In-Person Talk 

Consider a smooth manifold with a Riemannian metric satisfying some sort of curvature or other geometric constraint like, for example, positive scalar curvature, non-negative Ricci or negative sectional curvature, being Einstein, Kaehler, Sasaki, etc. A natural question to ponder is then what the space of all such metrics does look like. Moreover, one can also pose this question for the corresponding moduli spaces of metrics, i.e., quotients of the former by (suitable subgroups of) the diffeomorphism group of the manifold, acting by pulling back metrics, and the study of spaces of metrics and their moduli has been a topic of  interest for differential geometers, global and geometric analysts and topologists alike. In my talk, I will introduce to and present some recent results and open questions in the field, with special focus placed on manifolds of non-negative Ricci or sectional curvature. Moreover, I'll also discuss broader and non-traditional approaches to the study of moduli spaces via metric geometry and analysis.