Abstract

The study of arithmetic groups has played a fundamental role in the development of number theory, geometry and representation theory. Automorphic forms have been one of the most important guiding tools to study them. The study of Eisenstein cohomology was initiated by Harder, and he discovered that Eisenstein cohomology is fundamentally related to several important topics in number theory, e.g., special values of $L$-functions, extension of motives, to simply mention a few. Although lots of work have been done, our understanding of Eisenstein cohomology is still far from complete. In this 4 lecture course, we will aim to understand the basics of the Eisenstein and boundary cohomology associated to arithmetic groups.