Date | 2014-06-13 |
---|---|

Speaker | Roland van der Veen |

Dept. | Korteweg- de Vries Institute for Mathematics University of Amsterdam |

Room | 129-406 |

Time | 10:00-12:00 |

Ideal triangulations are an efficient way of encoding a 3-manifold with boundary.

Thurston showed how they allow one to quickly find a hyperbolic metric by solving a system of algebraic equations called the gluing equations. By eliminating variables one also obtains the A-polynomial: a complex curve that describes the variation of the hyperbolic volume.

I will spend one lecture on reviewing these notions and explaining the importance of the symplectic properties of the gluing equations.

In the second lecture I will use the symplectic viewpoint to show how the same computations may be deformed or quantized. This leads to many interesting new quantum invariants that are very closely related to the colored Jones polynomial.

Thurston showed how they allow one to quickly find a hyperbolic metric by solving a system of algebraic equations called the gluing equations. By eliminating variables one also obtains the A-polynomial: a complex curve that describes the variation of the hyperbolic volume.

I will spend one lecture on reviewing these notions and explaining the importance of the symplectic properties of the gluing equations.

In the second lecture I will use the symplectic viewpoint to show how the same computations may be deformed or quantized. This leads to many interesting new quantum invariants that are very closely related to the colored Jones polynomial.

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