Positivity for the skein algebra of the 4-puncture sphere

Abstract: The skein algebra of a topological surface is constructed from knots and links in the 3-manifold obtained by taking the product of the surface with an interval. A conjecture of Dylan Thurston predicts the positivity of the structure constants of a certain linear basis of the skein algebra. I will explain a recent proof of this conjecture for the skein algebra of the 4-punctured sphere. In a slightly surprising way, this proof of a topological result relies on complex algebraic geometry, and in particular the study of algebraic curves in complex cubic surfaces.

algebraic geometrydifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Boston University Geometry/Physics Seminar

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