Algebra/Topology seminar

Speaker: Shaul Barkan

Title: Modular infinity-operads

Abstract:

Inspired by ideas from physics, Getzler-Kapranov introduced the notion of a modular operad, a type of algebraic structure defined in terms of graphs, which has since found many applications to the cohomology of moduli spaces. In the talk I will explain a theory of modular infinity operads, developed in joint ongoing work w/ Jan Steinebrunner, which lifts the ideas of Getzler and Kapranov to the level of spaces. The theory incorporates examples from topology, such as manifolds and bordisms, as well algebraic examples such as the Morita theory of algebras and bimodules. Applications include the singular 1-dimensional bordism hypothesis, universal characteristic classes for Frobenius algebras and the stable homology of certain moduli spaces in low dimensional topology.