# Mathematics Colloquia and Seminars

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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.