Explore a groundbreaking lecture on the intersection of homological mirror symmetry and representation theory, solving the knot categorification problem. Delve into a theory generalizing Heegard-Floer theory from gl(1|1) to arbitrary simple Lie (super) algebras, presented by UC Berkeley's Mina Aganagic. Discover the unique features of the corresponding category of A-branes that make it explicitly solvable. Learn how this theory is solved and how homological link invariants emerge from it, offering new insights into the field of algebraic topology and geometric representation theory.