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Quantum Geometry of Hyperbolic 3-Manifolds

Mathematical Physics & Probability

Speaker: Sergei Gukov, Harvard
Location: 693 Kerr
Start time: Thu, Mar 4 2004, 4:10PM

Let K be a knot in the 3-sphere. It is well known that, for a N-dimensional representation of SU(2), the Reshetikhin-Turaev-Witten invariant of K is related to the value of the N-colored Jones polynomial, J_N (K,q), where q is a root of unity. Motivated by the ideas in physics, in this talk I present some evidence that, when q is not a root of unity, the colored Jones polynomial encodes quantum invariants associated with flat SL(2,C) connections on the knot complement. This approach allows to explain a number of curious facts and to predict some new and rather surprising relations between the A-polynomial, the colored Jones polynomial, and invariants of hyperbolic 3-manifolds.

There will be an introductory session for graduate students at 11:00am, room 693.