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Talk

April 15, 2025
Laurent Côté (Universität Bonn): On Floer homotopy theory

Abstract

Floer theory is a rather general framework for producing invariants in symplectic and low-dimensional topology by counting solutions to non-linear elliptic PDEs. Traditionally, Floer theory outputs invariants which are linear over a discrete ring (e.g. Hamiltonian Floer cohomology, the Fukaya category, etc). The subject of Floer homotopy theory is concerned with lifting these constructions to ring spectra. I will give an introduction to this circle of ideas, assuming no background in symplectic geometry (and with the important caveat that I am an interested but mostly innocent bystander).

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