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Quantum Geometry of Hyperbolic 3-Manifolds
Probability| Speaker: | Sergei Gukov, Harvard |
| Location: | 693 Kerr |
| Start time: | Thu, Mar 4 2004, 4:10PM |
Description
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.