Mark Walsh, National University of Ireland, Maynooth

Title: H-spaces, Loop spaces and k-Ricci Curvature

Abstract: In recent years, the problem of understanding the topology of
spaces of Riemmanian Metrics on a smooth manifold M, which satisfy
some particular curvature constraint, has attract considerable attention.
We discuss some developments in this subject and show how under
reasonable conditions, deeper algebraic structures such as H-space and
loop space structure can be uncovered. In particular, we discuss some
recent results concerning the space of positive k-Ricci curvature metrics
on the sphere. These results are joint work with David Wraith.