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