Hecke Surfaces and Duality transformations for Lattice Spin models
M. Monastyrsky (Institute for Theoretical and Experimental Physics)
Tuesday 3rd May, 2011 15:00-16:00 Mathematics Building, room 515
We discuss two related subjects: Hecke surfaces and K regular graphs, and duality transformations for general Potts models. Each is related with deep mathematical and physical theories. At a first glance, they have nothing in common, however, it becomes more evident in the last years that a deep internal relations between all these problems exist. Especially interesting and mysterious is the role of Hecke groups in this context. I consider a few examples of these topics: A. Hecke surfaces with large cusps, B. Hecke graphs and Ramanujan graphs, C. Potts models and the cluster behavior of zeros of the chromatic polynomials on lattices.