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Research talks

In the way of Arnoux-Ito, we give a general geometric criterion for a subshift to be measurably conjugated to a domain exchange and to a translation on a torus. For a subshift coming from an unit Pisot irreducible substitution, we will see that it becomes a simple topological criterion. More precisely, we define a topology on $\mathbb{Z}^d$ for which the subshift has pure discrete spectrum if and only if there exists a domain of the domain exchange on the discrete line that has non-empty interior. We will see how we can compute exactly such interior using regular languages. This gives a way to decide the Pisot conjecture for any example of unit Pisot irreducible substitution.
Joint work with Shigeki Akiyama.
In the way of Arnoux-Ito, we give a general geometric criterion for a subshift to be measurably conjugated to a domain exchange and to a translation on a torus. For a subshift coming from an unit Pisot irreducible substitution, we will see that it becomes a simple topological criterion. More precisely, we define a topology on $\mathbb{Z}^d$ for which the subshift has pure discrete spectrum if and only if there exists a domain of the domain ...

37B10 ; 28A80 ; 11A63 ; 68R15

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Research talks

We will talk about recent work showing there are infinitely many primes with no $7$ in their decimal expansion. (And similarly with $7$ replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most $X^{1-c}$ elements less than $X$) which is typically vey difficult.
The proof relies on a fun mixture of tools including Fourier analysis, Markov chains, Diophantine approximation, combinatorial geometry as well as tools from analytic number theory.
We will talk about recent work showing there are infinitely many primes with no $7$ in their decimal expansion. (And similarly with $7$ replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most $X^{1-c}$ elements less than $X$) which is typically vey difficult.
The proof relies on a fun mixture of tools including Fourier analysis, Markov chains, Diophantine approximation, com...

11N05 ; 11A63

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Research talks

Given $x\in(0, 1]$, let ${\mathcal U}(x)$ be the set of bases $\beta\in(1,2]$ for which there exists a unique sequence $(d_i)$ of zeros and ones such that $x=\sum_{i=1}^{\infty}{{d_i}/{\beta^i}}$. In 2014, Lü, Tan and Wu proved that ${\mathcal U}(x)$ is a Lebesgue null set of full Hausdorff dimension. In this talk, we will show that the algebraic sum ${\mathcal U}(x)+\lambda {\mathcal U}(x)$, and the product ${\mathcal U}(x)\cdot {\mathcal U}(x)^{\lambda}$ contain an interval for all $x\in (0, 1]$ and $\lambda\ne 0$. As an application we show that the same phenomenon occurs for the set of non-matching parameters associated with the family of symmetric binary expansions studied recently by the first speaker and C. Kalle.
This is joint work with V. Komornik, D. Kong and W. Li.
Given $x\in(0, 1]$, let ${\mathcal U}(x)$ be the set of bases $\beta\in(1,2]$ for which there exists a unique sequence $(d_i)$ of zeros and ones such that $x=\sum_{i=1}^{\infty}{{d_i}/{\beta^i}}$. In 2014, Lü, Tan and Wu proved that ${\mathcal U}(x)$ is a Lebesgue null set of full Hausdorff dimension. In this talk, we will show that the algebraic sum ${\mathcal U}(x)+\lambda {\mathcal U}(x)$, and the product ${\mathcal U}(x)\cdot {\mathcal ...

28A80 ; 11A63 ; 37B10

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V

- 168 p.
ISBN 978-0-88385-557-7

Localisation : Loisir bastide

récréation mathématique # problème numérique # curiosités numérique # symbolisme des nombres

00A08 ; 11A63

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V

- 402 p.
ISBN 978-3-540-44141-0

Lecture notes in mathematics , 1794

Localisation : Collection 1er étage

combinatoire des mots # transcendance # dynamique symbolique # fractal # théorie ergodique # suite de Sturm # fraction continue # système dynamique # suite automatique

11B85 ; 11A55 ; 11A63 ; 11J70 ; 11Kxx ; 11R06 ; 28A80 ; 28Dxx ; 37Axx ; 37BXX ; 40A15 ; 68Q45 ; 68R15

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V

- 276 p.

Localisation : Réserve

analyse # cinématique # courbure # dynamique des systèmes # dérivée partielle # enseignement # intégrale # mathématique générale # mécanique # résistance des matériaux # statique # série trigonométrique # théorie des erreurs # vecteur # équation différentielle

00A05 ; 11A63 ; 11Axx ; 30Bxx ; 34-01

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y

- viii; 190 p.
ISBN 978-3-03719-142-2

EMS series of lectures in mathematics

Localisation : Ouvrage RdC (FOUR)

théorie des nombres # transcendance # nombre algébrique # théorème subspatial de Schmidt # fraction continue # expansion digitale # approximation Diophantienne

11-02 ; 11J81 ; 11A63 ; 11J04 ; 11J13 ; 11J68 ; 11J70 ; 11J87 ; 68R15

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V

- 113 p.

Localisation : Salle de manutention

dimension de Hausdorff # ensemble auto-affine # ensemble à similitude interne # fractals # matrice de structure # mesure de Hausdorff # système de numération # système de restes

11A63 ; 26E35 ; 28A80 ; 54B20

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