INMS Workshop — The geometry of double affine Hecke algebras and Coulomb branches

The past several years have seen landmark progress in the interplay between representation theory, geometry and mathematical physics. Particularly notable have been Braverman, Finkelberg and Nakajima's definition of the Coulomb branch of an N=4 supersymmetric (SUSY) 3d gauge theory, and Mellit's proof of the Hausel-Letellier-Rodriguez-Villegas conjecture on the Poincar\'e polynomials of character varieties. The area has also seen exciting connections to other fields, such as significant progress on the conjectures of Gorsky, Negut and Rasmussen relating coherent sheaves on Hilbert schemes to Khovanov-Rozansky homology. The goal of this conference is to push forward research in areas at the nexus between these results: affine Springer theory, double affine Hecke algebras and Coulomb branches, creating new connections between experts, and exposing young mathematicians to this fast-progressing and exciting research area.