2025 Clay Research Conference and Workshops
The 2025 Clay Research Conference will held on Wednesday and Thursday, 1-2 October. Associated workshops will be held Monday, Tuesday, 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.
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.
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.
Navier-Stokes Equation
This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.
Geometry, Higher Structures, and Physics
ICMS Edinburgh
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Operator Algebras and Mathematical Physics
ICMS Edinburgh
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Geometry and Topology in Low Dimensions: Lasting Trends and Emerging Directions
Hungarian Academy of Sciences
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Mathematical Developments in Geophysical Fluid Dynamics
Institut Henri Poincaré
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