AbstractKhovanov homology and its relatives are known to be governed by the representation theory ofKLRW algebras (quiver Hecke algebra). Here we discuss a way to realize the KLRW algebra as theendomorphism algebra of certain Lagrangian in the (partially) wrapped Fukaya category on a 3dN=4 Coulomb branch. This is joint work with Mina Aganagic, lvan Danilenko, Yixuan Li and VivekShende
AbstractIn the marriage of low dimensional topology and symplectic topology, there lives Legendrians knots and their exact Lagrangian fillings. Legendrian knots are smooth knots satisfying some tangency conditions, such that their projection diagrams have certain cusps. The Lagrangian fillings are filling surfaces of knots in the 4-dimensional ball, again satisfying some extra conditions. Legen...