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Title:
Atiyah—Floer conjecture and a story of two A_\infty categories
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Abstract:
In this talk, I will start by reviewing the definition of an A_\infty category in Yang—Mills gauge theory. This category is a gauge theoretical analogue of the more well-known Fukaya category for Lagrangian submanifolds of a symplectic manifold. In fact, a functorial version of the Atiyah—Floer conjecture asserts that this category is related to the Fukaya categories of moduli spaces of flat connections on Riemann surfaces. After stating a more precise version of this conjecture, I will discuss some recent progress on the functorial Atiyah--Foer conjecture.
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