Department of Mathematics

Seminar in Cluster algebras

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

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.

 

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Department of Mathematics
Michigan State University
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C212 Wells Hall
East Lansing, MI 48824

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