## Jean-Morlet chair > TILING & DISCRETE GEOMETRY - 2017, SEMESTER 2

SCIENTIFIC PROGRAMMEA variety of events are planned for the semester which will start late August 2017 and will finish by mid February 2018. Additional events may still appear and will be displayed on the dedicated website.All events listed below will take place at Cirm-Luminy. |
PROGRAMME OF INVITATIONSLa Ville de Marseille (City Council) and CIRM (through the Labex Carmin initiative) grant special funding to each semester in order to extend full invitations to special guests. This programme is meant to support - in particular but not exclusively - longer stays of several weeks. It can also be used to cover travelling expenses, as well as board and lodging.http://akiyama-arnoux.weebly.com/invitations.html |

Tiling dynamical system gives a generalization of substitutive dynamical system. It gives a nice model of quasi-crystals, recognized as another new stable state of real materials. International experts on this topic will meet PhD students interested in this developing area. The week will focus in particular on Basic terminology in tiling and point sets, Spectral property of tiling dynamical systems, and Recurrence property of tilings.
http://akiyama-arnoux.weebly.com/school.html |

This conference will look at 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, quasi-crystal, computer science and discrete geometry. It will focus particularly on the areas of Recurrence properties of tiling and number theory, Spectral property of tiling dynamical systems, and Aperiodic tile set and quasi-crystals.
http://akiyama-arnoux.weebly.com/conference.html |

This workshop intends to focus on zero entropy systems and their self-inducing structures. Such systems arose as a model of physical phenomena in absolute zero temperature. A historically difficult problem is to show their stability. More precisely, we would like to prove the rareness of unstable configuration.
Key words: Billiards - Interval Exchange and Piecewise isometry - Discretized rotation http://akiyama-arnoux.weebly.com/small-group.html |

Bernoulli convolutions are probably the simplest and most well studied examples of self-similar measures with overlaps. They form a family of self-similar measures, each associated to some parameter lambda, but despite extensive study over the years there are very few classes of lambda for which we know whether the corresponding Bernoulli convolution is absolutely continuous.
We shall study Bernoulli convolutions associated to Salem numbers by first constructing a countable Markov shift associated with the corresponding set of finite polynomials, and then studying the structure of this shift and its recurrence properties. This project lies at the interface between dynamical systems, fractal geometry and number theory. http://akiyama-arnoux.weebly.com/pairs-1.html |

RESEARCH IN PAIRS
II(2122)Tree Shifts, Quasi-Similarity and their ApplicationsDates: 5-16 Feb 2018 |
It is well known that two dimensional subshift is much more involved than di-
mensional one, e.g., it is already difficult to compute the entropy of 2-dim subshift of finite type. In this research in pairs, we discuss possible applications of tree shifts and quasi self-similar tilings, both of which have intermediate complexity. We expect their possible applications in a wide range of problems, such as semi- group action via two different algorithms, space filling curve property of fractal tiles, and construction of quasi-self similar polygonal tilings. https://akiyama-arnoux.weebly.com/pairs-2.html |

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