ArithRand

Arithmetic Randomness


     

Project

The aim of the Austrian-French joint project ArithRand ("Arithmetic Randomness", 2021-2025) is to make progress on various questions that interrelate and link the notion of randomness (or pseudo-randomness) with the notion of determinism in the context of analytic number theory, combinatorics on words, automata theory, quasi-random sequences and nearby disciplines. It is financially supported by the FWF (Fonds zur Förderung der wissenschaftlichen Forschung, I 4945-N) and the ANR (Agence Nationale de la Recherche, ANR-20-CE91-0006).

Research topics

Many numbertheoretic sequences are per se deterministic but resemble much of the overall behaviour of a random sequence. One important example is the Möbius function. In this context we are interested in studying the independence between the Möbius function and various deterministic functions such as functions that are produced by a dynamical system of zero entropy or by a simple algorithm based on the binary digital representation. Informally, the difficulty of this independence problem reflects the difficulty of the transition from the digital representation of an integer to its multiplicative representation as a product of prime factors. This field of questions is the source of many important open problems in mathematics and computer science. In particular, we mention the construction of normal numbers, the analysis of pseudo-random and complexity measures, and the search for optimal discrepancy estimates for digitally based sequences or other quasi-random sequences which are some of the major lines of research in this joint project.

Members

The Austrian-French Consortium consists of 16 researchers and is based in Graz, Vienna, Bordeaux, Calais, Marseille, Nancy and St Etienne.

Postdoctoral researchers:

Doctoral students:

  • Vincent Gozé (Calais-Littoral)

Events

  • Workshop ArithRand 22 Workshp ArithRand 22
  • Talks by visitors (or online)
    Arithrand-related talks at Ernest seminar (Luminy, Marseille, FR)
  • 2021-12-07: Joni Teräväinen, On a hybrid of the Hardy-Littlewood and Chowla conjectures
  • 2021-06-08: Gregory Debruyne, Malliavin-type remainders for Beurling generalized prime number systems
  • 2021-05-11: Johann Verwee, Théorèmes d'Erdős-Wintner effectifs
  • 2021-04-13: Pierre-Adrien Tahay, Corrélations discrètes d’ordre 2 de suites généralisées de Rudin-Shapiro par une approche combinatoire
  • 2020-12-08: Youness Lamzouri, La répartition du maximum des sommes partielles de sommes d'exponentielles


    Seminars with links to ArithRand ("Metz-Nancy Number Theory Seminar" at IECL, Nancy)
  • 9/12/2021, Journée Scientifique FCH "Pseudorandomness, cryptography and number theory" (IECL/LORIA)
  • 2/12/2021 Benli Kübra (IECL), Changes in digits of primes
  • 18/11/2021 Sébastien Darses (Aix-Marseille Université), On probabilistic generalizations of the Nyman-Beurling criterion for the Zeta function
  • 21/10/2021 Manfred Madritsch (IECL), Construction d'un nombre normal tel que son inverse soit également normal
  • 30/09/2021 Yann Bugeaud, Approximation rationnelle des nombres sturmiens
  • 20/05/2021 (online) Kübra Benli, Small prime power residues modulo p
  • 15/04/2021 (online) Gérald Tenenbaum (IECL), Répartition des fonctions multiplicatives dans les progressions arithmétiques de grands modules et applications
  • 08/04/2021, (online) Paul Pollack (University of Georgia), Multiplicative orders mod p
  • 01/04/2021 (online) Sarah Peluse (IAS/Princeton), Modular zeros in the character table of the symmetric group
  • 11/03/2021 (online) Alessandro Languasco, On computing L'/L(1,chi) and related problems
  • 18/02/2021 (online) Brad Rodgers, The distribution of random polynomials with multiplicative coefficients
  • 07/01/2021 (online) Marc Munsch, Comportement aléatoire local des suites réelles: résultats métriques, énergie additive et inégalités diophantiennes
  • 10/12/2020 (online) Johann Verwee, Théorèmes d'Erdös-Wintner effectifs
  • 19/11/2020 (online) Amri Myriam, Sur la répartition jointe de la représentation d'Ostrowski dans les classes de résidus
  • 12/11/2020 (online) Jakub Konieczny, Automatic multiplicative sequences
  • 15/10/2020 Shuo Li, On the classification of completely multiplicative automatic sequences

