**Regina Rotman, University of Toronto**

**Title:** Ricci curvature, the length of a shortest periodic geodesic and
quantitative Morse theory on loop spaces

**Abstract:** I am planning to present the following result of

mine: Let M^{n} be a closed Riemannian manifold of dimension n and Ric
≥(n-1).

Then the length of a shortest periodic geodesic can be at
most 8πn.
The technique involves quantitative Morse theory on loop spaces. We will

discuss some related results in geometry of loop spaces on Riemannian

manifolds.