2026 Clay Research Conference and Workshops
The 2026 Clay Research Conference will be held on Wednesday 23 September, with associated workshops held Monday, Tuesday, Thursday and Friday during the week of the conference.
The Clay Mathematics Institute is a global organisation dedicated to furthering the beauty, power and universality of mathematical thought.
P vs NP
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.
Poincaré Conjecture
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.
Hodge Conjecture
The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. The Hodge conjecture is known in certain special cases, e.g., when the solution set has dimension less than four. But in dimension four it is unknown.
A CMI event
Multi-valued Harmonicity
Mathematical Institute, University of Oxford
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Young Topologists Meeting
University of Copenhagen
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A CMI event
2026 Clay Research Conference and Workshops
Mathematical Institute, University of Oxford
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Early Career Number Theorists in South-Eastern Europe (ECNTSEE)
American University of Beirut Mediterraneo
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