Speaker: Harold Williams (UC Berkeley)
2012.09.20 |
| Date | Thu 20 Sep |
| Time | 15:00 — 16:00 |
| Location | Aud. D4 (1531-219) |
Abstract
Cluster ensembles axiomatize certain structures appearing in higher Teichmuller theory, and extend the notion of a cluster algebra. The essential data is a canonical transformation between a collection of cluster variables and another type of coordinates, often called coefficient variables or X-coordinates. This same structure arises in a number of other contexts where cluster algebras are present, though often in a disguised form. We will explain a particular example of this coming from Lie theory, related in particular to loop groups and integrable systems. In fact, we will see that the notion of a cluster ensemble turns out in retrospect to provide a useful point of view on the Chamber Ansatz, a key formula in the theory of total positivity in simple algebraic groups.
