Beijing Institute of Mathematical Sciences and Applications

Perverse sheaves are a powerful tool to study singular spaces. They form an abelian category inside the derived category of complexes of sheaves which is moreover closed with respect to Verdier duality. Together with the Goresky-MacPherson construction of a canonical perverse sheaf on each good enough singular space, this provides a theory of Poincare duality in the non-smooth setting. We are going to introduce perverse sheaves and study some of the important applications. The end goal of this course is the Riemann-Hilbert correspondence between regular holonomic D-modules and perverse sheaves on a smooth complex manifold. The theory of D-modules will be explained in a parallel course by Y. Makedonsky