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The skein algebra of the 4-punctured sphere from curve counting


Date: Thursday, November 25, 2021 14:00 - 16:00
Speaker: Pierrick Bousseau (ETH Z├╝rich)
Location: https://mathseminars.org/seminar/AGNTISTA
Series: Mathematics and CS Seminar
Host: Tamas Hausel

The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the SL_2 character of a topological surface. I will explain how to realize the skein algebra of the 4-punctured sphere as the output of a mirror symmetry construction based on higher genus Gromov-Witten invariants of a log Calabi-Yau cubic surface. This leads to the proof of a previously conjectured positivity property of the bracelets bases of the skein algebras of the 4-punctured sphere and of the 1-punctured torus.

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