Scientific Committee
Comité scientifique
Nathalie Aubrun (CNRS, Université Paris-Saclay)
Aernout van Enter (University of Groningen)
Michael Hochman (The Hebrew University)
Anthony Quas (University of Victoria)
Organizing Committee
Comité d’organisation
Jean-René Chazottes (CNRS, École polytechnique)
Mao Shinoda (Ochanomizu University)
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.
Le but de cette rencontre est de rassembler des chercheurs de trois domaines a priori distincts qui se sont rapprochés ces dernières années, mais sans doute insuffisamment : la physique statistique sur réseau et la dynamique symbolique, en particulier multidimensionnelle, qui a un lien fort avec l’informatique théorique.
Ce rapprochement a commencé à s’opérer avec l’étude de la convergence ou la non-convergence des mesures de Gibbs et des mesures d’équilibre quand la température tend vers zéro. Ces travaux ont réservé des surprises et soulevé de nombreuses questions.
L’un des grands buts est de démontrer l’existence de transitions de phases congelantes donnant lieu à des quasi-cristaux qui sont modélisés, quand d ě 2, par des pavages de Wang apériodiques, c.-à-d., des sous-décalages de type fini n’ayant aucune configuration périodique. Quand d “ 1, les sous-décalages modélisant des quasi-cristaux ne sont pas de type fini car ils ne peuvent pas être apériodiques. Quand d “ 2, seules des expériences numériques attestent de l’existence de transitions de phases congelantes.
Il y a bien sûr d’autres questions qui se posent, par exemple celle de la robustesse des quasi-cristaux. Nous en formulerons certaines plus bas et l’un des buts de cette rencontre est assurément d’en faire émerger des nouvelles.
Nous sommes convaincus que l’interaction entre les trois domaines mentionnés ci-dessous alimentera chacun d’eux en nouvelles questions.
Mots-clés : sous-décalages de type fini en dimension plus grande que un, pavages de Wang, quasi-cristaux, transitions de phase congelantes, mesures de Gibbs, mesures d’équilibre, machines de Turing.
TALKS
Michael Baake (University of Bielefeld) Dynamical and spectral properties of some shift spaces of number-theoretic origin
Nishant Chandgotia (Tata Institute of Fundamental Research) An introduction to cluster swapping
Jean-René Chazottes (CNRS École polytechnique) Multidimensional symbolic dynamics and lattice models of quasicrystals
Daniel Coronel (Catholic University of Chile) Gibbs phase rule for intermittent maps
Shmuel Friedland (University of Illinois Chicago) Entropy, pressure, and densities for Zd-SOFT
Guilhem Gamard (LORIA Université de Lorraine) Wang tiles, the Kari tileset, and computation in tilings
Felipe García-Ramos (Autonomous University of San Luis Potosi) Topological aspects of discrete spectrum
Léo Gayral (Université Toulouse III-Paul Sabatier) Chaotic finite-range lattice models
Pascal Hubert (Aix-Marseille Université) Thue-Morse substitution and freezing phase transition
Bryna Kra (Northwestern University) Symmetries in symbolic dynamics
Tamara Kucherenko (The City College of New York) Phase transitions on one-dimensional symbolic systems
Sébastien Labbé (CNRS Université de Bordeaux) Metallic mean Wang tiles
Tom Meyerovitch (Ben Gurion University) Pressure, equilibrium measures, Gibbs measures, the variational princi- ple and the Lanford-Ruelle theorem in the context of sofic approximations
Jacek Miękisz (University of Warsaw) Homogeneity and stability of non-periodic ground states
Ronnie Pavlov (University of Denver) Approximating entropy/pressure for multidimensional shifts of finite type
Samuel Petite (Université de Picardie Jules Verne) Minimal configurations for Frenkel-Kontorova model on a quasicrystal
Lorenzo Sadun (University of Texas at Austin) Cohomology and tiling spaces
Shrey Sanadhya (Hebrew University of Jerusalem) Universality in dynamical systems
Siamak Taati (American University of Beirut) On the stability of quasicrystal models at positive temperature
Philippe Thieullen (Université de Bordeaux) Zero temperature convergence of Gibbs measures for locally a finite po- tential in a 2-dimensional lattice
Zizhu Wang (University of Electronic Science and Technology of China) Quantum foundations and the marginal problem
SHORT-TALKS
Rodrigo Bissacot (University of São Paulo) Multidimensional Contours à la Fröhlich-Spencer for Long-Range Ising Models
Christopher Cabezas (Université de Liège) Substitutive structures on general countable groups
Juliano Dos Santos Gonschorowski (Federal Technological University of Parana) Support stability of maximizing measures
Hyeeun Jang (Abilene Christian University) Directional Expansiveness for tiling dynamical
Jennifer Jones-Baro (Northwestern University) Eigenvalues and the stabilized automorphism group of minimal systems
Renaud Leplaideur (Université de la Nouvelle Calédonie) About stability under small perturbation in the selection process at zero temperature
Misato Ogawa (Ochanomizu University) Gibbs measures and Double Variational Principle for a potential depending on the first coordinate on XY model
Yaar Solomon (Ben-Gurion University of the Negev) Periodicity of joint co-tiles in Zd
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