Macdonald Dualities in Genus One and Two

Explore Macdonald dualities in genus one and two in this 45-minute lecture by Philippe Di Francesco from Institut des Hautes Etudes Scientifiques (IHES). Delve into the unified presentation of dualities in Macdonald/Koornwinder polynomial theory, focusing on its natural formulation within the spherical Double Affine Hecke Algebra on a torus. Discover how duality extends to the recently introduced genus two Macdonald theory by Arthamonov and Shakirov. This talk, based on joint work with R. Kedem, offers valuable insights for researchers and advanced students in mathematical physics and algebraic combinatorics.