Seminar

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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.