# Mathematics Colloquia and Seminars

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### R-matrices and Yangians

**Algebra & Discrete Mathematics**

Speaker: | Sachin Gautam, OSU |

Location: | Zoom |

Start time: | Thu, Feb 25 2021, 9:30AM |

An R-matrix is a solution to the Yang-Baxter equation (YBE), a central object in Statistical Mechanics, discovered in 1970's. The R-matrix also features prominently in the theory of quantum groups formulated in the eighties. In recent years, many areas of mathematics and physics have found methods to construct R-matrices and solve the associated integrable system.

In this talk I will present one such method, which produces meromorphic solutions to (YBE) starting from the representation theory of a family of quantum groups called Yangians. Our techniques give (i) a constructive proof of the existence of the universal R-matrix of Yangians, which was obtained via cohomological methods by Drinfeld in 1983, and (ii) prove that Drinfeld's universal R-matrix is analytically well behaved. This talk is based on joint works with Valerio Toledano Laredo and Curtis Wendlandt.

Please contact mjvazirani@ucdavis.edu if you need the Zoom link/password. Zoom: 994 0826 8795