For more information about this meeting, contact Sergei Tabachnikov.
|Title:||Dimers and integrability|
|Seminar:||Department of Mathematics Colloquium|
|Speaker:||Richard Kenyon, Brown University|
|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
|Date:||10 / 07 / 2010|
|Time:||04:00pm - 05:00pm|