    Talks at the Ernest seminar in Marseille :
  • 2022-12-01,  Jared D. Lichtman,  "A proof of the Erdős primitive set conjecture"
  • 2022-10-18, Michael Drmota,  "Primes as sums of Fibonacci numbers" >li>2022-10-04, Olivier Ramaré, "A Stronger Model for Peg Solitaire"
  • 2022-06-14, Cécile Dartyge, "Valeurs polynomiales quartiques avec un grand facteur premier : les cas diédraux et cycliques"
  • 2022-05-10, Andreas Weingartner, "A general sieve problem"
  • 2022-04-05, Nicole Raulf, "Sur le comportement d'un produit de fonctions L"
  • 2022-03-01, Kübra Benli, "Small prime 𝑘-th power residues modulo 𝑝"
  • 2022-02-01, Corentin Darreye, "Oscillations dans la suite des coefficients d'une forme modulaire"
  • 2022-01-18, Jakub Konieczny, "Finitely-valued generalised polynomials"
  • Reading seminar at IECL Nancy, Primes as sums of Fibonacci numbers (Fall 2021-Spring 2022)
  • ---Seminars related to ArithRand on Nancy
  • Questions d'équirépartition de sommes exponentielles indexées par un sous-groupe, 27 janvier 2022, Théo Untrau (IMB, Bordeaux)
  • Ensembles de formes linéaires de complexité maximale, 3 février 2022, Michel Waldschmidt (Sorbonne Université)
  • Gowers uniformity of thin subsets of primes, 3 mars 2022, Fernando Xuancheng Shao (University of Kentucky)
  • Valeurs polynomiales quartiques avec un grand facteur premier : les cas diédraux et cycliques, 7 avril 2022,Cécile Dartyge (IECL)
  • The distribution of character sums, 28 avril 2022, Jonathan Bober (Université de Bristol)
  • A general sieve problem, 5 mai 2022, Andreas Weingartner (Southern Utah University, États-Unis)
  • Summing $\mu(n)$: an even faster elementary algorithm, 12 mai 2022, Lola Thompson (Université de Utrecht)
  • Loi Gaussienne du nombre d'entiers sans facteur carré dans les intervalles courts, 19 mai 2022, Sacha Mangerel (Université de Durham)
  • Optimality for Tauberian theorems, 22 juin 2022, Gregory Debruyne (Ghent University)
  • Well-behaved Beurling number systems,  22 juin 2022, Frederik Broucke (Ghent University)
  • Sums of Kloosterman sums with multiplicative coefficients, 23 juin 2022, Igor Shparlinski (University of New South Wales)

Guests (selection)

  • to come
For your upcoming or to be published papers, please include : "This paper was supported by the joint FWF-ANR project Arithrand: FWF: I 4945-N and ANR-20-CE91-0006."

Publications-Preprints - in preparation (explicitely mentioning ArithRand)

