Mathematical Sciences Research Institute

Home » Floer Homotopy Foundations Seminar: Breaking Everything to Cohere Everything


Floer Homotopy Foundations Seminar: Breaking Everything to Cohere Everything October 11, 2022 (01:00 PM PDT - 02:00 PM PDT)
Parent Program:
Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Hiro Tanaka (Texas State University)
Description No Description
No Video Uploaded

To participate in this seminar, please register HERE.

In symplectic geometry, how does the Floer theory of J-holomorphic disks give rise to Algebra (like chain complexes, Aoo-algebras, E_2-algebras, and Aoo-categories)? I'll ignore all smoothness and bubbling issues -- by working in the exact setting, for example -- and talk about a mechanism that produces such objects automatically, premised on certain orientation classes on moduli of disks and certain module actions. Importantly, this mechanism can be fed any symmetric monoidal stable oo-category, so in particular gives a framework for producing Spectral Algebra (i.e., spectral versions of all the above structures). The key player is a stack of broken holomorphic objects (mapping to a point). We'll proceed mainly with the example of broken lines/strips. This is old joint work with Jacob Lurie; I most likely won't speak about newer joint work that attempts to get rid of the module premise.

No Notes/Supplements Uploaded No Video Files Uploaded