Jacek Miękisz
Ergodic theory and topology of nonperiodic tilings and Gibbs states of interacting particles
We will present lattice models of interacting particles based on nonperiodic tilings. Basic ergodic and topological properties of tiling spaces will be discussed. The main open problem is stability of ground states (minimizers of certain energy functionals) corresponding to tilings. The important property here seems to be rapid convergence to equilibrium of local patterns – the so called strict boundary property of uniquely ergodic tiling (ground-state) measures. No tiling system with such property is known.
The interested reader of this abstract may look at slides of my recent presentation.
