# Homotopy Theory and Closed Geodesics

### John McCleary

### Mathematics Department

Vassar College

### Thursday, January 22, 1998

4:00 PM

### Room 102, Bradley Hall

Given a compact Riemannian manifold M, one can ask whether there is
a closed geodesic lying on M and further, if so, how many? A long standing
conjecture is that there are infinitely many closed geodesics. In this
talk, I will explain how this problem divides up into a geometric and a
homotopy-theoretic part and I will discuss progress on the homotopy-theoretic
side.

Much of the talk will be elementary and accessible to graduate
students.