# Mathematics Colloquia and Seminars

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### Reconstruction theorems for quantum groups and applications

**Student-Run Applied & Math Seminar**

Speaker: | Valentin Buciumas, Stanford University |

Location: | 2112 MSB |

Start time: | Fri, May 22 2015, 12:10PM |

Starting with a rigid tensor category with certain properties, one can build a Hopf algebra whose finite dimensional comodules form a category "similar" to the one we started with. I will present a series of reconstruction theorems for Hopf algebras, and highlight how extra properties of the initial category translate to properties of the Hopf algebra we build. In the second part, I will use the theorems to construct new Hopf algebras starting from a (parametrized) Yang-Baxter equation. These Hopf algebras are quantizations of coordinate rings on certain groups and are in duality with the better known quantized universal enveloping algebras. Time permitting, I will say some things about their representation theory and about a newly discovered Hopf algebra.