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.
Birch and Swinnerton-Dyer Conjecture
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.
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.
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.
Representation Theory and Noncommutative Geometry
CIRM and IHP
Read more
Arithmetic, K-theory, and Algebraic Cycles
Ohio State University
Read more
Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups
Simons Laufer Mathematical Sciences Institute
Read more
Topological and Geometric Structures in Low Dimensions
Simons Laufer Mathematical Research Institute
Read more
