The Clay Mathematics Institute has announced that UBC Mathematics Professors Pablo Shmerkin and Joshua Zahl (currently on leave at Nankai University), along with Tuomas Orponen (University of Jyväskylä) and Hong Wang (IHES and NYU), have been awarded the 2026 Clay Research Award. This award, which recognizes exceptional contributions to mathematical research, honours Professors Shmerkin and Zahl, together with their collaborators, for developing new techniques that ultimately resolved two of the most technically challenging conjectures in modern analysis: the Furstenberg set problem and the three‑dimensional Kakeya conjecture.

Solving the Furstenberg set problem and the Kakeya conjecture in three dimensions was not a single breakthrough but the culmination of ten years of collaborative work, during which the researchers gradually overcame each stumbling block one-by-one. A central part of Professor Shmerkin’s research, and mathematical analysis as a whole, is the use of multiscale decompositions—the breaking up of complicated ideas into smaller pieces that can be examined in detail at different levels. Professor Shmerkin contributed to these problems by introducing a twist on this method where “the scales are chosen more carefully based on a combinatorial analysis of the object under study.” This approach proved crucial in untangling the Furstenberg problem by breaking it up into more manageable pieces. Likewise, Professor Zahl contributed to these problems by developing new ways to find structure in arrangements of simple geometric objects like thickened lines and planes. This allowed for powerful tools such as induction on scale to be effectively used to study these types of arrangements. 

Reflecting on the award, Professor Shmerkin notes: “In addition to being a great and unexpected honour, this award recognizes the importance of my research area within mathematics, and I'm excited about further progress to come—especially by younger people. It is important to recognize that my mentors, family, colleagues, and community all played a role, and I am grateful to all of them for their support.”

Similarly, Professor Zahl shared, “This award is a recognition of the importance of the Kakeya and Furstenberg set conjectures in the development of modern harmonic analysis and geometric measure theory. It serves as an encouragement for myself and others to continue pursuing these types of questions.”

The Clay Research Award is presented annually to celebrate the outstanding achievements of the world’s most gifted mathematicians. Professors Shmerkin and Zahl, along with their collaborators, will receive their award at the Clay Research Conference in September 2026.