Geometry, Topology and Categorification Seminar: Asymptotics of quantum invariants of surface diffeomorphisms

Monday, August 31, 2020 at 2:30pm to 3:45pm

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Virtual Event


Francis Bonahon, USC

Abstract:
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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https://usc.zoom.us/j/99698082212?pwd=eVVjNTcrSm5XL1Zaa2VGUTkvUkNtUT09

Meeting ID: 996 9808 2212
Passcode: 102110

Event Type

Lecture / Talk / Workshop

Department
Mathematics
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