Hodge theoretic aspects of Soergel bimodules and representation theory

Abstract

In the last years, methods coming from Hodge theory have proven to be fruitful in representation theory, most remarkably leading to a new algebraic proof of the Kazhdan-Lusztig conjectures based on the Hodge theory of Soergel bimodules. In this thesis we study several aspects of connection between Hodge theory and representation theory, following several directions.