### Sebastián Barbieri

**Title: Topological Markov properties**

**Abstract:** It is known that a subshift satisfies the pseudo-orbit tracing property (POTP) if and only if it is an SFT. I shall present a series of properties for subshifts which are weaker than being an SFT, and which are inspired in the POTP. I will provide examples and present two results on these properties that link asymptotic pairs and topological entropy.

### Raimundo Briceño

**Title: Shifts of finite type as constraint satisfaction problems**

**Abstract:** A constraint satisfaction problem (CSP) is a mathematical question involving a set variables and a domain of values, where the main goal is to find a value assignment to the variables that simultaneously satisfies a number of given constraints. On the other hand, a shift of finite type (SFT), one of the most studied objects in symbolic dynamics, can be understood as the space of solutions of a particular class of CSP, where the set of variables is some countable group and the domain of values is a finite alphabet.

In this talk, we will explore this and deeper connections between the theory of CSPs and the theory of SFTs. First, we will view SFTs as a particular space of homomorphisms between relational structures and then proceed to relate notions of dismantlability, connectedness of the space of solutions, mixing, and finite duality. Time permitting, we will also describe a hierarchy that interpolates two well-known mixing properties that have many applications in symbolic dynamics (namely, strong irreducibility and the existence of a safe symbol) and explain how they fit in the previous framework.

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### Ben Call

**Title: The K Property for Some Systems with Unique Equilibrium States**

**Abstract:** The \(K\) property is a mixing property stronger than mixing of all orders and weaker than Bernoulli. Ledrappier reduced the problem of showing the \(K\) property to one of establishing uniqueness of equilibrium states in the Cartesian product of a system with itself. I will present some easy to state conditions that establish the \(K\) property for a wide class of equilibrium states. These conditions are based on machinery developed by Climenhaga and Thompson.

### Van Cyr

**Title: Subshifts, complexity, and Boshernitzan’s condition.**

**Abstract:** When is a minimal subshift uniquely ergodic? Boshernitzan found a condition on the decay of measure of cylinder sets that implies unique ergodicity. In this talk we investigate how high the complexity of a subshift satisfying Boshernitzan’s condition (B) can be.

### Sebastián Donoso

**Title: The complexity of \(\mathcal{S}\)-adic subshifts.**

**Abstract:** A \(\mathcal{S}\)-adic subshift is a subshift generated by a sequence of morphisms between (eventually different), finite alphabets. I will show some recent ideas developed in a joint work with F. Durand, S. Petite and A. Maass to give upper bounds for the complexity of \(\mathcal{S}\)-adic subshifts. If time permits, I will mention some applications. For instance we give conditions so that a \(\mathcal{S}\)-adic subshift has a sublinear complexity.

### Bastián Espinoza

**Title: Asymptotic pairs in topological finite rank systems**

**Abstract:** Recently, it was proved that transitive subshifts of non superlinear complexity have virtually \(\mathbb{Z}\) groups of automorphisms. I will present a generalization of this result to all finite topological rank subshifts and some applications of the underlying technique to related problems.

### Joshua Frisch

**Title: Strong Amenability, The ICC property, and Symbolic Dynamics**

**Abstract:** I will define proximality and strong amenability, notions from Topological dynamics, and explain how symbolic dynamical ideas allow one to classify the strongly amenable groups. This is joint work with Omer Tamuz and Pooya Vahidi Ferdowsi.

### Ricardo Gómez

**Title: Loop systems and analytic combinatorics**

**Abstract:** Loop systems are a certain class of Markov shifts that are represented by power series with non-negative coefficients. They have been a useful tool to study isomorphisms of Markov shifts. In this talk, we will focus on loop systems of finite type, from points of view of analytic combinatorics. We will state some recent problems and results of both dynamic and analytic combinatorial nature.

### Kevin McGoff

**Title: Ubiquity of entropies of intermediate factors**

**Abstract: **In this talk I will describe recent joint work with Ronnie Pavlov. We consider the setting of topological dynamical systems \((X,S)\), where \(X\) is a compact metrizable space and \(S\) denotes an action of a countable amenable group \(G\) on \(X\) by homeomorphisms.

