Math 7890: Automorphic forms and the cohomology of arithmetic groups

For a course description, prerequisites, and requirements, please see the syllabus. Please email me if you do not have the Overleaf link to the course notes!

Selected References:

For an accessible introduction to cohomology of sheaves, especially on smooth and complex manifolds, see Voisin, Hodge Theory and Complex Algebraic Geometry I. Also see Harder, Lectures on Algebraic Geometry I.

For general homological algebra beyond what's covered in the above references, see the chapters of The Stacks Project on Homological Algebra and Derived Categories.

For the theory of classical modular forms, see Miyake, Modular Forms, Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Diamond-Shurman, A First Course in Modular Forms, or the very nice survey article Diamond-Im, Modular Forms and Modular Curves.

For structure theory of semi-simple Lie groups, see Knapp, Lie Groups: Beyond and Introduction. For the more classical aspects of the representation theory of semi-simple Lie groups, see Knapp, Representation Theory of Semisimple Groups: An Overview Based on Examples.

For Lie algebra cohomology and its connection to the cohomology of arithmetic groups (at least in the co-compact case), see Borel-Wallach, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups.

A very good text that ties much of this material together, but is less self-contained than some of the other references, is Cohomology of Arithmetic Groups.