MATH 7580 - Perverse Sheaves

Bruce Fontaine, spring 2015.

In this course we will study derived/triangulated categories, t-structures, intersection (co)homology, perverse sheaves and their relation to d-modules. The major goal of the course will be the proof of the decomposition theorem which is the main tool used in many applications of perverse sheaves. With time permitting we will discuss some applications. Possibilities include the Kazhdan-Lusztig conjecture, the geometric Satake correspondence and Ngo's work on the fundamental lemma (Ngo's support theorem). Some prior knowledge of sheaves will be assumed.