Title: Yangians and rational R-matrices
Speaker: Sachin Gautam
Abstract: In 1983, Drinfeld defined a family of Hopf algebras, called Yangians, in order to systematically construct rational solutions to the famous Yang-Baxter equation (i.e, rational R-matrices). He also coined the term ``Yangians", in honor of C.N. Yang who gave the first non-trivial example of a rational R-matrix.
In this talk, I will explain what the Yang-Baxter equation is, what are Yangians, and how Drinfeld's idea works in practice. I will also present an explicit construction of Drinfeld's R-matrix and some open questions, based on my recent joint works with A. Appel, V. Toledano Laredo and C. Wendlandt.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for one or two credit hours of Math 6193 with Professor Nimish Shah.