The shoulders we stand on
Hendrik Lenstra’s opening Clay Lecture presented at the Arizona Winter School, March 7, 2026
https://drive.google.com/file/d/1QyaXtLV1JGJl7FgLEwa2s6BdR-7e1Dky/view
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Speaker: Hendrik Lenstra (Leiden)
Hendrik Lenstra’s opening Clay Lecture presented at the Arizona Winter School, March 7, 2026
https://drive.google.com/file/d/1QyaXtLV1JGJl7FgLEwa2s6BdR-7e1Dky/view
Speaker: Hendrik Lenstra (Leiden)
Hendrik Lentra’s closing Clay Lecture presented at the Arizona Winter School, March 11, 2026
https://drive.google.com/file/d/10vsARkUlrwqfVXRUXgn2zDY9mScNlUPT/view
Speaker: Hendrik Lenstra (Leiden)
Congratulations to Torin Fastnedge (Oxford), winner of the Parliamentary & Scientific Committee’s STEM for Britain Gold Medal, sponsored by CMI, for his poster Mathematical Modelling of Microfibre Released by Washing Machines, based on research with fellow Oxford mathematicians Chris Breward and Ian Griffiths.
Javier Gómez-Serrano’s Millennium Prize Problem lecture presented at Harvard Science Center, March 11, 2026
Speaker: Javier Gómez-Serrano (Brown)
Barry Mazur’s Millennium Prize Problem lecture presented at Harvard Science Center, February 4, 2026
Speaker: Barry Mazur (Harvard)
The Clay Mathematics Institute is pleased to announce that Oliver Edtmair and Qiuyu Ren have been awarded Clay Research Fellowships.
Oliver Edtmair received his PhD in 2024 from UC Berkeley, where he worked under the supervision of Michael Hutchings. He is currently a Junior Fellow at the Institute for Theoretical Studies at the ETH Zürich. Oliver has been appointed as a Clay Research Fellow for three years beginning 1 July 2026.
Qiuyu Ren will receive his PhD in 2026 from UC Berkeley, where he works under the supervision of Ian Agol. Qiuyu has been appointed as a Clay Research Fellow for five years beginning 1 July 2026.
Clay Research Fellowships are awarded on the basis of the exceptional quality of candidates’ research and their promise to become mathematical leaders.
Qiuyu Ren will receive his PhD in 2026 from UC Berkeley, where he works under the supervision of Ian Agol. Qiuyu has been appointed as a Clay Research Fellow for five years beginning 1 July 2026.
Ren’s work as a doctoral student has already had a significant impact across low dimensional topology, combinatorics, and spectral theory. Most significantly, in a spectacular work with Willis, he achieved a goal that had eluded leading researchers in four-dimensional manifold theory for many years: the detection of exotic smooth structures on compact four-manifolds using combinatorial methods (as opposed to analytic ones). To achieve this, Ren and Willis showed that the skein lasagna module (a four-manifold invariant derived from Khovanov homology) can take different values on a pair of homeomorphic, compact four-manifolds with boundary. This breakthrough builds on Ren’s earlier work in knot theory, wherein he developed new computational methods for the Khovanov-Lee homology of cables, and proved an adjunction inequality for the Rasmussen invariant.
Photo: Zhongkai Tao
Oliver Edtmair received his PhD in 2024 from UC Berkeley, where he worked under the supervision of Michael Hutchings. He is currently a Junior Fellow at the Institute for Theoretical Studies at the ETH Zürich. Oliver has been appointed as a Clay Research Fellow for three years beginning 1 July 2026.
Edtmair employs tools from symplectic topology to tackle fundamental problems arising in dynamical systems. In collaboration with various coauthors, he has made significant contributions to symplectic dynamics and continuous symplectic topology. Notably, he was a key contributor to the proof of the Smooth Closing Lemma for area-preserving surface diffeomorphisms, which resolved a foundational problem originating in the 1960s that was for a long time seen as one of the central open questions in dynamical systems. He has also made substantial progress on a problem posed by Arnold in 1973, related to fluid dynamics, that concerns the topological extension of helicity, a conserved quantity for the three-dimensional Euler equations. His extensive portfolio of achievements also includes the resolution of celebrated questions from the 1990s regarding Hamiltonian dynamics on convex hypersurfaces in Euclidean space.
Photo: Emily Windes
Professor Manolescu has been appointed as a Clay Senior Scholar to participate in the IAS/PCMI program Knotted Surfaces in Four-Manifolds.
Professor Roman Bezrukavnikov as been appointed as a Clay Senior Scholar to participate in Representation Theory under the Influence of Quantum Field Theory at the Simons Laufer Mathematical Sciences Institute.
Professor Oliver Röndigs has been appointed as a Clay Senior Scholar to participate in Motivic Homotopy Theory: Connections and Applications at the Simons Laufer Mathematical Sciences Institute.
Nora Alon’s Clay Lecture presented at PCMI, July 14, 2025
Speaker: Noga Alon (Princeton)