Alex Dimca (Nize, France)

Elementary Aspects of Perverse Sheaves and Applications

Lecture 1: Local systems and twisted cohomology
fundamental groups of algebraic varieties;
sheaves and cohomology;
local systems and twisted cohomology;
basic example: global Milnor bers of homogeneous singularities.
Lecture 2: Constructible sheaves
regular stratifications;
constructible sheaves;
the derived category of bounded complexes of constructible sheaves;
nearby and vanishing cycles.
Lecture 3: Perverse sheaves
perverse sheaves on algebraic varieties;
Artin vanishing theorem.
Lecture 4: Topological applications of the perverse sheaves
Milnor fibers and monodromy for non-isolated singularities;
Twisted cohomology of hyperplane arrangement complements.


1. A. Dimca: Sheaves in Topology, Universitext, Springer-Verlag, 2004.