Date: October 25; November 15,22,29

Time: 9:00-11:00

A constructible sheaf is a sheaf of abelian groups over some topological space X, such that X is the union of a finite number of locally closed subsets on each of which the sheaf is a locally constant sheaf. It is a generalization of constructible topology in classical algebraic geometry. Perverse sheaves refers to a certain abelian category associated to a topological space X, which may be a real or complex manifold, or a more general topologically stratified space, usually singular. The justification is that perverse sheaves are complexes of sheaves which have several features in common with sheaves: they form an abelian category, they have cohomology, and to construct one, it suffices to construct it locally everywhere.   These notions are fundamental objects in mathematics which have many application in the study of singular spaces. In this series of reading seminars, we will introduce definitions, properties of  constructible sheaves, perverse sheaves,  intersection cohomology as well as  their application in the study of singularities.