Bilbao Celebrates Forty Years of Analysis and Partial Differential Equations

From 31 August to 4 September, Bilbao hosted the international congress 40 Years of Analysis and PDE in Bilbao, organised by the University of the Basque Country (UPV/EHU) and the Basque Center for Applied Mathematics (BCAM). The gathering marked four decades of activity by the Analysis and Partial Differential Equations seminar, which has played a central role in establishing this field of research in the Basque Country.

The sessions, held mainly at the Iberdrola Tower and Bizkaia Aretoa, brought together specialists from leading international institutions. The programme covered recent advances in harmonic analysis, dispersive equations, kinetic theory and nonlinear equations, among other areas.

One of the highlights was the participation of two of the four winners of the 2026 Fields Medal. Yu Deng, a professor at the University of Chicago, took part in the congress in person. His work has established rigorous connections between the microscopic dynamics of particles and the macroscopic equations that describe fluids and gases, making a decisive contribution to Hilbert's sixth problem. Hong Wang, a professor at the Courant Institute of New York University and at IHES, took part online. Among other fundamental contributions to harmonic analysis, the medal recognises her work with Joshua Zahl on the three-dimensional Kakeya conjecture.

The scientific programme also featured figures such as Pierre-Louis Lions, a Fields Medallist in 1994, John Ball, Marie Doumic, Eugenia Malinnikova, Gigliola Staffilani, Xavier Tolsa and Juan J. L. Velázquez, among other leading researchers.

As one of the congress's public engagement events, Javier Gómez-Serrano, a professor at Brown University, gave a talk entitled Modern Mathematics in the Age of Artificial Intelligence at the Guggenheim Museum Bilbao auditorium on 2 September. The talk, chaired by Juan Ignacio Pérez Iglesias, the Basque Government's Minister for Science, Universities and Innovation, gave the audience insight into the profound changes that artificial intelligence, scientific computing and computer-assisted proofs are bringing to mathematical research.

The congress thus celebrated the legacy of a mathematical community firmly rooted in Bilbao, while at the same time opening a window onto some of the most promising directions in contemporary mathematics.