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PQLHT | Conference Talk 8 by Hoel Queffelec: "Surface skein algebras, categorification and positivity"

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Lukas Lewark

PQLHT | Conference Talk 8 by Hoel Queffelec: "Surface skein algebras, categorification and positivity"

Skein algebra for surfaces are natural generalizations of the Jones polynomial to thickened surfaces. Khovanov homology can be extended beyond the 3-sphere following a similar process, but the algebra structure is trickier to understand at the categorical level, partly because of the lack of functoriality of Khovanov's original construction. I'll review ways to understand the skein category of a surface, and explain how we're trying to use these tools to prove a conjecture by Fock-Goncharov-Thurston claiming that the skein algebras have positive structure constants.
This is joint work with Kevin Walker and Paul Wedrich.

This talk was part of the conference "Perspectives on quantum link homology theories", see https://cbz20.raspberryip.com/Perspectives-2021