  • C. Aistleitner, B. Borda: Quantum invariants of hyperbolic knots and extreme values of trigonometric products. Preprint, arXiv:2006.08578
  • C. Aistleitner, D. El-Baz, M. Munsch: A pair correlation problem, and counting lattice points with the zeta function. GAFA 31 (2021), no. 3, 483--512
  • C. Aistleitner, S. Baker, N. Technau, N. Yesha: Gap statistics and higher correlations for geometric progressions modulo one. Preprint, arxiv:2010.10355
  • C. Aistleitner, N. Gantert, Z. Kabluchko, J. Prochno, K. Ramanan: Large Deviation Principles for Lacunary Sums. Preprint, axriv:2012.05281
  • C. Aistleitner, B. Borda: Maximizing Sudler products via Ostrowski expansions and cotangent sums. Preprint, arXiv:2104.01379
  • C. Aistleitner, D. El-Baz, M. Munsch: Difference sets and the metric theory of small gaps. Preprint, arXiv:2108.02227
  • C. Aistleitner, B. Borda: A conjecture of Zagier and the value distribution of quantum modular forms. Preprint, arXiv:2110.07407
  • Aloui, K.; Jamet, D., Kaneko, H., Kopecki, S., Popoli, P; Stoll, T. On the binary digits of n and n^2, (2022), Theoretical Computer Science 939 (2022), 119--139. https://arxiv.org/abs/2203.05451, https://doi.org/10.1016/j.tcs.2022.10.018
  • Benli, K.; Stoll, T. Subword complexity of the Fibonacci-Thue-Morse sequence along polynomials, in preparation.
  • Bettin, S.; Drappeau, S. Two arithmetic applications of perturbations of composition operators. J. Anal. Math. 144 (2021), 335--349. DOI: 10.1007/s11854-021-0184-1. arXiv:2002.11417. hal-02493843v1.
  • Bettin, S.; Drappeau, S. Effective estimation of some oscillatory integrals related to infinitely divisible distributions. Ramanujan J. 57 (2022) 849--861. DOI: 10.1007/s11139-020-00362-y. arXiv: 2010.15494. HAL:hal-02998544v1.
  • Bettin, S.; Drappeau, S. Modularity and value distribution of quantum invariants of hyperbolic knots. Math. Ann. 382 (2022) no. 3-4, 1631--1679. DOI: 10.1007/s00208-021-02288-2. arXiv:1905.02045. HAL: hal-02998581v1.
  • Bettin, S.; Drappeau, S. Limit laws for rational continued fractions and value distribution of quantum modular forms. Proc. London Math. Soc. 125 (2022), no 6, 1377--1425. DOI: 10.1112/plms.12485. arXiv:1903.00457. HAL: hal-02998562v1.
  • Bettin, S.; Drappeau, S. On quantum modular forms of non-zero weights, submitted. arXiv:2210.07854.
  • Bienvenu, P.-Y. and Geroldinger, A., On algebraic properties of power monoids of numerical monoids, Isr. J. Math., to appear.
  • La Bretèche, R.; Dress, F.; Tenenbaum, G., Remarques sur une somme liée à la fonction de Möbius, Mathematika 66, no. 2 (2020), 416--421.
  • La Bretèche, R.; Munsch, M.; Tenenbaum, G., Small Gál sums and applications, J. London Math. Soc. 103}(2021), 336--352.
  • La Bretèche, R. Tenenbaum, G., Remarks on the Selberg--Delange method, Acta Arith. 200.4 (2021), 349-369.
  • La Bretèche, R. Tenenbaum, G., On strong and almost sure local limit theorems for a probabilistic model of the Dickman distribution, Lith. Math. J. 61, n°3 (2021), 301-311.
  • La Bretèche; R. Tenenbaum, G., On the gap distribution of prime factors, Proc. Amer. Math. Soc., to appear.
  • La Bretèche, R.; Tenenbaum, G., Friable averages of oscillating multiplicative functions, in: H.~Maier, J. Steuding, R. Steuding, {\it Number Theory. Dedicated to the memory of Eduard Wirsing}, Springer, to appear.
  • La Bretèche, R.; Tenenbaum, G., Two upper bounds for the Erd\H os--Hooley Delta-function, preprint.
  • La Bretèche, R.; Tenenbaum, G., Note on a conjecture of Hildebrand regarding friable integers, preprint.
  • Fernando Chamizo, Bruno Martin,  The convergence of certain Diophantine series. Journal of Number Theory, to appear.  DOI: 10.1016/j.jnt.2021.04.022
  • Chamizo, F ; Martin, B. The approximate functional equation of some Diophantine series,  submitted.
  • Dartyge, C; Feutrie, D.;  Tenenbaum, G., Entiers ultrafriables en progressions arithmétiques, Quart. J. Math. (Oxford) 73 (2022), 149-74. Dartyge, C.; Maynard, J.; On the largest prime factor of quartic polynomial values: the cyclic and dihedral case, arXiv:2212.03381.
  • Ddamulira, M., Luca, F. & Tichy, R., On the Shorey–Tijdeman Diophantine equation involving terms of Lucas sequences; Indagationes Mathematicae. 33, 2, (2022), p. 314--321.
  • Debruyne, G.; Tenenbaum, G., The saddle point method for general partitions, Indag. Math. 31 (2020), 728-738.
  • Jean-Marc Deshouillers, Michael Drmota, Clemens Müllner, Andrei Shubin, Lukas Spiegelhofer; Synchronizing automatic sequences along Piatetski-Shapiro sequences; manuscript; arXiv:2211.01422
  • Jean-Marc Deshouillers, Michael Drmota, Clemens Müllner; Coprimality of consecutive elements in a Piatetski-Shapiro sequence; in: Number Theory in Memory of Eduard Wirsing, Springer, to appear.
