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 --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <Techm@leeor.math.technion.ac.il>