Equidistribution, fractal measures and arithmetic

Project Information

EFMA

Grant agreement ID: 803711

DOI 10.3030/803711

Project closed

EC signature date 30 August 2018

Start date 1 October 2018

End date 31 March 2024

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 334 109,00

EU contribution € 1 334 109,00

Coordinated by

THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
United Kingdom

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (38)

Winding of geodesic rays chosen by a harmonic measure

Author(s): Timothée Bénard
Published in: Math. Ann., 2024, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-023-02754-z

Mixing time of the Chung–Diaconis–Graham random process

Author(s): Sean Eberhard, Péter P. Varjú
Published in: Probability Theory and Related Fields, Issue 179/1-2, 2021, Page(s) 317-344, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-020-01009-1

Dyadic Approximation in the Middle-Third Cantor Set

Author(s): Demi Allen, Sam Chow, Han Yu
Published in: Sel. Math. New Ser., 2023, ISSN 1022-1824
Publisher: Birkhauser Verlag
DOI: 10.1007/s00029-022-00814-x

Babai's conjecture for high-rank classical groups with random generators

Author(s): Sean Eberhard, Urban Jezernik
Published in: Inventiones mathematicae, 2022, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-021-01065-x

Equidistribution of mass for random processes on finite-volume spaces

Author(s): Timothée Bénard
Published in: Isr. J. Math., 2023, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-022-2422-3

Bernoulli decomposition and arithmetical independence between sequences

Author(s): HAN YU
Published in: Ergodic Theory and Dynamical Systems, Issue 41/5, 2021, Page(s) 1590-1600, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2019.117

Fourier decay of self-similar measures and self-similar sets of uniqueness

Author(s): Péter P. Varjú, Han Yu
Published in: Anal. PDE, Issue 15, 2022, Page(s) 843-858, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2022.15.843

Dimensions of the popcorn graph

Author(s): Haipeng Chen, Jonathan M. Fraser, Han Yu
Published in: Proceedings of the American Mathematical Society, 2022, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/15729

Bernoulli convolutions with Garsia parameters in (1,√2] have continuous density functions

Author(s): Han Yu
Published in: Proceedings of the American Mathematical Society, 2022, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/15971

Optimal Diophantine Exponents for SL(n)

Author(s): Subhajit Jana, Amitay Kamber
Published in: Advances in Mathematics, Issue 443, 2024, Page(s) 1-58, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2024.109613

The apparent structure of dense Sidon sets

Author(s): Sean Eberhard, Freddie Manners
Published in: Electron. J. Combin., 2023, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/11191

A note on dyadic approximation in Cantor's set

Author(s): Demi Allen, Simon Baker, Sam Chow, Han Yu
Published in: Indagationes Mathematicae, 2023, ISSN 0019-3577
Publisher: Elsevier BV
DOI: 10.1016/j.indag.2022.11.002

Testability in group theory

Author(s): Oren Becker, Alexander Lubotzky, Jonathan Mosheiff
Published in: Israel J. Math., Issue 256, 2023, Page(s) 61-90, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-023-2503-y

Probabilistically nilpotent groups of class two

Author(s): Sean Eberhard, Pavel Shumyatsky
Published in: Math. Ann., 2024, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-023-02567-0

Times two, three, five orbits on T2

Author(s): Han Yu
Published in: Advances in Mathematics, 2022, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108289

Effective density of non-degenerate random walks on homogeneous spaces

Author(s): Wooyeon Kim, Constantin Kogler
Published in: International Mathematics Research Notices, 2024, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnae011

A nonlinear version of Bourgain's projection theorem

Author(s): Pablo Shmerkin
Published in: J. Eur. Math. Soc., 2023, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1283

Fractal projections with an application in number theory

Author(s): Han Yu
Published in: Ergod. Th. & Dynam. Sys., 2023, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2022.2

Cut-off phenomenon for the ax+b Markov chain over a finite field

Author(s): Emmanuel Breuillard, Péter P. Varjú
Published in: Probab. Theory Relat. Fields, Issue 184, 2022, Page(s) 85-113, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-022-01161-w

Sharply transitive sets in PGL 2 ( K )

