Title: The geometry and arithmetic of locally symmetric spaces

Abstract: Locally symmetric spaces form a particular class of smooth manifolds, the smooth structures of which carry a large group of symmetries. But despite the highly differential-geometric nature of these objects, much of the mathematical interest in them lies in arithmetic data which is, rather mysteriously, encoded in the differential forms on them.

In this talk, I will give an introduction to locally symmetric spaces from the point of view of their geometry, and then I will try to reveal the source of their arithmetic significance. If time permits, I will briefly explain some of my own results about the differential forms on these spaces which have seen applications to algebraic number theory.