## Seminar in Cluster algebras

•  Panupong Vichitkunakorn, University of Illinois at Urbana-Champaign
•  Conserved quantites of Q-systems from dimer integrable systems
•  11/01/2016
•  1:00 PM - 1:50 PM
•  C304 Wells Hall

In 2013, Goncharov and Kenyon constructed integrable systems from a class of quivers on a torus, parametrized by integral convex polygons. Associating a Y-pattern to the quiver, the phase space coordinates of the dynamical systems are y-variables together with two extra variables. A Y-seed mutation at a vertex having two incoming and two outgoing arrows gives a change of coordinates. We study this dimer integrable system on Cluster variables, extend it to some quivers outside the class, and construct conserved quantities of Q-systems.

## Contact

Department of Mathematics
Michigan State University