Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics
A graduate-level MIT OpenCourseWare course on double affine Hecke algebras (DAHA), also known as Cherednik algebras, and their representations. The course reviews the basic structure theory of DAHA and traces its connections across integrable systems such as the Calogero-Moser and Ruijsenaars models, algebraic geometry through Hilbert schemes, orthogonal polynomials, Lie theory, and quantum groups. Lecture notes and course materials cover the foundational algebraic framework before moving into open problems linking these areas together. The course is aimed at students already familiar with representation theory and Lie theory who want to see how a single algebraic structure ties together seemingly distant fields of mathematics and mathematical physics. Materials are provided free through MIT OpenCourseWare under its standard license, with no certificate offered.