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.
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.
Farey’s Legacy in Frieze Patterns and Discrete Geometry
ICMS Edinburgh
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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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