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 Clay Mathematics Institute is a global organisation dedicated to furthering the beauty, power and universality of mathematical thought.
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.
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.
Yang-Mills & The Mass Gap
Experiment and computer simulations suggest the existence of a “mass gap” in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known.
Geometric Problems in Linear and Nonlinear PDEs
Sabhal Mor Ostaig, the Isle of Skye
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Representation Theory and Noncommutative Geometry
CIRM and IHP
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Arithmetic, K-theory, and Algebraic Cycles
Ohio State University
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Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups
Simons Laufer Mathematical Sciences Institute
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