CONFERENCE
Diophantine Approximation and Transcendence
Approximation diophantienne et transcendance
10 – 14 September 2018
|
Scientific Committee
Comité scientifique Michael A. Bennett (University of British Columbia) |
Organizing Committee
Comité d’organisation Boris Adamczewski (CNRS, Université Claude Bernard Lyon 1) |
|
The initial goal of Diophantine approximation is the study of the approximation of a real point by rational points and the tools which have been created to that purpose remain at the basis of transcendence’s results. There exists a Diophantine mathematical community concerned with the topic which has nowadays multiple aspects. The proposed meeting, which takes place at CIRM every four years, intends to gather an important part of this community and to present the most prominent recent results. Among the new developments we plan to address, let us mention the various extensions and refinements of the Schmidt subspace theorem in its quantitative forms; the works concerning the Zilber-Pink conjecture and the “unlikely intersections”; recent progress towards Littlewood conjecture and its links with the theory of dynamical systems; and finally the emerging topic of “arithmetical dynamics”.
|
L’approximation diophantienne a pour objet initial l’étude de l’approximation d’un point réel par des points rationnels et les outils qui ont été élaborés à cet égard restent à la base des résultats de transcendance actuels. Il existe une communauté mathématique diophantienne qui se reconnaît dans cette thématique comportant aujourd’hui de multiples aspects. La conférence proposée, qui a d’ailleurs un caractère récurrent au CIRM (tous les quatre ans), a pour but de réunir une partie importante de cette communauté et d’exposer l’état de l’art. Cinq sujets ayant connu des progrès spectaculaires ces dernières années seront mis en avant. Parmi les nouveaux développements, mentionnons les diverses extensions et raffinements du théorème du sous-espace de Schmidt dans ses formes quantitatives ; les travaux relatifs à la conjecture de Zilber-Pink et les “intersections improbables” ; les progrès récents autour de la conjecture de Littlewood et ses liens avec la théorie des systèmes dynamiques ; et enfin un sujet émergent: la “dynamique arithmétique”.
|
Speakers
Boris Adamczewski (CNRS, Université Claude Bernard Lyon 1) Mahler’s method in several variables (pdf) – VIDEO –
Shabnam Akhtari (University of Oregon) Lower bounds for the Mahler measures of polynomials that are sum of a bounded number of monomials
Francesco Amoroso (Université de Caen) Factorization of bivariate sparse polynomials
Mike Bennett (University of British Columbia) Quartic forms : computations in search of a theorem
Victor Beresnevich (University of York) Simultaneous rational approximations to several functions of a real variable – VIDEO –
Laura Capuano (University of Oxford) An effective criterion for periodicity of p-adic continued fractions – VIDEO –
Maria Carrizosa (Université Claude Bernard Lyon 1) Counting polarisations on abelian varieties
Michael Coons (University of Newcastle) Two regular questions (pdf)
Laura DeMarco (Northwestern University) Height pairings, torsion points, and dynamics
Julian Demeio (Scuola Normale Superiore Pisa) Hilbert Property and Elliptic Fibrations
Jan-Hendrik Evertse (Leiden University) S-parts of values of polynomials
Stéphane Fischler (Université Paris-Sud) Irrationality of odd zeta values, with (or without) Shidlovsky’s lemma
Hajime Kaneko (Tsukuba Unversity) Diophantine approximation and base-b expansion of smooth numbers
Lajos Hajdu (University of Debrecen) On the smallest number of terms of vanishing sums of units in number fields (pdf)
Dong Han Kim (Dongguk University Seoul) The Lagrange and Markov Spectra of Pythagorean triples (pdf)
Noriko Hirata-Kohno (Nihon University) Linear forms in logarithms via Padé approximations and their applications