  • Drappeau, S.; Hanna, G. The Thue–Morse and Rudin–Shapiro sequences at primes in principal number fields. Acta Math. Hung. 162 (2020), 130--186. Zbl 1398.11121; MR4169024. DOI: 10.1007/s10474-020-01030-9. arXiv:2001.07017. HAL:hal-02493862v1.
  • Drappeau, S.; Fiorilli, D. The first moment of primes in arithmetic progressions: beyond the Siegel-Walfisz range. Trans. London Math. Soc. 8 (2021), no 1, 174--185. DOI: 10.1112/tlm3.12030. arXiv: 2003.02201. HAL:hal-02567736v1.
  • Drappeau, S.; Pratt, K.; Radziwiłł, M. One-level density estimates for Dirichlet L-functions with extended support. Algebra Number Theory, to appear. arXiv:2002.11968. HAL: hal-02493847v1.
  • M. Drmota, M. Lemańczyk, C. Müllner, J. Rivat; Some recent developments on the Sarnak conjecture, in: "Panoramas et Syntheses", Soc. Math. de France, to appear.
  • Michael Drmota, Christian Mauduit, Joël Rivat, Lukas Spiegelhofer: Möbius orthogonality of sequences with maximal entropy. Journal d'Analyse Mathématique 146 (2022), 531--548; arxiv:2001.07898
  • Michael Drmota, Clemens Müllner, Lukas Spiegelhofer; Primes as sums of Fibonacci numbers; Memoirs of the American Mathematical Society, to appear; arXiv:2109.04068
  • Elsholtz, C.; Planitzer, S., Sums of four and more unit fractions and approximate parametrizations. Bull. Lond. Math. Soc. 53 (2021), no. 3, 695--709.
  • Elsholtz, C. Fermat's last theorem implies Euclid's infinitude of primes. Amer. Math. Monthly 128 (2021), no. 3, 250--257.
  • Elsholtz, C.; Klahn, B.; Technau, M.; On polynomials with roots modulo almost all primes Acta Arithmetica 205 (2022), 251-263. DOI: 10.4064/aa220407-9-7
  • Rainer Dietmann, Christian Elsholtz, Alexander Kalmynin, Sergei Konyagin, James Maynard, Longer gaps between values of binary quadratic forms, IMRN https://doi.org/10.1093/imrn/rnac130
  • Elsholtz, C.; Lipnik, G.; Exponentially Larger Affine and Projective Caps Mathematika, https://doi.org/10.1112/mtk.12173
  • Elsholtz, C.; Klahn, B.; Lipnik, G.; Large subsets of (Z_m)^n without arithmetic progressions Designs, Codes and Cryptography (2022) https://doi.org/10.1007/s10623-022-01145-w
  • Elsholtz, C.; Heuberger, C; Krenn, D. Algorithmic counting of nonequivalent compact Huffman codes, Applicable Algebra in Engineering, Communication and Computing (2023)
  • Fouvry, É.; Tenenbaum, G., Multiplicative functions in large arithmetic progressions and applications, Trans. Amer. Math. Soc. 75, no. 1 (2022), 245-299.
  • Jamet, D.; Popoli, P.; Stoll, T. Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences. Cryptography and Communications 13 (2021),  791--814. https://doi.org/10.1007/s12095-021-00507-w, https://arxiv.org/abs/2106.09959
  • Kaneko, H.; Stoll T. Products of integers with few nonzero digits. Uniform Distribution Theory (2021), 17pp, to appear. http://arxiv.org/abs/2112.03077
  • Elżbieta Krawczyk, Clemens Müllner, Automaticity of uniformly recurrent substitutive sequences, https://arxiv.org/abs/2111.13134
  • Dijana Kreso, Joel Rivat, Robert Tichy (editors). Diophantine Problems: Determinism, Randomness and Applications
  • Marcovici, I.; Tahay, P.-A.; Stoll, T. Discrete correlations of order 2 of generalised Golay-Shapiro sequences: a combinatorial approach. Integers 21 (2021), A45, 21pp. http://math.colgate.edu/~integers/vol21.html, https://arxiv.org/abs/2006.13162
  • Paolo Minelli, Athanasios Sourmelidis & Marc Technau, Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums, Math. Ann. (2022). https://doi.org/10.1007/s00208-022-02452-2
  • Paolo Minelli, Athanasios Sourmelidis, Marc Technau, On restricted averages of Dedekind sums, submitted.
  • O. Ramare, Notes on restriction theory in the primes, arXiv:2109.10180
  • A. Shubin, Möbius orthogonality of Thue-Morse sequence along Piatetski-Shapiro numbers, submitted, https://arxiv.org/abs/2207.11840
  • Spiegelhofer, L., Gaps in the Thue--Morse word. J. Aust. Math. Soc. 114, no. 1 (2023), 110-144, https://www.doi.org/10.1017/S1446788721000380, arXiv:2102.01018v2
  • Spiegelhofer, L., Collisions of digit sums in bases 2 and 3. Israel J. Math., to appear. arXiv:2105.11173v2
  • Tenenbaum, G., A note on the normal largest  gap between prime factors, J. Théor. Nombres Bordeaux 31, no. 3 (2019), 747-749.
  • Tenenbaum, G.;  Verwee, J., Effective Erd\H os--Wintner theorems, Proc. Steklov Inst. Math. 314 (2021), 275--289.
  • Tenenbaum, G.; Weingartner, A., An Erd\H{o}s-Kac theorem for  integers with dense divisors, preprint.
  • Tichy, R., Vukusic, I., Yang, D. & Ziegler, V., Integers representable as differences of linear recurrence sequences; Research in Number Theory 7, (2021), 24.  

