Monday, August 31, 2020 at 2:30pm to 3:45pm
Francis Bonahon, USC
The Kashaev-Murakami-Murakami Volume Conjecture connects the colored Jones polynomials of a knot to the hyperbolic volume of its complement. More precisely, for each integer n, one evaluates the n-th Jones polynomial of the knot at the n-root of unity exp(2 pi i/n). The Volume Conjecture predicts that this sequence grows exponentially as n tends to infinity, with exponential growth rate related to the hyperbolic volume of the knot complement. I will discuss a closely related conjecture for diffeomorphisms of surfaces, based on the representation theory of the quantum Teichmüller spaceand/or the Kauffman bracket skein algebra of the surface. I will present experimental evidence for this conjecture, and describe partial results obtained in work in progress. This is joint work with Tian Yang and Helen Wong.
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Meeting ID: 996 9808 2212