Knot homology and coherent sheaves on Coulomb branches

Abstract: 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).

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar