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Title:
Homological link invariants from Floer theory
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Abstract:
The link categorification problem is to give a uniform categorification of Chern-Simons link invariants which originates from geometry and physics. The resulting theory, predicted by string theory, generalizes Heegard-Floer theory from gl(1|1) to other Lie (super-)algebras. The resulting category of A-branes has many special features which render it solvable explicitly. In this talk, I will describe how the theory is solved, and how homological link invariants arise from it. I will focus on the two simplest cases, the gl(1|1) theory itself, and the su(2) theory, categorifying respectively the Alexander and the Jones polynomials.
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