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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