Laboratoire de Mathématiques J.A. Dieudonné, Nice - France

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Conférence "Multidimensional symbolic dynamics and lattice models of quasicrystals"

1er avril 2024


"The aim of this meeting is to bring together researchers from three a priori distinct fields that have come closer in recent years, but probably not sufficiently so:statistical physics on the lattice Zd and multidimensional symbolic dynamics, which has a strong link with theoretical computer science.
This rapprochement began with the study of the convergence, or the non-convergence of Gibbs and equilibrium measures, when the temperature tends to zero. This work has provided some surprises and raised many questions.
A major goal is to demonstrate the existence of freezing phase transitions giving rise to quasicrystals that are modeled, when d ě 2, by aperiodic Wang tilings, i.e., subshifts of finite type having no periodic configuration. When d “ 1, the subshifts modeling quasicrystals are not of finite type because they cannot be aperiodic. When d “ 2, only numerical experiments attest to the existence of freezing phase transitions.
There are of course other questions that arise, for example the robustness of quasicrystals. We formulate some of them in the main document about scientific content, and one of the goals of this meeting is certainly to bring out new ones.
We believe that the interaction between the three areas mentioned below will feed each of them with new questions.
Keywords:Zd-subshifts in dimension greater than one, Wang tilings, quasicrystals, freezing phase transitions, Gibbs measures, equilibrium states, ground states, Turing machines."

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