### Algebra and Discrete Mathematics Seminar, UC Davis

**Sachin Gautam, Ohio State University**

*R-matrices and Yangians*

Organizer's time: 2021-02-25 09:30 America/Los_Angeles

Duration: 1 hour

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

Submitted by: Eugene Gorsky