Technion
 
Seminar on Dimers
 
Speaker : Michael Polyak
 
Title : Introduction to dimers
 
Place : Amado 619
 
Date: Monday 23/4/2012
 
Time : 16:30
 
(Note the time change from an earlier announcement that some of you may have seen.)
 
Abstract:
 
We start an introduction to dimers following lecture notes of Kenyon.
 
Sender name : Michael Polyak
Sender email :  <polyak@math.technion.ac.il>
 
(I (M.C.) take the liberty of inserting this further info which may be relevant for some
readers of this message:
 
=====================
 
Hi all,
 
I would like to organize a reading seminar on dimers and their relation to
knots, cluster varieties, Poisson geometry and integrable systems.
 
Dimer covers of graphs are perfect matchings, i.e. subsets of edges which
cover every vertex exactly once. If the graph is equipped with weights on
edges, one can define a dimer statistical sum (as a sum over all dimer
states of products of the dimer edge weights). It turns out that a number
of important topological/geometric constructions may be defined and studied
using dimer models. One of the topics which naturally appears in this way
is the theory of random surfaces and the related algebraic and tropical
geometry. Another topic is a discrete differential geometry of bundles with
connections over graphs. Lately, relation of dimer models to cluster
algebras, Poisson geometry and integrable systems surfaced.
 
I propose to follow lecture notes
 
--  R. Kenyon "Lectures on dimers" arxiv:0910.3129
 
to learn the basics of dimer models on bipartite graphs, and then switch to
 
-- A. B. Goncharov, R. Kenyon, "Dimers and cluster integrable systems",
  arXiv:1107.5588
 
to try to understand their relation to cluster algebras, Poisson geometry
and integrable systems. (We will also need to choose some readable text on
cluster algebras and their duals - cluster X-varieties.) If there are other
topics folks are interested in, I'll be happy to learn as well.
 
I volunteer for several introductory talks.
 
Best,
Misha Polyak
 
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