Knot homology and coherent sheaves on Coulomb branches

Geometry, Symmetry and Physics
Event time: 
Monday, November 16, 2020 - 4:30pm to 6:00pm
Location: (password was emailed by Ivan on 9/11, also available from Ivan by email)
Ben Webster
Speaker affiliation: 
University of Waterloo and Perimeter Institute
Event description: 

Recent work of Aganagic proposes the construction of a homological knot invariant categorifying the Reshetikhin-Turaev invariants of miniscule representations of type ADE Lie algebras, using the geometry and physics of coherent sheaves on a space which one can alternately describe as a resolved slice in the affine Grassmannian, a space of G-monopoles with specified singularities, or as the Coulomb branch of the corresponding 3d quiver gauge theories. We give a mathematically rigorous construction of this invariant, and in fact extend it to an invariant of annular knots, using the theory of line operators in the quiver gauge theory and their relationship to non-commutative resolutions of these varieties (generalizing Bezrukavnikov's non-commutative Springer resolution).