3/2/2007

Brian Weber
University of Wisconsin

Appearance of orbifold singularities in moduli spaces of certain
Riemannian metrics

Since Gromov's precompactness theorem was proved, ways have been sought to strengthen its conclusions or weaken its hypotheses. When restricted to certain classes of metrics with only energy, diameter, and volume bounds, moduli spaces are precompact and degeneration can only yields the micest of singular objects, Riemannian orbifolds. The analytic and geometric methods first used for these theorems have expanded to cover much larger classes of manifolds. We'll explore these methods, and mention a new result in the class of Extremal Kahler manifolds.