Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Collection Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Organizer(s) Rivat, Joël ; Tichy, Robert

Date(s) 23/11/2020 - 27/11/2020

linked URL https://www.chairejeanmorlet.com/2256.html

00:00:00 / 00:00:00

1 28

Classification and statistics of cut-and-project sets

We introduce a class of so-called "Ratner-Marklof-Strombergsson measures". These are probability measures supported on cut-and-project sets in Euclidean space of dimension d>1 which are invariant and ergodic for the action of the groups ASL_d(R) or SL_d(R) (affine or linear maps preserving orientation and volume). We classify the measures that can arise in terms of algebraic groups and homogeneous dynamics. Using the classification, we prove analogues of results of Siegel, Weil and Rogers about a Siegel summation formula and identities and bounds involving higher moments. We deduce results about asymptotics, with error estimates, of point-counting and patchcounting for typical cut-and-project sets. Joint work with Rene Ruehr and Yotam Smilansky.

Information about the video

Date of recording 23/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19690003
Cite this video Weiss, Barak (23/11/2020). Classification and statistics of cut-and-project sets. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19690003
URL https://dx.doi.org/10.24350/CIRM.V.19690003

Domain(s)

Dynamical Systems

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