Noticias en español
On subsets with no arithmetic progressions
ABSTRACT For $N\in \mathbb{N}$, let $\nu(N)$ be the maximal cardinality of a subset of \{1,\ldots,N\} that contains no arithmetic progression of length 3. Finding upper and lower bounds for $\nu(N)$ has been a challenging problem for decades. In this talk I will survey this problem and present a proof of a theorem by Behrend in the 40’s, that gave a surprising lower bound to $\nu(N)$.
Read MoreUnderstanding physical mixing processes via transfer operator approach
ABSTRACT: Industrial and chemical mixing processes of various kinds occur throughout nature and are vital in many technological applications.In the context of discrete dynamical systems, the transfer operator approach has been shown as a powerful tools from both theoretic and numerical viewpoint. In this talk, I will use a toy model (i.e., the one dimensional stretch and fold map) as an example to provide a brief introductionon the relationships between the spectral properties of the associated transfer operator and the estimations of the optimal mixing rate of the mixing process. Moreover,...
Read MoreComputing the entropy of multidimensional subshifts of finite type
ABSTRACT : Multidimensional subshifts of finite type are discrete dynamical systems as a set of colorings of an infinite regular grid with elements of a finite set A together with the shift action. The set of colorings is defined by forbidding a finite set of patterns all over the grid (also called local rules). The most simple and most considered grids of this type are Z2 and more generally Zd for d = 1. In this case, one can consider a coloring as a bi-dimensional and infinite word on the alphabet A. They are notably involved in statistical physics in the study of so-called lattice models....
Read MoreRestrictions on the group of automorphisms preserving a minimal subshift
ABSTRACT : A subshift is a closed shift invariant set of sequences over a finite alphabet. An automorphism is an homeomorphism of the space commuting with the shift map. The set of automorphisms is a countable group generally hard to describe. We will present in this talk a survey of various restrictions on these groups for zero entropy minimal subshifts.
Read MoreDecidability of the isomorphism and the factorization for minimal substitution subshifts
ABSTRACT Classification is a central problem in the study of dynamical systems, in particular for families of systems that arise in a wide range of topics. Hence it is important to have algorithms deciding wether a dynamical system have some given property. Let us mention subshifts of finite type that appear, for example, in information theory, hyperbolic dynamics, $C^*$-algebra, statistical mechanics and thermodynamic formalism. The most important and longstanding open problem for this family originates in [Williams:1973] and is stated in [Boyle:2008] as follows : Classify subshifts of...
Read MoreOn the action of the semigroup of non singular integral matrices on $\R^n$
Abstract. Let Γ be the multiplicative semigroup of all n × n matrices with integral entries and nonzero determinant. Let 1 ≤ p ≤ n−1 and V = Rnp = Rn ⊕···⊕Rn (p copies). Consider the action of Γ on V , given by the natural action on each component, by matrix multiplication on the left. Then for x= (x1, . . . , xp) ∈ V , the Γ-orbit is dense in V if and only if there is no linear combination pj=1 λjxj, with λj ̸= 0 for some j, which is a rational vector in Rn; in fact the assertion holds also for the orbit of the subgroup SL(n, Z) that is contained in Γ. When x is such that the...
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