# Calvin Fletcher

Date

Thursday September 28, 20234:00 pm - 5:00 pm

Location

Jeffery Hall, Room 102## Curves Seminar

**Thursday, September 28th, 2023**

**Time:** 4:00 p.m. **Place:** Jeffery Hall, Room 102

**Speaker:** Calvin Fletcher

**Title:** Total positivity of flag minors

**Abstract:** Last week we saw our first piece of motivation for studying cluster algebras. In this talk we explore another motivational example, namely, total positivity of flag minors. These are an important subset of matrix minors and are related to the basic affine space by invariant theory. In much the same modus as last week we will construct a ring corresponding to these flag minors, study its generators and see how these generators form extended clusters with important combinatorial data. We will also compare and contrast the examples given to help motivate further the topic of cluster algebras.