Author(s): Sean Eberhard
Published in: Advances in Geometry, Issue 21/4, 2021, Page(s) 611-612, ISSN 1615-715X
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/advgeom-2021-0029

Non-Salem sets in metric Diophantine approximation

Author(s): Kyle Hambrook, Han Yu
Published in: International Mathematics Research Notices, 2022, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnac206

The characteristic polynomial of a random matrix

Author(s): Sean Eberhard
Published in: Combinatorica, 2022, ISSN 0209-9683
Publisher: Springer Verlag
DOI: 10.1007/s00493-020-4657-0

On the metric theory of inhomogeneous Diophantine approximation: An Erdős-Vaaler type result

Author(s): Han Yu
Published in: Journal of Number Theory, Issue 224, 2021, Page(s) 243-273, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2021.01.012

Additive properties of numbers with restricted digits

Author(s): Han Yu
Published in: Algebra & Number Theory, 2021, ISSN 1937-0652
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/ant.2021.15.1283

On the dimension of Bernoulli convolutions for all transcendental parameters

Author(s): Varjú
Published in: Annals of Mathematics, Issue 189/3, 2019, Page(s) 1001, ISSN 0003-486X
Publisher: Princeton University Press
DOI: 10.4007/annals.2019.189.3.9

Low-degree learning and the metric entropy of polynomials

Author(s): Alexandros Eskenazis, Paata Ivanisvili, Lauritz Streck
Published in: Discrete Analysis, 2023, ISSN 2397-3129
Publisher: Alliance of Diamond Open Access Journals
DOI: 10.48550/arxiv.2203.09659

Fusions of tensor powers of Johnson schemes

Author(s): Sean Eberhard, Mikhail Muzychuk
Published in: Algebraic Combinatorics, 2023, ISSN 2589-5486
Publisher: Comb. Consort. (TCC)
DOI: 10.5802/alco.271

An improvement on Furstenberg's intersection problem

Author(s): Han Yu
Published in: Transactions of the American Mathematical Society, 2021, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8410

Exponential multiple mixing for commuting automorphisms of a nilmanifold

Author(s): Timothée Bénard, Péter P. Varjú
Published in: Ergodic Theory and Dynamical Systems, 2023, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2023.73

Hamming sandwiches

Author(s): Sean Eberhard
Published in: Combinatorica, 2023, ISSN 0209-9683
Publisher: Springer Verlag
DOI: 10.1007/s00493-023-00004-z

Random walks with bounded first moment on finite-volume spaces

Author(s): Timothée Bénard, Nicolas de Saxcé
Published in: Geom. Funct. Anal., 2022, ISSN 1016-443X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00039-022-00607-6

On the metric theory of multiplicative Diophantine approximation

Author(s): Han Yu
Published in: Journal d'Analyse Mathématique, 2023, ISSN 0021-7670
Publisher: Magnes Press
DOI: 10.1007/s11854-022-0266-8

An asymptotic for the Hall--Paige conjecture

Author(s): Sean Eberhard, Freddie Manners, Rudi Mrazović
Published in: Advances in Mathematics, 2022, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108423

Digit expansions of numbers in different bases

Author(s): Stuart A. Burrell, Han Yu
Published in: Journal of Number Theory, Issue 226, 2021, Page(s) 284-306, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2021.01.003

Transversals in quasirandom latin squares

Author(s): Sean Eberhard, Freddie Manners, Rudi Mrazović
Published in: Proceedings of the London Mathematical Society, 2023, ISSN 0024-6115
Publisher: Oxford University Press
DOI: 10.1112/plms.12538

Self-similar measures associated to a homogeneous system of three maps

Author(s): Ariel Rapaport, Péter P. Varjú
Published in: Duke Math. J., Issue 173(3), 2024, Page(s) 513-602, ISSN 0012-7094
Publisher: Duke University Press
DOI: 10.1215/00127094-2023-0019

An improved bound for the dimension of (α,2α)-Furstenberg sets

Author(s): Kornélia Héra, Pablo Shmerkin, Alexia Yavicoli
Published in: Rev. Mat. Iberoam., 2022, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1281

On sets containing a unit distance in every direction

Author(s): Pablo Shmerkin, Han Yu
Published in: Discrete Analysis, 2021, ISSN 2397-3129
Publisher: Alliance of Diamond Open Access Journals
DOI: 10.19086/da.22058

