Michael Munn

My research interests lie broadly in the area of Riemannian geometry and geometric analysis. Currently, I am interested in questions regarding synthetic definitions of Ricci curvature in metric measure spaces. Recently Lott-Villani and Sturm have developed a the notion of a lower Ricci curvature bound to in these spaces and have shown a number of very interesting results.

Starting Sept 2009, I will be at the University of Warwick as an NSF postdoctoral research fellow. My proposal aims to investigate a number of questions concerning Ricci curvature lower bounds in metric measure spaces. I will be working closely with Peter Topping and the geometric analysis research group there.

My dissertation examines manifolds with non-negative Ricci curvature and large volume growth. Specifically, I show how the volume growth controls the topology of this class of manifolds. This work extends results of G. Perelman from 1994 and can be see on the arXiv here.

I have also recently completed a joint project with Dan Garbin and Prof. Jay Jorgenson. This paper has been accepted for publication and will appear in Commentarii Mathematici Helvitici. A preprint is available here: On the appearance of Eisenstein series through degeneration.

Research

Here is a link to my research statement.

Publications:

Garbin, D., Jorgenson, J., and Munn, M. On the appearance of Eisenstein series through

degeneration, Comentarii Mathematici Helvetici 83 (2008) pp. 701-721.

Munn, M. Volume growth and the topology of manifolds with nonnegative Ricci curvature, (2008) submitted arXiv: 0712.0827v2