Seminarium KMMF "Teoria Dwoistości"

The first part of the presentation is a colloquium-style introduction to the mathematics of quasicrystals as seen from the theoretical physicist point of view. We will discuss simple examples of optimization problems in kissing numbers, packing spheres, non-periodic tilings, and classical-lattice gas models of statistical mechanics. We will also formulate the main open problem - the existence of non-periodic Gibbs measures for finite-range Hamiltonians. In the second part of the talk, we will discuss various connections between ergodic theory, substitution dynamics, dynamical systems of finite type, and classical lattice gas-models. I will outline a research project supported by NCN Harmonia grant "Mathematical models of quasicrystals". We are looking for young people to collaborate within the framework of the grant.