AbstractFloer defined Floer homology in two different cases. One is the case of Instanton Floer homology of 3 manifolds (homology sphere). The other uses pseudo-holomorphic curves. (The first Floer homology Floer defined using pseudo-holomorphic curves is Lagrangian Floer homology.) Atiyah-Floer conjecture says that those two coincide in certain situations. This is > 30 year old conjecture. I w...
AbstractA powerful technique in representation theory is localization, wherein one identifies categories of modules for an algebra of interest with categories of D-modules or perverse sheaves. After reviewing the classical Beilinson”ŖBernstein theorem, which introduced localization for semisimple Lie algebras, we will describe some analogues for certain vertex algebras, notably W-algebras and...