ℒ-modules and the cohomology of locally symmetric spaces. International conference on Représentations des groupes de Lie et applications. Institut Henri Poincaré, Paris, France. December 15, 2008
Invited Lectures: The theory of ℒ-modules was developed to solve the conjecture of Rapoport and Goresky-MacPherson: the intersection cohomology of the Baily-Borel-Satake compactification of a Hermitian locally symmetric space is isomorphic to the intersection cohomology of the reductive Borel-Serre compactification. However it applies more generally and is an powerful combinatorial tool to study constructible sheaves on the reductive Borel-Serre compactification of a general locally symmetric space. We will survey the theory and give applications to several areas, including cohomology of arithmetic groups, L²-cohomology, L²-harmonic forms, and weighted cohomology.