University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The stack "Broken" and associative algebras

The stack "Broken" and associative algebras

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact info@newton.ac.uk.

HHH - Homotopy harnessing higher structures

 After reviewing some aspects of Morse theory, I'll talk about “Broken,” the moduli stack of constant Morse trajectories (possibly broken) on a point. Surprisingly, this stack has the following property: Factorizable sheaves on it are the same thing as (possibly non-unital) associative algebras. We all know that having geometric descriptions of algebraic structures should buy us mileage; so what mileage does this property buy us? If time allows, I'll try to explain why this theorem leads to a roadmap for constructing Morse chain complexes, and in fact, for constructing the stable homotopy type of a compact manifold with a Morse function. (That is, this gives a different way to realize ideas of Cohen-Jones-Segal.) The motivation is to construct a stable homotopy type for Lagrangian Floer Theory—the latter is an important invariant in symplectic geometry and mirror symmetry. This is all joint work with Jacob Lurie.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity