The Geometry of Double Affine Hecke Algebras and Coulomb Branches

Scientific organisers

Gwyn Bellamy, University of Glasgow
Dinakar Muthiah , University of Glasgow
Peng Shan , Tsinghua University
Ben Webster, University of Waterloo/Perimeter Institute

About:

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 Poincare 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 was 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.

Programme:

Resources

Talk recordings

Monday 20 March
Registration with tea & coffee
Introduction
David Jordan, University of Edinburgh	Skeins, tori and DAHA	abstract D Jordan.pdf
Anton Mellit, University of Vienna	Hecke algebras. Basic structure and representations
Lunch
Anne Moreau, Université Paris-Saclay (Orsay)	Associated varieties and finite extension of vertex algebras	abstract A Moreau.pdf
Tea & Coffee
Oscar Kivinen, EPFL	Orbital L-functions and knot superpolynomials	abstract O Kivinen.pdf
Drinks reception at ICMS
Tuesday 21 March
Zijun Zhou, IPMU	Virtual Coulomb branch and quantum K-theory	abstract Z Zhou_0.pdf
Tea & Coffee
Alexis Bouthier, Sorbonne Université	Singular support for ind-schemes	abstract A Bouthier.pdf
Lunch
Juliet Cooke, University of Nottingham	Skein Algebras and Spherical DAHAs	abstract J Cooke.pdf
Tea & coffee
Hiraku Nakajima, IPMU	Coulomb branches and DAHA	abstract H Nakajima .pdf
Wednesday 22 March
Vasily Krylov, MIT	On Hikita-Nakajima conjecture for quiver varieties and Slodowy slices	abstract V Krylov rev.pdf
Tea & coffee
Anton Mellit, University of Vienna	Hecke algebras. Geometric actions
Yakov Varshavsky, The Hebrew University of Jerusalem	Finiteness properties of Affine Springer sheaves and Lusztig conjecture	abstract Y Varshavsky.pdf
Lunch and free afternoon
Thursday 23 March
Roman Bezrukavnikov, MIT	Double affine Hecke category and affine Springer fibers	abstract R Bezrukavnikov.pdf
Tea & coffee
Alex Weekes, University of Saskatchewan	Embeddings of Kac-Moody affine Grassmannian slices and fundamental monopole operators	abstract A Weekes.pdf
Lunch
Zhiwei Yun, MIT	An irregular Deligne-Simpson problem and Cherednik algebras	abstract Z Yun_0.pdf
Tea and coffee
Pablo Boixeda Alvarez, Yale	Affine Springer fibers, Procesi bundles and Cherednik algebras	abstract P Boixeda Alvarez.pdf
Workshop dinner
Friday 24 March
Anton Mellit, University of Vienna	Hecke algebras. Applications to Higgs moduli spaces
Tea and coffee
Michela Varagnolo, CY Cergy Paris Université	Critical Convolution Algebras and Quantum Loop Groups	abstract M Varagnolo.pdf
Tudor Dimofte, University of Edinburgh	Higgs branches, Coulomb branches, and link homology	abstract T Dumofte 1.pdf
Boxed lunch and end of workshop