THERMOGAMAS

Forthcoming speakers

2025/09/30:
Loren Coquille (Université de Grenoble Alpes)
Title: Extremal Ising Gibbs States on hyperbolic lattices

Abstract: I will explain how to exhibit an uncountable family of extremal (non-automorphism invariant !) Gibbs measures of the low temperature Ising model on regular tilings of the hyperbolic plane. These states arise as low temperature perturbations of local ground states having a sparse enough set of frustrated edges, the sparseness being measured in terms of the isoperimetric constant of the graph. Deducing extremality of Series-Sinai states (having one interface along a continuous geodesic of H^2) amounts to answer a nice question about hyperbolic billiards.

Hebert Milton Ccalle Maquera (Universidade de Saõ Paulo : Saõ Carlos)
Title: Self-Consistent Transfer Operator for heterogeneous networks

Abstract: In this talk, I will present statistical properties of heterogeneous systems modeled using graphons, which represent the continuum limit of large networks, also known as the thermodynamic limit. This limit is governed by a nonlinear operator called the Self-Consistent Transfer Operator. Suitable functional spaces are constructed to formulate a fixed point problem and study its stability. This approach combines operator theory and graph limits to analyze emergent behaviors in complex networks.
2025/10/14:
Joäo Tiago Assuncäo Gomes (Universidade Federal do Recôncavo da Bahia)
Title: Maximizing measures for countable alphabet shifts via blur shift spaces

Abstract: For upper semi-continuous potentials defined on shifts over countable alphabets, we ensure sufficient conditions for the existence of a maximizing measure. We resort to the concept of blur shift as a compactification method for countable alphabet shifts consisting of adding new symbols given by blurred subsets of the alphabet.
This is joint work with Eduardo Garibaldi and Marcelo Sobottka.

Sébastien Labbé (Université de Bordeaux, Labri)
Title: A family of metallic mean Wang tiles

Abstract: In this talk, we present a family of metallic mean Wang tiles. This is a family of aperiodic sets of Wang tiles (unit squares with labeled edges) whose dynamics involves the positive root of the polynomial $x^2-nx-1$. This root is sometimes called the $n$-th metallic mean, and in particular, the golden ratio when $n=1$ and the silver ratio when $n=2$. The metallic mean Wang shifts are self-similar, aperiodic, minimal and uniquely ergodic. When n=1, the set contains 16 tiles which are equivalent to the Ammann set of Wang tiles deduced from the Ammann A2 L-shapes.
2025/10/28:
Nicolas Bédaride (Université d'Aix Marseille.)
Title: Phase transition and Thue Morse substitution

Abstract: In this talk we will review some results related to previous work of Bruin, Leplaideur and explain how to improve them. We consider as dynamical system the full shift on a two letter alphabet, and the potential will be related to the distance to the subshift defined by Thue Morse substitution. We will look at the question of existence of a phase transition.

Douglas Coates (Universidade Federal do Rio de Janeiro UFRJ)
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2025/11/18:
Jérôme Buzzi (Université Paris Saclay)
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Bernat Bassols Cornudella (Imperial College London)
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2025/11/25:
Noé Cuneo (??)
Title: Decoupled probability measures on shift spaces: some large deviation aspects

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Rodrigo Bissacot (University of São Paulo, IME-USP)
Title: Length-Type Phase Transitions and Extendable Shift Maps on Generalized Countable Markov Shifts

Abstract: We consider transitive countable Markov shifts and their corresponding generalized countable Markov shifts (compactifications which are the spectrum of Exel-Laca algebras). These spaces are given by the usual countable Markov shift union with a special set of finite allowed words (including empty words, where the shift map a priori is not defined), $X_A = \Sigma_A \cup Y_A$, where both S_A and Y_A are dense subspaces of X_A. We review some recent results about when we can continuously extend the shift map from $\Sigma_A$ to $X_A$, and also presents an example where a potential $f$ for which there exists a $\beta_c$ such that $\beta f$-conformal measures give full mass to the space $\Sigma_A$ when $\beta < \beta_c$, while for $\beta > \beta_c$ the mass is fully concentrated in $Y_A$.

References:
[1] Extendable Shift Maps and Weighted Endomorphisms on Generalized Countable Markov Shifts. Rodrigo Bissacot, Iván Díaz-Granados, and Thiago Raszeja. arXiv:2506.07487, (2025).
[2] Thermodynamic Formalism for Generalized Markov Shifts on Infinitely Many States Rodrigo Bissacot, Ruy Exel, Rodrigo Frausino, and Thiago Raszeja. arXiv:1808.00765, (2022).
2025/12/09:
Christian da Silva Rodrigues (Universidade Estadual de Campinas, IMECC)
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2025/12/16:
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Past speakers

2025/09/16:
Matheus Manzatto de Castro (University of New South Wales)
PDF Title: Building thermodynamic formalism for hyperbolic random dynamical systems

Abstract: We present conditions under which thermodynamic formalism can be built for families of random hyperbolic diffeomorphisms. We also establish the uniqueness of equilibrium states and their statistical properties. This is joint work with Lucas Amorim, Benoît Saussol and Sandro Vaienti.

