## Department Colloquium

### Friday, January 29th, 2021

**Time:** 2:30 p.m. **Place:** Online (via Zoom)

**Speaker:** Milen Yakimov (Northeastern University)

**Title:** Noncommutative Discriminants.

**Abstract: ** The notion of discriminant plays an important role in various algebraic, geometric and combinatorial settings. The discriminant of a noncommutative algebra is modeled on Dedekind's definition for algebraic number fields. The discriminants in the former class have many applications but have only been computed in few situations. We will present an introduction to this subject and will then describe three general theorems for computing discriminants of noncommutative algebras based on Poisson geometry, Representation Theory and Cluster Algebras, respectively. The three theorems can be applied to compute the discriminants of many families of algebras of wide interest: quantum matrices at roots of unity, quantum Weyl algebras, quantum Schubert cell algebras, algebras in noncommutative projective algebraic geometry and others. The talk is based on joint work with Kenneth Brown (Glasgow University), Bach Nguyen (Xavier University) and Kurt Trampel (University of Notre Dame).

**Milen Yakimov** is a Professor in the Department of Mathematics at Northeastern University. His research interests include noncommutative algebra, quantum groups, Poisson geometry, cluster algebras, representation theory and integrable systems. Before joining Northeastern University, he was the Michael F. and Roberta Nesbit McDonald Professor in the Department of Mathematics at the Louisiana State University. He became a Fellow of the American Mathematical Society in 2018.