# Luke Steverango

Date

Thursday April 4, 20244:00 pm - 5:00 pm

Location

Jeffery Hall, Room 319Event Category

## Curves Seminar

**Thursday, April 4th, 2024**

**Time:** 4:00 p.m. **Place:** Jeffery Hall, Room 319

**Speaker:** Luke Steverango

**Title:** Defining Cluster Algebras by Generators and Relations

**Abstract:** A traditional way to describe a commutative algebra over a ring is as a quotient of a polynomial ring. One would hope to get an analogous way of describing cluster algebras in a similar way. Unfortunately, that runs into two issues. These issues are that the set of cluster variables is typically infinite and the exchange relations do not, in general, generate the ideal of all relations among cluster variables. We explore each of these issues, with particular emphasis on the second issue.