Mina Aganagic - Knot categorification from geometry and mirror symmetry, via string theory
I will describe how two geometric approaches to categorification of RTW invariants of knots emerge from string theory. The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two. This talk is mostly based on joint work with Andrei Okounkov.