaboration with Nazarov and Volberg, he solved the David–Semmes conjecture on Riesz transforms and rectifiability, which led them to receive the Frontiers of Science Award 2023. In recent years, he has solved several open problems in analysis, such as the famous Carleson epsilon conjecture, the unique continuation at the boundary problem for harmonic functions in Lipschitz domains with small constant, the regularity problem for the Laplace equation in irregular chord-arc domains, and the geometric characterization of corkscrew Ahlfors regular domains for which the Dirichlet problem is solvable in L^p.
He has received several awards for his mathematical contributions, such as the National Research Award Julio Rey Pastor (2024), the King James I Prize (2019), the European Mathematical Society Prize (2004), the Salem Prize (2002), and two ERC Advanced Grants, the second of which funds his current project on geometric analysis and potential theory.
With this exceptional career, it is a source of pride for the Catalan mathematical community that Xavier Tolsa has been invited as a plenary speaker at the International Congress of Mathematicians ICM 2026. In fact, he was already invited in 2006 as a speaker in a thematic section, which is also a great recognition.
Xavier Cabré Vilagut (UPC, ICREA and CRM) is one of the most prominent mathematicians in the field of partial differential equations and mathematical analysis.
PhD in Mathematics in 1994 at the Courant Institute of New York University (NYU), he was a member of the’Institute for Advanced Study in Princeton, and a full professor in Texas. Since 2003, he has been an ICREA research professor at the Polytechnic University of Catalonia (UPC). He has supervised doctoral theses of prominent mathematicians such as Xavier Ros-Oton and Joaquim Serra.
Among his results, we could highlight an improved version of the Alexandroff-Bakelman-Pucci inequality, the extension of the Krylov-Safonov Harnack inequality for diffusion processes on Riemannian manifolds, the proof of the De Giorgi conjecture on phase transitions in dimension 3, a new proof of the classical isoperimetric inequality, gradient estimates for nonlocal minimal graphs, and the proof of Hölder regularity of stable solutions of semilinear elliptic equations up to the optimal dimension 9.
Cabré has been awarded the Frontiers of Science Award 2023, is a Fellow of the American Mathematical Society, and was a plenary speaker at the 8th European Congress of Mathematics in 2021 in Portoroz (Slovenia). He has also been an academic member of the Institute of Catalan Studies (IEC) since 2025, of which the Catalan Society of Mathematics is an affiliated society.
In July of next year, 2026, he will give a lecture in the Partial Differential Equations section of the International Congress of Mathematicians.
Joaquim Ortega Cerdà (UB), is a mathematician specialized in complex analysis and harmonic analysis, internationally recognized for his contributions in areas such as inhomogeneous Cauchy-Riemann equations, Dirichlet series, Bergman kernels, and random point processes.
Ortega has made very notable contributions to the study of spaces of holomorphic functions, especially in the metric/geometric characterization of sampling and interpolation sequences, which led him to solve a problem posed by Duffin and Schaeffer in 1952, about when exponentials form a basis in L² of an interval. He has also developed precise inequalities for functions of an infinite-dimensional polydisc, contributing to the theory of Dirichlet series. One of his most well-known results in this area is the proof that the Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive. More recently, he has made a systematic study of the equidistribution of points on complex manifolds, in both deterministic and random settings. His works on Fekete points and the resolution of the Shub and Smale problem, finding optimal conditions for polynomial roots to be well-distributed and for Newton's method to be efficient, stand out.
David Asperó (UEA, University of East Anglia), is one of the world leaders in Set Theory, especially in forcing, axioms of forcing, large cardinals, and infinite combinatorics. He has developed new sophisticated methods of forcing using systems of models as side conditions and working on various types of axioms of forcing.
Trained at the University of Barcelona, where he earned his PhD in 2000, he is currently an associate professor at the University of East Anglia (UEA).
He is especially known for the Asperó-Schindler theorem, which proves that Martin's maximum implies the Woodin axiom (*), culminating decades of research on strong axioms of forcing and validating the Woodin axiom as a possible fundamental axiom of set theory, solving many questions independent of ZFC, including Cantor's continuum problem. For this work, Asperó and Schindler were awarded the Hausdorff Medal (2022) by the European Set Theory Society, the Best Paper Prize by BIMSA (2023), and the Dov Gabbay Prize (2024).
Previously, together with Larson and Moore, he had already solved the Woodin problem.
David Asperó will give a sectional lecture at ICM 2026 in the area of logic, together with Ralf Schindler.
Gabriel Navarro (UV) is a professor of Mathematics at the University of Valencia and one of the international references in the representation theory of finite groups.
He earned his PhD at the University of Valencia and did a postdoctoral stay in the United States. He has been a visiting researcher at institutions such as MSRI (Berkeley) and the University of Wisconsin–Madison, where he has collaborated and taught on several occasions.
He has made fundamental contributions to the proofs of the McKay conjecture and the Brauer height zero conjecture, which have paved the way to address other deeper conjectures such as Alperin's weight conjecture. He is especially recognized for having formulated a Galoisian version of the McKay conjecture, which has become a central tool in character theory.
Navarro is Fellow of the’American Mathematical Society, a member of the Royal Academy of Exact, Physical and Natural Sciences, and was named the first Distinguished Speaker by the European Mathematical Society. For some years, he has also been a member of the Catalan Society of Mathematics.
He has co-organized international reference meetings in group theory at centers such as Oberwolfach, MSRI, Banff, and Princeton University. He has published more than 200 articles in international journals and is the author of the books Character Theory and the McKay Conjecture i Blocks and Characters of Finite Groups, highly referenced in the field.
In recognition of his career and impact within the representation theory of finite groups, Gabriel Navarro has been invited to give a sectional lecture at ICM 2026 in the algebra section.
The presence of these researchers in such an exclusive global scenario represents a great recognition for the mathematical research carried out in Catalonia, demonstrating the level of’excellence achieved by the mathematics departments of the Universitat Autònoma de Barcelona (UAB), the Universitat Politècnica de Catalunya (UPC) and the Universitat de Barcelona (UB), in conjunction with the Centre de Recerca Matemàtica (CRM), projecting the Catalan mathematical community into a relevant position within international mathematical research.
Until now, only three Catalan mathematicians have given lectures at the International Congress of Mathematicians, all as sectional speakers: Xavier Tolsa in analysis, and David Nualart on applications of mathematics to science, both at the edition held in 2006 in Madrid, and previously Esteban Terradas, who spoke on Mechanics, Mathematical Physics and Astronomy in 1912 in Cambridge.
Thus, in July 2026 Xavier Tolsa he will become the first Catalan researcher to give a plenary lecture at the ICM, and also the only one to have participated as a speaker in more than one edition.
This milestone is also an encouragement for new generations of mathematicians, and an opportunity to make this fundamental discipline visible.