Other (17)

On the local L2-Bound of the Eisenstein Series

Author(s): Subhajit Jana, Amitay Kamber
Published in: arXiv preprint, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2210.16291

On the absolute continuity of radial and linear projections of missing digits measures

Author(s): Han Yu
Published in: arXiv preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2309.01298

Rational points near self-similar sets

Author(s): Han Yu
Published in: arXiv preprint, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2101.05910

Counting rationals and diophantine approximation in missing-digit Cantor sets

Author(s): Sam Chow, Peter P. Varju, Han Yu
Published in: arXiv preprint, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2402.18395

Missing digits points near manifolds

Author(s): Han Yu
Published in: arXiv preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2309.00130

Growth in linear groups

Author(s): Sean Eberhard, Brendan Murphy, László Pyber, Endre Szabó
Published in: arXiv preprint, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2107.06674

Local limit theorems for random walks on nilpotent Lie groups

Author(s): Timothée Bénard, Emmanuel Breuillard
Published in: arXiv preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2304.14551

Lifting all elements in SLn(Z/qZ)

Author(s): Amitay Kamber, Péter P. Varjú
Published in: arXiv preprint, 2023, Page(s) 1-26
Publisher: arXiv
DOI: 10.48550/arxiv.2310.10269

Biased multilinear maps of abelian groups

Author(s): Sean Eberhard
Published in: arXiv preprint, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2108.01580

Local limit theorem for random walks on symmetric spaces

Author(s): Constantin Kogler
Published in: arXiv preprint, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2211.11128

On absolute continuity and maximal Garsia entropy for self-similar measures with algebraic contraction ratio

Author(s): Lauritz Streck
Published in: arXiv preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2303.07785

Finer geometry of planar self-affine sets

Author(s): Balázs Bárány, Antti Käenmäki, Han Yu
Published in: arXiv preprint, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2107.00983

On equidistribution of polynomial sequences in quotients of PSL2(R)

Author(s): Lauritz Streck
Published in: arXiv preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2305.02730

Covering the Sierpiński carpet with tubes

Author(s): Aleksi Pyörälä, Pablo Shmerkin, Ville Suomala, Meng Wu
Published in: arXiv preprint, 2020
Publisher: arXiv
DOI: 10.48550/arxiv.2006.00499

Absolute Continuity of Self Similar Measures

Author(s): Samuel Kittle
Published in: arXiv preprint, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2103.12684

The central limit theorem on nilpotent Lie groups

Author(s): Timothée Bénard, Emmanuel Breuillard
Published in: arXiv preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2302.06024

Absolutely continuous Furstenberg measures

Author(s): Samuel Kittle
Published in: arXiv preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2305.05757

Conference proceedings (3)

Combinatorics via closed orbits: number theoretic Ramanujan graphs are not unique neighbor expanders

Author(s): Amitay Kamber, Tali Kaufman
Published in: STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, Issue June 2022, 2022, Page(s) 426-435, ISBN 978-1-4503-9264-8
Publisher: Association for Computing Machinery
DOI: 10.1145/3519935.3519992

Testability of relations between permutations

Author(s): Oren Becker, Alexander Lubotzky, Jonathan Mosheiff
Published in: 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), 2022, Page(s) 286-297, ISBN 978-1-6654-2055-6
Publisher: IEEE Computer Society
DOI: 10.1109/focs52979.2021.00037

Self-similar sets and measures on the line

Author(s): Péter P. Varjú
Published in: International Congress of Mathematicians 2022 July 6-14, Issue Volume V, 2023, Page(s) 3610–3634, ISBN 978-3-98547-063-1
Publisher: EMS Press
DOI: 10.4171/icm2022/94

Book chapters (1)

On the multiplicative group generated by two primes in Z/QZ

Author(s): Péter P. Varjú
Published in: Analysis at Large, Dedicated to the Life and Work of Jean Bourgain, Issue 2022, 2022, Page(s) 373-388, ISBN 978-3-031-05330-6
Publisher: Springer Cham
DOI: 10.1007/978-3-031-05331-3_16