PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Sergei Tabachnikov.

Title:Dimers and integrability
Seminar:Department of Mathematics Colloquium
Speaker:Richard Kenyon, Brown University
Abstract:
This is joint work with A. Goncharov. The dimer model is the probability model of random perfect matchings on a graph. In the case of a planar graph Kasteleyn showed that one can calculate the number of perfect matchings using the determinant of a modified adjacency matrix. This simple tool leads to a deep understanding of the dimer model on planar graphs. We show that the parameter space of dimer models on planar bipartite periodic graphs has the structure of a cluster variety, equipped with a Poisson structure defining an integrable system. A complete set of commuting Hamiltonians is given explicitly in terms of dimers.

Room Reservation Information

Room Number:MB114
Date:10 / 07 / 2010
Time:04:00pm - 05:00pm