Français
Classification and statistics of cut-and-project sets
Virtualconference
Authors : Weiss, Barak (Author of the conference)
CIRM (Publisher )
CIRM (Publisher )
Loading the player...
|
Abstract :
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.
MSC Codes : |
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/12/2020 Conference Date : 23/11/2020 Subseries : Research talks arXiv category : Dynamical Systems Mathematical Area(s) : Number Theory ; Mathematical Physics ; Probability & Statistics ; Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:49:22 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-23_Barak Weiss.mp4 
|
Information on the Event
Event Title : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireEvent Organizers : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Event Year : 2020 Event URL : https://www.chairejeanmorlet.com/2256.html
Citation Data
DOI : 10.24350/CIRM.V.19690003Cite this video as: Weiss, Barak (2020). Classification and statistics of cut-and-project sets. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19690003 URI : http://dx.doi.org/10.24350/CIRM.V.19690003 |
See Also
- [Virtualconference] Improved cap constructions, and sets without arithmetic progressions / Author of the conference Elsholtz, Christian.
- [Virtualconference] On S-Diophantine Tuples / Author of the conference Ziegler, Volker.
- [Virtualconference] Poisson-generic points / Author of the conference Weiss, Benjamin.
- [Virtualconference] On binary quartic Thue equations and related topics / Author of the conference Walsh, Gary.
- [Virtualconference] Multidimensional continued fractions and symbolic codings of toral translations / Author of the conference Thuswaldner, Jörg.
- [Virtualconference] On generalised Rudin-Shapiro sequences / Author of the conference Stoll, Thomas.
- [Virtualconference] Pseudorandomness at prime times and digits of Mersenne numbers / Author of the conference Shparlinski, Igor.
- [Virtualconference] Zaremba's conjecture and growth in groups / Author of the conference Shkredov, Ilya.
- [Virtualconference] Large values of the remainder term of the prime number theorem / Author of the conference Pintz, Janos.
- [Virtualconference] Number of solutions to a special type of unit equations in two unknowns / Author of the conference Pink, István.
- [Virtualconference] Bertini and Northcott / Author of the conference Pazuki, Fabien.
- [Virtualconference] Dynamical irreducibility of polynomials modulo primes / Author of the conference Ostafe, Alina.
- [Virtualconference] Diophantine exponents, best approximation and badly approximable numbers / Author of the conference Moshchevitin, Nikolay.
- [Virtualconference] Some interactions between number theory and multifractal analysis / Author of the conference Martin, Bruno.
- [Virtualconference] The sum-of-digits function in linearly recurrent number systems and almost primes / Author of the conference Madritsch, Manfred.
- [Virtualconference] Fibonacci numbers and repdigits / Author of the conference Luca, Florian.
- [Virtualconference] Skolem's conjecture and exponential Diophantine equations / Author of the conference Hajdu, Lajos.
- [Virtualconference] Equidistribution of roots of unity and the Mahler measure / Author of the conference Habegger, Philipp.
- [Virtualconference] Effective finiteness results for diophantine equations over finitely generated domains / Author of the conference Györy, Kalman.
- [Virtualconference] Constructing abelian extensions with prescribed norms / Author of the conference Frei, Christopher.
- [Virtualconference] $D(n)$-sets with square elements / Author of the conference Dujella, Andrej.
- [Virtualconference] (Logarithmic) densities for automatic sequences along primes and squares / Author of the conference Drmota, Michael.
- [Virtualconference] Modularity of the q-Pochhammer symbol and application / Author of the conference Drappeau, Sary.
- [Virtualconference] Higher moments of primes in intervals and in arithmetic progressions, II / Author of the conference De la Bretèche, Régis.
- [Virtualconference] The Rudin-Shapiro function in finite fields / Author of the conference Dartyge, Cécile.
- [Virtualconference] Independence of actions of (N,+) and (N,×) and Sarnak's Möbius disjointness conjecture / Author of the conference Bergelson, Vitaly.
- [Virtualconference] On some diophantine equations in separated variables / Author of the conference Bérczes, Attila.
Bibliography
