The Poincaré Conjecture and Mathematical Discovery
Michael Freedman’s Millennium Prize Problem lecture presented at Harvard Science Center, September 17, 2025
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Speaker: Michael Freedman (Harvard)
Michael Freedman’s Millennium Prize Problem lecture presented at Harvard Science Center, September 17, 2025
Speaker: Michael Freedman (Harvard)
Congratulations to Edwina Yeo (University College London), winner of The Parliamentary & Scientific Committee’s STEM for Britain Gold Medal, sponsored by CMI, for her poster Preventing bacterial surface contamination via mathematical modelling.
Marie-France Vignéras’s Clay Lecture presented at the Arizona Winter School, March 12, 2025
https://arizona.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=46a64805-410b-4ec0-9381-b28e0126b431
Speaker: Marie-France Vignéras (Jussieu)
Marie-France Vignéras’s Clay Lecture presented at the Arizona Winter School, March 8, 2025
https://arizona.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=435cfd5a-e13d-4a98-9716-b28e01268f1b
Speaker: Marie-France Vignéras (Jussieu)
Oxford’s History of Science Museum holds important material associated with Charles Babbage, including components of Babbage’s first (unfinished) mechanical computing machine and an archive of his personal notes about his machines. With support from CMI, the Museum undertook a project to conserve and digitise this precious archive of Babbage material.
Image courtesy of the History of Science Museum
Professor Noga Alon has been appointed as a Clay Senior Scholar to participate in the IAS/PCMI program Extremal and Probabilistic Combinatorics.
Professor János Pach has been appointed as a Clay Senior Scholar to participate in the IAS/PCMI program Extremal and Probabilistic Combinatorics.
The Clay Mathematics Institute is pleased to announce that Ryan Chen, Alex Cohen and Anna Skorobogatova have been awarded Clay Research Fellowships.
Ryan Chen will receive his PhD from the Massachusetts Institute of Technology in 2025, where he works under the guidance of Wei Zhang. Ryan has been appointed as a Clay Research Fellow for five years beginning 1 July 2025.
Alex Cohen will receive his PhD from the Massachusetts Institute of Technology in 2025, under the supervision of Larry Guth. Alex has been appointed as a Clay Research Fellow for five years beginning 1 July 2025.
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. Anna has been appointed as a Clay Research Fellow for four years beginning 1 July 2025.
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 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 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
Professor Hendrik Weber has been appointed as a Clay Senior Scholar from August to December 2025 to participate in Recent Trends in Stochastic Partial Differential Equations at the Simons Laufer Mathematical Sciences Institute.