Miquel dynamics for circle patterns

Circle patterns are one of the ways to uniformize graphs on surfaces, by embedding them in such a way that every face admits a circumcircle. In this talk I will describe a discrete-time dynamical system on circle patterns with the combinatorics of the square grid. This dynamics, based on the classical six-circles theorem of Miquel, is called Miquel dynamics. It was introduced by Richard Kenyon as an attempt to find a connection between circle patterns and the dimer model. I will present some properties of this dynamics which suggest its integrability. Partly joint work with Alexey Glutsyuk.