# 2024 Clay Research Conference and Workshops

The 2024 Clay Research Conference was held on Wednesday, 2 October. Videos of the plenary talks can be viewed in our Video Library.

The 2024 Clay Research Conference was held on Wednesday, 2 October. Videos of the plenary talks can be viewed in our Video Library.

CMI invites proposals under the Enhancement and Partnership Program for fiscal year 2026 (1 October 2025-30 September 2026) and later. The principal aim of the program is to enhance activities that are already planned and financially viable.

The Clay Mathematics Institute (CMI) calls for nominations for its competition for the 2025 Clay Research Fellowships.

The Clay Mathematics Institute is a global organisation dedicated to furthering the beauty, power and universality of mathematical thought.

In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston’s geometrization conjecture. Perelman’s proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries.

If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit, how can one do this without visiting a city twice? If you give me a solution, I can easily check that it is correct. But I cannot so easily find a solution.

Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles’ proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three.

6 January - 4 April 2025
### Representation Theory and Noncommutative Geometry

CIRM and IHP

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26 - 31 May 2025
### Arithmetic, K-theory, and Algebraic Cycles

Ohio State University

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20 January - 22 May 2026
### Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups

Simons Laufer Mathematical Sciences Institute

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20 January - 22 May 2026
### Topological and Geometric Structures in Low Dimensions

Simons Laufer Mathematical Research Institute

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