Talks


    by Pierre Bienvenu
  • Talks on "On algebraic properties of power monoids of numerical monoids":
  • June 2022, Hebei Open seminar (online/invited)
  • November 2022, Mississippi Number Theory Seminar (online)
  • December 2022, Uni Graz Algebra and Number Theory Seminar (online)
  • Talks on "Metric decomposability theorems on sets of integers" July 2022, Arith Rand workshop (in person)
  • Algebra and Number Theory Seminar, University College Dublin, Februar 2023.
    by Cecile Dartyge
  • 27/09/2021 Rencontres de théorie analytique et élémentaire des nombres (Paris), "Valeurs polynomiales quartiques avec un grand facteur premier, les cas diédraux et cycliques".
  • 17 mars 2022, séminaire de théorie des nombres de Grenoble, "Valeurs polynomiales quartiques avec un grand facteur premier, les cas diédraux et cycliques".
  • 31 mars 2022 Séminaire de théorie des nombres de Nancy-Metz, "Répartition des nombres premiers dans des suites d'entiers".
  • 1er avril 2022 Séminaire Bourbaki du vendredi, "Répartition des nombres premiers dans des suites d'entiers".
  • 21 juin 2022 Séminaire ADA à Calais, "Valeurs polynomiales quartiques avec un grand facteur premier, les cas diédraux et cycliques".
  • 4--8 Juillet 2022, Number Theory Conference 2022 à Debrecen (Hongrie), conférence en l'honneur de K\'alm\'an Gy\H ory, J\'anos Pintz et Andr\'as S\'ark\''ozy. (Exposé annulé en raison du COVID).
  • 25 novembre 2022, Séminaire de théorie des nombres de Bordeaux, "Valeurs polynomiales quartiques avec un grand facteur premier, les cas diédraux et cycliques".
  • 6--12 novembre 2022, Workshop "Analytic Number Thoery", Oberwolfach, Allemagne, On the largest prime factor of quartic polynomial^Mvalues: the cyclic and dihedral cases
  • 5--9 septembre 2022, A celebration of analytic number theory, a conference in honor of Andrew Granville, CRM Montréal, Canada. On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases
  • 8 décembre 2022, Xi'an Jiatong University (Chine), On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases (exposé en ligne).
  • 19 janvier 2023, Number Theory Web Seminar, On the largest prime factor of quartic polynomial^Mvalu\ es: the cyclic and dihedral cases (exposé en ligne).
  • 13 mars 2023, Number Theory Seminar, Warwick University, (Grande Bretagne)
  • 4--6 mai 2023, 7th Minisymposium of the Roman number theory association, (Italie)
    by Sary Drappeau
  • "Modularity of the q-Pochhammer symbol and application", 2020-11-27, CIRM Conference "Diophantine Problems, Determinism and Randomness".
  • "The distribution of the Estermann function and other quantum modular forms", 2021-03-01, Mittag-Leffler semester on Number Theory.
  • "Fractions continues et lois limites pour quelques valeurs de fonctions L", 2021-05-21, Séminaire de Dynamique de l'IMJ-PRG.
  • "Continued fractions and limit laws for values of L-functions", 2021-05-28, N-Cube days.
  • "Shifted convolutions, arithmetic progressions, exponential sums", 2021-06-28 to 2021-07-02, 4 talks at the Paris Summer School in Analytic Number
  • "Quantum modularity for central values of additively twisted Maass L function", 2022-05-31, Genova-Graz Number Theory Workshop, Genova, Italy
  • "Quantum modularity of additive twists of Maass L values", 2022-09-06, Celebrating Analytic Number Theory, conference in honour of Andrew Granville, Montreal, Québec, Canada
  • "The central limit theorem for values of the Estermann function", 2022-09-28, Stanford Number Theory Students online seminar
  • "Formes modulaires quantiques de poids non nul", 2022-10-03, Rencontres de Théorie Analytique et Élémentaire des Nombres, IHP Paris, France
  • "Modularité quantique pour les tordues additives de fonctions L des formes de Maass", 2022-11-15, Séminaire de Théorie des Nombres de Clermont-Ferrand, France