For two such systems \((X,T)\) and \((Y,S)\) and a factor map \(\pi : X \rightarrow Y\), an intermediate factor is a topological dynamical system \((Z,R)\) for which \(\pi\) can be written as a composition of factor maps \(\psi : X \rightarrow Z\) and \(\varphi : Z \rightarrow Y\).

Our main result establishes that for any countable amenable group \(G\), for any \(G\)-subshifts \((X,T)\) and \((Y,S)\), and for any factor map \(\pi :X \rightarrow Y\), the set of entropies of intermediate subshift factors is dense in the interval \([h(Y,S), h(X,T)]\). As corollaries, we also prove that the set of entropies of intermediate zero-dimensional factors is equal to the interval \([h(Y,S), h(X,T)]\), and even when \((X,T)\) is a zero-dimensional \(G\)-system, the set of entropies of its zero-dimensional factors is equal to the interval \([0, h(X,T)]\). Our proofs rely on a generalized Marker Lemma for countable amenable groups that may be of independent interest.

### Etienne Moutot

**Title: Nivat’s conjecture holds in the uniformly recurrent case**

**Abstract:**

We continue to develop algebraic tools introduced by Kari and Szabados to tackle Nivat’s conjecture, stating that any two-dimensional with pattern complexity \(P(m,n)\leq m \cdot n\) (called a low complexity configuration) is periodic.

By using ideas introduced by Cyr and Kra we are able to prove that any low-complexity configuration contains a periodic one in its orbit closure.

This have two interesting consequences: Nivat’s conjecture holds for uniformly recurrent configurations, and the domino problem is decidable for low-complexity subshifts.

### Ronnie Pavlov

**Title: Subshifts with slow forbidden word growth**

**Abstract:** I will give a brief outline of some recent work in which I treat subshifts with infinite forbidden lists, but where the number of forbidden words grows “slowly enough” as a function of the length. Such subshifts have many nice behaviors close to those of subshifts of finite type, including existence of a unique MME with the K-property and Gibbs bounds on measure-theoretically large portions of the space. The main tool in our proofs is a sort of measure-theoretic specification property, which I will also briefly describe.

### Samuel Petite

**Title: S-adic subshifts and finite topological rank minimal Cantor systems**

**Abstract:** Minimal Cantor systems of finite topological rank (that can be represented by a Bratteli-Vershik diagram with a uniformly bounded number of vertices per level) are known to have dynamical rigidity properties. In a common work with S. Donoso, F. Durand and A. Maass, we establish that such expansive systems define the same class of systems, up to topological conjugacy, as primitive and recognizable S-adic subshifts. This is done establishing necessary and sufficient conditions for a minimal subshift to be of finite topological rank. As an application, we show that minimal subshifts with non-superlinear complexity (like all classical zero entropy examples) have finite topological rank.

### Ayse Sahin

**Title: Low complexity dynamics and the Loosely Bernoulli Property**

**Abstract:** TBA

### Scott Schmieding

**Title: Stabilized automorphism groups**

**Abstract:** Given a subshift, the automorphism group is the group consisting of all self-conjugacies of the subshift. We’ll talk about a certain stabilization of the automorphism group, and two main results: that for full shifts on certain size symbol sets these stabilized groups are not isomorphic, and that for full shifts, this stabilized group is an extension of a free abelian group by an infinite simple group. Joint work with Yair Hartmand and Bryna Kra.

### Omer Tamuz

**Title: Characteristic measures of symbolic dynamical systems, with Joshua Frisch**

**Abstract:** TBA

### Rodrigo Treviño

**Title: Quantitative weak mixing for random substitution tilings**

**Abstract:** I will talk about some very recent work on weak mixing which extends results and ideas of Bufetov-Solomyak to random substitution tilings in dimensions greater than 1. Warning: I will say the words “renormalization”, “cohomology”, “deformations” and “Lyapunov exponents”, but that should not scare you away.