Two of the latest 2026 fields medallists are coming to Bilbao in September

• The Fields Medal is one of the most prestigious awards in mathematics, presented every four years by the International Mathematical Union to mathematicians under the age of 40 for their most influential contributions.
• Hong Wang (Courant Institute, New York University, IHES), along with her colleague Joshua Zahl, solved the Kakeya conjecture in three dimensions—a question that had remained open since 1917.
• Yu Deng (University of Chicago) bridged the gap between the worlds of particles and fluids, making key contributions to one of the open problems on Hilbert's 1900 list of problems.
• The two award winners will attend the international conference celebrating 40 years of the Analysis and Partial Differential Equations group, taking place at Torre Iberdrola and the Guggenheim Museum from 31 August to 4 September.

It is uncommon for a city like Bilbao to host, at a single event, two of the world's leading mathematicians fresh from winning the most exclusive honour in their field. Yet that is precisely what will happen in September. Hong Wang and Yu Deng, two of the four 2026 Fields Medallists, will feature as speakers at the conference 40 Years of Analysis and PDEs in Bilbao, organised by BCAM and UPV/EHU from 31 August to 4 September.

Hong Wang, a professor at the Courant Institute at New York University and the Institut des Hautes Études Scientifiques (IHES) in France, is a past recipient of the Maryam Mirzakhani New Frontiers Prize (2022) and the Salem Prize (2025), among others. Wang, who has made fundamental contributions to harmonic analysis and partial differential equations, was awarded the medal for proving the Kakeya conjecture in three dimensions, an open problem since 1917. The initial question sounds almost innocent: what is the minimum area required to rotate a needle through all possible orientations? Answering it with mathematical rigour in three dimensions required decades of progress in geometric measure theory and harmonic analysis, and the problem remains open in higher dimensions. Her Courant Institute colleague Eyal Lubetzky described the result as "one of the greatest mathematical achievements of the 21st century". In an interview given to El País, Wang acknowledged that she learned about the restriction conjecture—which is closely linked to the Kakeya problem—through studying works by the Spanish mathematician Luis Vega, currently a professor at the University of the Basque Country (EHU) and former scientific director of BCAM.

Yu Deng, professor of mathematics at the University of Chicago, has been awarded for his work on the rigorous derivation of the Boltzmann equation from Newton's laws of particle motion, thereby resolving the fluid mechanics component of Hilbert's Sixth Problem, an open question since 1900. In short, his team built for the first time the rigorous mathematical bridge between microscopic particle physics and the equations describing fluids and gases on a macroscopic scale—a challenge that had resisted 125 years of attempts. The results of his research have been published in the field's most prestigious journals, notably a recent contribution to Annals of Mathematics, co-authored with Zaher Hani and Xiao Ma. His recent accolades include the Oberwolfach Prize 2025, the MCA Prize 2025, the ICCM Gold Medal 2025, and the 2026 Eisenbud Prize from the American Mathematical Society (shared with Zaher Hani).

That both will be in Bilbao in September is no coincidence. Four decades ago, a group of mathematicians from the Basque Country who began meeting regularly to discuss the most demanding problems in analysis could hardly have imagined that their seminar would still be active 40 years later, and that, in 2026, it would give rise to an international conference. It is a celebration of all these years of high-level Basque mathematics, and the consolidation of a mathematical community with global significance.

The programme brings together sixteen international specialists from institutions such as MIT, Cambridge, Oxford, Stanford, the University of Bonn, and the Collège de France. Among them is Sir John Ball (Heriot-Watt University & Oxford University), former president of the International Mathematical Union and the London Mathematical Society, and member of the BCAM scientific committee until 2022. Another prominent figure at the conference is Pierre-Louis Lions (Collège de France), who was awarded the Fields Medal in 1994.

The scientific committee comprises Carlos Kenig (University of Chicago), former president of the International Mathematical Union; María Jesús Esteban (CEREMADE & Université Paris Dauphine), former president of the International Council for Industrial and Applied Mathematics and former chair of the BCAM Scientific Committee; and Luz Roncal (Ikerbasque & BCAM).

The conference also features a public lecture on Wednesday 2 September at the Guggenheim Museum Bilbao, given by Professor Javier Gómez-Serrano (Brown University) on Artificial Intelligence and Mathematics, and chaired by Juan Ignacio Pérez Iglesias, Minister for Science, Universities and Innovation of the Basque Government. The lecture will be free and open to the general public—a rare opportunity to engage with cutting-edge mathematical ideas from one of their leading exponents, set within a culturally unique venue. Professor Javier Gómez-Serrano brings a transformative vision of modern mathematics situated at the intersection of Artificial Intelligence, computer-assisted proofs, and partial differential equations (PDEs). In this field, Gómez-Serrano and Terence Tao (Fields Medallist, UCLA) have formed a key collaboration to tackle historic open problems, combining traditional analytical rigour with computational mathematics and machine learning tools.

BCAM, based in the heart of Bilbao, is a leading mathematical research centre, designated a Basque Excellence Research Centre (BERC) by the Basque Government and a three-time recipient of the Severo Ochoa distinction from the State Research Agency. The organising committee for the international conference, which will run from 31 August to 4 September, is made up of researchers from the Analysis and Partial Differential Equations Group at the University of the Basque Country and BCAM, with the support of the Basque Government, the State Research Agency, and European bodies.

"Mathematical analysis has a very solid tradition in the Basque Country," note the organisers, "and this event is a unique opportunity for the local and international mathematical community to share the latest advances and chart new directions for the field."