Abstract: 
The “Algebra of the Infrared” refers to a collection of homotopical algebra structures (discovered by Gaiotto-Moore-Witten) that one associates to a massive two-dimensional N=(2,2) quantum field theory (subject to certain constraints). This provides a powerful framework for working out the category of boundary conditions of such QFTs. Specializing to the example of massive Landau-Ginzburg models, one is lead to a novel “web-like” construction of the Fukaya-Seidel category. In this talk, after reviewing these developments, I will discuss work-in-progress with Greg Moore which seeks to generalize the web framework to N=(2,2) theories with non-trivial twisted masses. In the Landau-Ginzburg context this amounts to studying LG models defined by a holomorphic one-form dW which is closed but not necessarily exact. Among the results we will announce are a Koszul duality theorem for boundary algebras in such theories, and a categorification of the wall-crossing formula for the CP^1 model with twisted masses.

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My bio can be found at: https://www.ias.edu/scholars/ahsan-z-khan