    by Michael Drmota
  • online, contributed, (Logarithmic) Densities for Automatic Sequences along Primes and Squares AG Diskrete Mathematik, TU Wien,  March 16, 2021
  • online, invited, (Logarithmic) Densities for Automatic Sequences along Primes and Squares One World Numeration Seminar, March 30, 2021
  • in person, contributed, Primes as Sums of Fibonacci Numbers AG Diskrete Mathematik, TU Wien,  October 12, 2021
  • in person, contributed, Subsequences of Automatic Sequences and Uniform Distribution, SFB-Meeting Traunkirchen, January 14, 2022.
  • in person, invited, Primes as Sums of Fibonacci Numbers, Univ. Tours, Seminar, March 17, 2022.
  • in person, invited, Primes as Sums of Fibonacci Numbers I., ArithRand 2022, TU Graz, July 2, 2022.
  • online, constributed, The Sarnak conjecture and related questions on the Fibonacci-Thue-Morse sequence, Russian-Austrian Joint Meeting, July 12, 2022.
  • in person, invited, Primes as Sums of Fibonacci Numbers, Univ. Aix-Marseille, Marseille, Seminar, October 10, 2022.
  • online, invited, Moebius orthogonalily: a classical and modern topic in number theory, Univ. Xiamen, China, October 27, 2022.

    by Christian Elsholtz
  • Large sets in (Z_m)^n without progressions 7 Sep 2020 - 11 Sep 2020, Cirm (Luminy, online)
  • Improved cap constructions, and sets without arithmetic progressions, Conference: Diophantine Problems: Determinism, Randomness, Applications 23 Nov 2020 - 27 Nov 2020, CIRM Luminy (online)
  • Sums of unit fractions, March 18, 2021, Karl Franzens University Graz
  • Improved cap constructions, and sets without arithmetic progressions, March 25, 2021, Karl Franzens University Graz
  • Fermat's Last Theorem implies Euclid's infinitude of the primes, Combinatorial and additive number theory, CANT 2021 (New York, online), 24 Mai 2020 - 28 May 2021
  • Improved cap constructions, and sets without arithmetic progressions, June 3, 2021, Laboratoire Analyse, Géométrie et Applications, Paris, Frankreich, invited.
  • Arithmetic progressions in arithmetic sets, June 11, 2021, Salzburg-Debrecen-Graz seminar, invited.
  • Fermat's last theorem implies Euclid's infinitude of primes, Jun 24, 2021. Karl-Franzens-Universität Graz.
  • Improved cap constructions in affine and projective spaces, 29.9.2021, DMV-ÖMG Tagung, Passau (contributed, virtual)
  • ^ Lower bound constructions for progression-free sets and caps in affine and projective spaces. Number theory seminar, Alfred Renyi-Institute, (invited, virtual)
  • Lower bound constructions for progression-free sets and caps in affine and projective spaces. COmbinatorial Number Theory And Connected Topics (CONTACT - I), India, (invited speaker, virtual)
  • Longer gaps between values of binary quadratic forms, Event title Number Theory Conference 2022: In honour of Professors Kálmán Győry, János Pintz and András Sárközy, Debrecen 2022.


