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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)

To see further

Hendrik Lentra’s closing Clay Lecture presented at the Arizona Winter School, March 11, 2026

https://drive.google.com/file/d/10vsARkUlrwqfVXRUXgn2zDY9mScNlUPT/view

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Speaker: Hendrik Lenstra (Leiden)

2026 Clay Research Fellows

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

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

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

Ciprian Manolescu

Professor Manolescu has been appointed as a Clay Senior Scholar to participate in the IAS/PCMI program Knotted Surfaces in Four-Manifolds.

Roman Bezrukavnikov

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.

Oliver Röndigs

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.

Graph-codes: problems, results and methods

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Speaker: Noga Alon (Princeton)

Anna Skorobogatova

Anna Skorobogatova obtained her PhD from Princeton University in 2024, supervised by Camillo De Lellis. She is currently an ETH-ITS Junior Fellow at the ETH in Zürich.

Skorobogatova works in geometric measure theory. She has made fundamental contributions to the regularity theory of minimal surfaces and to the structural understanding of their singularities. She established the rectifiability of the top-dimensional part of the singular set of area-minimizing integral currents, and the uniqueness of the tangent cones at almost every singular point, solving a problem that had remained completely open in codimensions greater than one, despite great efforts following Almgren’s Big Regularity Paper. She has also proved that the singular set of area-minimizing currents mod an integer q is a regular C^1 hypersurface aside from a lower-dimensional exceptional set, in all dimensions and codimensions and for all moduli q.

Anna Skorobogatova has been appointed as a Clay Research Fellow for four years beginning 1 July 2025.

Photo: Sameer Khan, IAS

Alex Cohen

Alex Cohen will receive his PhD from the Massachusetts Institute of Technology in 2025, under the supervision of Larry Guth.

Cohen is a broad and thoughtful researcher who has made innovative contributions to harmonic analysis, combinatorics, and microlocal analysis.  His work on the higher dimensional fractal uncertainty principle is of particular note. It has important applications to the field of quantum chaos, generalizing the celebrated work of Bourgain and Dyatlov to arbitrary dimensions. In this context, he also developed a higher-dimensional version of the Beurling-Malliavin theorem, a deep theorem about one complex variable from the early 1960s.

Alex Cohen has been appointed as a Clay Research Fellow for five years beginning 1 July 2025. He will be based initially at New York University.

Ryan Chen

Ryan Chen will receive his PhD in 2025 from the Massachusetts Institute of Technology, where he works under the guidance of Wei Zhang.

Chen is an arithmetic geometer of exceptional creativity with great technical expertise. His research focuses on themes surrounding the Gross–Zagier-type formula for high-dimensional Shimura varieties, where the main aim is to relate the arithmetic intersection numbers of algebraic cycles to the special values of L-functions and their derivatives. He has established, in great generality, a new Arithmetic Siegel–Weil formula, linking the Faltings heights of Kudla–Rapoport 1-cycles on integral models of unitary Shimura varieties to the first derivatives, near the central point, of non-singular Fourier coefficients of Siegel–Eisenstein series. His work has opened up new directions in understanding the arithmetic-geometric meaning of the sub-leading terms of various L-functions, including notable examples such as the standard L-functions and the adjoint L-functions associated to cohomological automorphic representations of unitary groups over totally real number fields.

Ryan Chen has been appointed as a Clay Research Fellow for five years beginning 1 July 2025. He will be based initially at Princeton University.

Photo: Jieru Chen