Holly Krieger (University of Cambridge) Height pairings, torsion points, and dynamics – VIDEO –
Lars Kühne (University of Basel) The Equidistribution Conjecture for Semiabelian Varieties
Samuel Le Fourn (ENS Lyon) Around Baker’s method for higher-dimensional varieties
Benjamin Matschke (Koc University) Solving Thue-Mahler equations via the Shimura-Taniyama conjecture
Niki Myrto Mavraki (University of British Columbia) Arithmetic equidistribution, dynamics and elliptic curves (pdf)
Nikolay G. Moshchevitin (Moscow State University) Irrationality measure functions and Diophantine spectra
Fabien Pazuki (Université de Bordeaux) Regulators of elliptic curves – VIDEO –
Gaël Rémond (Université Grenoble Alpes) Nouveaux théorèmes d’isogénie
Jeff Thunder (Northern Illinois University) Counting cubic extensions with a given discriminant in positive characteristic
Sanju Velani (University of York) Inhomogeneous Diophantine Approximation on M_0-sets with restricted denominators
Carlo Viola (Università di Pisa) Linear independence of 1, Li_1 and Li_2
Martin Widmer (Royal Holloway College) Averages for the l-torsion in class groups
Shabnam Akhtari (University of Oregon) Lower bounds for the Mahler measures of polynomials that are sum of a bounded number of monomials
Francesco Amoroso (Université de Caen) Factorization of bivariate sparse polynomials
Mike Bennett (University of British Columbia) Quartic forms : computations in search of a theorem
Victor Beresnevich (University of York) Simultaneous rational approximations to several functions of a real variable – VIDEO –
Laura Capuano (University of Oxford) An effective criterion for periodicity of p-adic continued fractions – VIDEO –
Maria Carrizosa (Université Claude Bernard Lyon 1) Counting polarisations on abelian varieties
Michael Coons (University of Newcastle) Two regular questions (pdf)
Laura DeMarco (Northwestern University) Height pairings, torsion points, and dynamics
Julian Demeio (Scuola Normale Superiore Pisa) Hilbert Property and Elliptic Fibrations
Jan-Hendrik Evertse (Leiden University) S-parts of values of polynomials
Stéphane Fischler (Université Paris-Sud) Irrationality of odd zeta values, with (or without) Shidlovsky’s lemma
Hajime Kaneko (Tsukuba Unversity) Diophantine approximation and base-b expansion of smooth numbers
Lajos Hajdu (University of Debrecen) On the smallest number of terms of vanishing sums of units in number fields (pdf)
Dong Han Kim (Dongguk University Seoul) The Lagrange and Markov Spectra of Pythagorean triples (pdf)
Noriko Hirata-Kohno (Nihon University) Linear forms in logarithms via Padé approximations and their applications
Holly Krieger (University of Cambridge) Height pairings, torsion points, and dynamics – VIDEO –
Lars Kühne (University of Basel) The Equidistribution Conjecture for Semiabelian Varieties
Samuel Le Fourn (ENS Lyon) Around Baker’s method for higher-dimensional varieties
Benjamin Matschke (Koc University) Solving Thue-Mahler equations via the Shimura-Taniyama conjecture
Niki Myrto Mavraki (University of British Columbia) Arithmetic equidistribution, dynamics and elliptic curves (pdf)
Nikolay G. Moshchevitin (Moscow State University) Irrationality measure functions and Diophantine spectra
Fabien Pazuki (Université de Bordeaux) Regulators of elliptic curves – VIDEO –
Gaël Rémond (Université Grenoble Alpes) Nouveaux théorèmes d’isogénie
Jeff Thunder (Northern Illinois University) Counting cubic extensions with a given discriminant in positive characteristic
Sanju Velani (University of York) Inhomogeneous Diophantine Approximation on M_0-sets with restricted denominators
Carlo Viola (Università di Pisa) Linear independence of 1, Li_1 and Li_2
Martin Widmer (Royal Holloway College) Averages for the l-torsion in class groups
SPONSORS
 |
 |
 Automata in number theory
|
 |
 |
 |