    by Bruno Martin
    invited online talk in the Conference "Diophantine Problems, Determinism and Randomness" in Cirm, 24th november 2020. Title " Some interactions between number theory and multifractal analysis".

    by Clemens Müllner
  • Multiplicative automatic sequences, Open University Dynamical Systems seminar of 2021, 13. January 2021 (invited)
  • Multiplicative automatic sequences, One World Numeration Seminar 9. February 2021 (contributed)
  • Substitution dynamical systems in the context of Sarnak's conjecture Seminar: AG Ergodic Theory (University of Vienna) am  10.11.2022 (in person).

    by O. Ramare
  • O. Ramaré, 4 octobre 2021, Séminaire de Théorie des Nombres de Paris, Polynomes trigonom'etriques arithm'etiques aux points de petites hauteurs, in person
  • 6-17 December 2021, Density Estimates and Additive Combinatorics, brainstorming session with four participants, with the support of ArithRand https://www.i2m.univ-amu.fr/events/density-estimates-and-additive-combinatorics/

    by Joel Rivat
  • "Pseudo-random properties of sums and products", Debrecen 2022.
    by Andrei Shubin
  • in person, contributed, Primes in subsets and exponential sums, AG Diskrete Mathematik, TU Wien,  Nov 9, 2021
  • 01/07/2022, in person, contributed, Automatic sequences along Piatetski-Shapiro sequences, ArithRand 22, Graz, 1-2 July, 2022
  • 22/08/2022, in person, contributed, Automatic sequences along Piatetski-Shapiro numbers, ELAZ, A conference on elementary and analytic number theory, August 2022
  • 25/01/2023, in person, contributed, On pair correlations of monomial sequences, Browning group working seminar, IST Austria, January 2023

    by Lukas Spiegelhofer
  • The level of distribution of the Thue--Morse sequence, Rencontres de th\'eorie analytique et \'el\'ementaire des nombres, Paris, France, in person, invited, 21 March 2022
  • Collisions of digit sums in different bases, Rencontres de th\'eorie analytique et \'el\'ementaire des nombres, Paris, France, in person, invited, 21 March 2022
  • Primes as sums of Fibonacci numbers, ArithRand 2022, TU Graz, Austria, in person, contributed, 2 July 2022
  • Primes as sums of Fibonacci numbers, One World Numeration Seminar, contributed online talk, 11 Oct 2022

    by Thomas Stoll
    On difference matrices and generalised Rudin-Shapiro sequences, Plenary talk, online, 7th International Conference on Uniform Distribution Theory (UDT2021), 24-02-2021.
  • online, invited, The sum of digits of polynomials, special lecture, Shandong University at Weihai (Chine), 16/1/23
    by G. Tenenbaum
  • Number Theory Web Seminar, 10 novembre 2020. Diophantine Problems, Determinism and Randomness, CIRM, Luminy, 23-27 novembre 2020.
  • Analytic & combinatorial number theory in honour of R. Balasubramanian, IMSc, Chennai 16 mars 2021.
  • Sommes de Gál et applications, invited, Colloquium université de Reims, 25/1/2022
  • Friable averages, a survey, invited, ELAZ 2022, a conference on Elementary and Analytic Number Theory, Poznań, 24/8/2022.
last modified: December 2021