JeanMorlet chair > shigeki akiyama  pierre arnoux (semester 2, 2017)
Description
In this conference, we are interested in the recent developments around the mathematical theory of tilings and its recurrence properties, which have a lot of connections with other areas like number theory, dynamical system, quasicrystal, computer science and discrete geometry. We intend to focus particularly on the following areas:
Recurrence properties of tiling and number theory There has been a series of recent developments on bounded remainder sets involving various methods (dynamical, topological, number theoretical, see [2, 3]). We plan to discuss and compare different approaches involved there. We would like to consider frequencies and recurrence properties in tiling spaces, by focusing on variants of ergodic averages in this framework. Spectral property of tiling dynamical systems Related to the first theme, we shall discuss the long standing Pisot substitution conjecture, the main remaining problem in this area. Pure discreteness of tiling is essentially the strongest recurrence property we can have, which is equivalent to almost periodicity of the associated point set (c.f. [6, 1]). On this occasion we wish to merge people working in these areas to produce possible breakthroughs. Aperiodic tile set and quasicrystals An aperiodic hexagonal monotile was found by TaylorSocolar [5]. More recently the number of aperiodic tile set of Wang tiles reached its theoretical minimum 11 with JeandelRao [4]. Their recurrence properties are quite fascinating and we shall discuss them as models of quasicrystals. References [1] S. Akiyama and J.Y. Lee, Algorithm for determining pure pointedness of selfaffine tilings, Adv. Math. 226 (2011), no. 4, 28552883. [2] A. Haynes, M. Kelly, and B. Weiss, Equivalence relations on separated nets arising from linear toral flows, Proc. Lond. Math. Soc. (3) 109 (2014), no. 5, 12031228. [3] A. Haynes, H. Koivusalo, L.Sadun, and J. Walton, Gaps problems and frequencies of patches in cut and project sets, ArXiv:1411.0578. [4] E. Jeandel and M. Rao, An aperiodic set of 11 wang tiles, ArXiv:1506:6492. [5] J. E. S. Socolar and J. M. Taylor, An aperiodic hexagonal tile, Journal of Combinatorial Theory 18 (2011), 22072231. [6] B. Solomyak, Dynamics of selfsimilar tilings, Ergodic Theory Dynam. Systems 17 (1997), no. 3, 695738. 
Scientific Committee
Organizing Committee

Speakers
 Michael Baake (Bielefeld University)  Autocorrelation and diffraction via renormalisation Part II: Extensions and generalisations
 Artemi Berlinkov (BarIlan University)  Singular substitutions of constant length
 Valérie Berthé (Université Paris Diderot)  Dimension groups and recurrence for tree subshifts (pdf)
 Adnene Besbes (Université Paris Diderot)  Thermodynamic formalism On Aperiodic Linearly Repetitive Tilings (pdf)
 Alexander I. Bufetov (AixMarseille Université)  Holder estimates for the spectrum of substitution systems and translation flows
 Danilo Antonio Caprio (UNESPIBILCE Brazil)  Dynamics of stochastic Bratteli diagrams
 Julien Cassaigne (AixMarseille Université)  A set of sequences of complexity 2n+1 (pdf)
 Thierry Coulbois (AixMarseille Université)  Tree substitutions and Rauzy fractals (pdf)
 Karma Dajani (Utrecht University)  Algebraic sums and products of univoque bases  VIDEO
 David Damanik (Rice University)  The Fibonacci Trace Map  VIDEO
 Hiromi Ei (Hirosaki University)  Tilings associated to the nearest integer complex continued fractions over imaginary quadratic fields  (pdf)
 Thomas Fernique (Université Paris 13)  Local rules for planar tilings
 Uwe Grimm (Open University)  Autocorrelation and diffraction via renormalisation  Part I: Concepts and examples in one dimension
 Pierre Guillon (AixMarseille Université)  Deterministic and expansive directions in 2D subshifts
 Alan Haynes (University of Houston)  Bounded remainder sets for rotations on padic solenoids  VIDEO
 Steven Hurder (University of Illinois at Chicago)  Wild solenoids and tilings  (pdf)
 Dong Han Kim (Dongguk University)  On the higherdimensional threedistance theorem
 Henna Koivusalo (University of Vienna)  Cut and project sets, linear repetition of patterns, and the Littlewood conjecture
 Sébastien Labbé (LaBRI Bordeaux)  On the dynamics of JeandelRao tilings  (pdf)
 Paul Mercat (AixMarseille Université)  Yet another characterization of the Pisot conjecture  VIDEO
 Yasushi Nagai (Montanuniversität Leoben)  A generalization of local derivability and its consequences
 Wolfgang Steiner (Université Paris Diderot)  Recognizability for sequences of morphisms  VIDEO