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Abstract |
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 (École normale supérieure de Lyon). |
