SGGTC this Friday: Artem Kotelskiy and Tasos Moulinos

[Oleg Lazarev]

Dear all, 

This Friday we have two speakers. Artem Kotelskiy from Indiana University will give a talk at 10:30 am in Math 520.  Tasos Moulinos from Toulouse ill give a talk at 1:00 pm in Math 407. We will meet at 11:35 in the lobby and go out for lunch.  

Best, 

Oleg

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 Artem Kotelskiy: Immersed curves in Khovanov homology 

Abstract: Consider a 2-sphere S intersecting a knot K in 4 points. This defines decomposition of a knot into two 4-ended tangles. We will show that Khovanov homology Kh(K), and its deformation due to Bar-Natan, are isomorphic to wrapped Lagrangian Floer homology of a pair of specifically constructed immersed curves on the dividing 4-punctured sphere S. This result is analogous to immersed curves description of bordered Heegaard Floer homology and knot Floer homology. The key step will be constructing a tangle invariant in the form of a chain complex over a certain algebra B (deformation of Khovanov's arc algebra), and showing that algebra B embeds into the wrapped Fukaya category of the 4-punctured sphere. As an application, we will prove that Conway mutation preserves Rasmussen's s-invariant of knots. This is joint work with Liam Watson and Claudius Zibrowius.

Tasos Moulinos: A universal HKR theorem

Abstract: The Hochschild-Konstant-Rosenberg theorem is a classic result identifying the Hochschild homology of a commutative ring with differential forms. In characteristic zero, this can be promoted to an equivalence at the level of differential graded algebras, giving rise to the Hodge decomposition on Hochschild homology. Moreover, via this description, one interprets the de Rham differential on differential forms as the natural -action on Hochschild homology. In fact, these constructions globalize, and so one obtains an equivalence of the derived loop space  (whose algebra of functions is Hochschild homology) with the shifted tangent bundle .