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

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Date
Thursday, November 25, 2021 14:00 - 16:00
Speaker
Pierrick Bousseau (ETH Zürich)
Location
https://mathseminars.org/seminar/AGNTISTA
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Tamas Hausel
Contact

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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