Geometric Analysis and Topology Seminar

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Cohomological Structures in Geometry and Topology Inspired by Mathematical Physics

Speaker: Hisham Sati, University of Pittsburgh

Location: Warren Weaver Hall 517

Date: Friday, February 13, 2015, 11 a.m.

Synopsis:

Cohomology comes in various flavors and plays important roles in many areas of mathematics. Recent interactions with mathematical physics have led to several interesting cohomological constructions in geometry and topology, including categorified notions of bundles associated to higher connected covers of Lie groups and twisted versions of generalized cohomology theories. I will describe mathematical results in this area, starting with twisted de Rham cohomology and twisted K-theory, and then generalizing to the newly constructed twisted elliptic cohomology, and twisted Morava K-theory and E-theory. Then I will discuss recent work on desirable differential geometric extensions of these theories, otherwise constructed by homotopy-theoretic means, building on Cheeger-Simons differential characters and Deligne-Belinson cohomolog.