Jean-René Chazottes (Ecole Polytechnique)
PDF Title: Phase Transitions to Aperiodic Order in Lattice Systems

Abstract: I will review recent results on freezing phase transitions (in arbitrary dimension) and discuss some open questions. The term freezing refers to the phenomenon whereby, for a given potential, there exists a strictly positive critical temperature $T_c$ such that the sets of equilibrium states at any two temperatures above $T_c$ are distinct, while they coincide for all temperatures below $T_c$.
2025/06/17:
Samuel Petite (Amiens)
PDF ZOOM Title: Language stable shifts

Abstract: language stable shifts form a rich class of shifts that was recently introduced by V. Cyr and B. Kra. This family contains many classical examples of subshifts, of various complexities ranging from systems of strictly positive entropy, such as subshift finite-type (SFT), to systems of low complexity, such as shifts of linear complexity. They are generic among the family of shifts. In this talk, we present some of their properties, in particular those concerning the cellular automata preserving them and their invariant measures

Cleber Fernando Colle (UFABC)
PDF ZOOM Title: Nonexpansive subspaces and Nivat's conjecture

Abstract: In his Ph.D. thesis, Michal Szabados showed that every configuration with low pattern complexity can be decomposed into a finite sum of periodic configurations. In this webinar, I will present some results and open problems related to nonexpansive subspaces, periodic decompositions, and Nivat's conjecture - a natural generalization of the Morse–Hedlund theorem to the two-dimensional case.
2025/06/03: Sandro Vaienti (Marseille)
PDF ZOOM Title: Quasi limit theorems for open systems

Abstract: We investigate deterministic and random open dynamical systems (with holes), and we give limit theorems characterizing the converge to the equilibrium state on the surviving set

Ali Messaoudi (UNESP)
PDF ZOOMTitle: Substitution dynamical systems on infinite alphabets

Abstract: A substitution is a map from an alphabet A to the set of finite words in A. To any substitution we can naturally associate a symbolic dynamical system that is well studied in the literature when the alphabet is a finite set and connected to several areas such as ergodic theory and number theory among others. In this work, we study ergodic and geometric properties of dynamical systems associated to substitutions in infinite alphabets. This study involves finite and infinite invariant measures, countably infinite matrices and Rauzy Fractals.
2025/05/20:
Mathieu Sablik (Toulouse)
PDF ZOOM Title: Characterization of zero-noise limit measures for cellular automata

Abstract: For a given cellular automaton F , define $F_\epsilon$ its perturbation by a noise of size $\epsilon$ and denote by $\pi_\epsilon$ one of its invariant measure. The zero-noise limit measures are the accumulation points of $\pi_\epsilon$ as $\epsilon$ goes to 0. Zero-noise limit measure represent invariant measures ``with a physical meaning'' because they appear even with a little noise.

We will illustrate this notion with some examples and look at which set can be realized as the set of zero-noise limit measures of a CA.

Marcelo Sobottka (UFSC)
PDF ZOOM Title: Blur Shifts

Abstract: Shift spaces are dynamical systems usually considered in symbolic dynamics. Given a nonempty set of symbols $A$ (alphabet), the full shift is defined as the space of all sequences over the alphabet $A$, $$A^\mathbb{N}:=\{(x_i)_{i\in\mathbb{N}}:\ x_i\in A\ \forall i\in\mathbb{N}\}.$$ In $A^\mathbb{N}$, we consider the prodiscrete topology and the shift map $\sigma:A^\mathbb{N}\to A^\mathbb{N}$ given by $$\sigma\big((x_i)_{i\in\mathbb{N}}\big)=(x_{i+1})_{i\in\mathbb{N}}.$$ A shift space is any subspace $\Lambda\subset A^\mathbb{N}$ that is closed in $A^\mathbb{N}$ and such that $\sigma(\Lambda)\subset\Lambda$.

When $A$ is a finite set, shift spaces are compact, and there is an extensive theory about them. On the other hand, if $A$ is infinite, the loss of compactness (and often even of local compactness) introduces several challenges to their study.

In this webinar I will present a new type of shift spaces, called blur shifts, that were proposed in a joint work with Tadeu Zavistanovicz de Almeida. These spaces are constructed from classical shift spaces by selecting certain infinite sets of symbols to be represented by a new symbol and then defining a suitable topology. In particular, blur shifts can be used as a compactification scheme for classical shift spaces. Finally, we present some examples of applications of blur shifts.
2025/05/06:
Eduardo Garibaldi (UNICAMP)
Title: Equilibrium states and statistical properties for intermittent maps

Léo Gayral (Nancy)
PDF Title: Robustness to Perturbations of the Gibbs Potential:

Philippe Thieullen (Bordeaux)
PDF Title: Genericity in ergodic optimization

	THERMOGAMAS
	Thermodynamical and geometrical approach to multi dimensional aperiodic structures