数学科学研究所
Insitute of Mathematical Science

Colloquium: Distinguishing Riemannian metrics of positive scalar curvature

Colloquium| Institute of Mathematical Sciences

Time14:30-15:30, July 23 Tuesay

LocationRoom S408, IMS


Speaker: Demetre Kazaras, Stonybrook University

Abstract: We begin by surveying the history of Riemannian metrics with positive scalar curvature. When does a given manifold admit such a metric? What can be said about the moduli space of such objects? These open questions have non-trivial interaction with subjects in General Relativity, geometric analysis, and algebraic topology. To quote Gromov: unlike well-understood conditions such as positive sectional or Ricci curvature, “the domain of manifolds with positive scalar curvature protrudes in all directions as a gigantic octopus…” I will also discuss some recent work on the topology of the space of positive scalar curvature metrics on a fixed manifold. In particular, I will mention two results: work with Ruberman and Saveliev on a situation when bordism classes of positive scalar curvature manifolds can be distinguished and another situation when they cannot.


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