Twisted cohomology and Soergel bimodules

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• Tomas Mejia Gomez (Johns Hopkins University)
• Tuesday 11 June 2024, 16:45-17:15
• External.

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TRHW01 - Workshop on topology, representation theory and higher structures

We will explore a homotopy theoretical perspective on Soergel bimodules. These are objects of representation theory origin, and they feature in knot theory when defining categorified link invariants such as Khovanov-Rozansky homology. Algebraic topology comes into the mix when looking at Soergel bimodules and related algebraic objects (such as their Hochschild homology) as equivariant cohomologies of certain spaces with torus actions. This gives a nice framework to interpret the algebra of Soergel bimodules and link homologies. We place a particular focus on what twisted cohomology theory can say about various flavors of link homology, and point at further directions suggested by this topological point of view.

This talk is part of the Isaac Newton Institute Seminar Series series.

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