Hyperbolic volume, the Jones polynomial, and q-Hypergeometric functions

Dylan Thurston

Harvard University

February 23,
refreshments at 3:45pm


We present the Kashaev-Murakami-Murakami conjecture which relates the asymptotic growth rate of certain values of the colored Jones polynomial of a knot to the hyperbolic volume of its complement. We prove the conjecture in the simplest case, the figure eight knot complement, and give heuristic reasons why the conjecture should be true in general; we also explain why you should not trust the heuristics. We close with speculations about relations between hyperbolic geometry and q-hypergeometric functions in general.

Speaker's Contact Info: dpt(at-sign)math.harvard.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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