Broken lines and Floer Theory over spectra

Abstract: I will discuss a program, joint with Jacob Lurie, to enrich Lagrangian Floer theory over stable homotopy theory. Success would open new, symplecto-geometric techniques for studying stable homotopy theory. In this talk I will discuss a stack of broken lines and explain how factorizable structures on sheaves on this stack encode the higher homotopical data of $A_\infty$-algebras. If time allows, I will discuss the deformation-theoretic data encoded in natural examples, and explain how this allows one to enrich Floer theory over spectra.

References:

[1] Lurie, Jacob and Tanaka, Hiro Lee, Associative algebras and broken lines, arXiv:1805.09587.

Mathematics

Audience: researchers in the topic

Opening Workshop (IRP Higher Homotopy Structures 2021, CRM-Bellaterra)