Positivity for cluster algebras

Cluster algebras were discovered by Fomin and Zelevinsky in 2001. Since then, they have been shown to be related to diverse areas of mathematics such as Total positivity, Quiver representations, String theory, Statistical physics models, Non-commutative geometry, Teichm\"uller theory, Hyperbolic geometry, Tropical geometry, KP solitons, Discrete integrable systems, Quantum mechanics, Lie theory, Polyhedral combinatorics and Poisson geometry. As an introduction, I'll explain how they occur in such a wide variety of branches of mathematics. If time permits, I'll sketch the idea of proof for the long standing positivity conjecture, which is joint work with Ralf Schiffler.

The talk will be totally elementary, does not assume any preliminary knowledge of cluster algebras, and should be accessible to undergraduate students.

Tuesday, March 12, 2013

3:00– 4:00 P.M.

372 Science and Engineering Building

(Refreshments at 2:30-3:00 PM in the kitchen area adjacent to 368 SEB)