CIRM - Videos & books Library - Diophantine exponents, best approximation and badly approximable numbers

Virtualconference

Auteurs : Moshchevitin, Nikolay (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : We will discuss recent progress in analysis of uniform and ordinary Diophantine exponents $\hat\omega $ and $\omega$ for linear Diophantine approximation as well as some applications of the related methods. In particular, we give a new criterion for badly approximable vectors in $\mathbb{R}^{d}$ the behavior of the best approximation vectors in the sense of simultaneous approximation and in the sense of linear form. It turned out that compared to the one-dimensional case our criterion is rather unusual. We apply this criterion to the analysis of Dirichlet spectrum for simultaneous Diophantine approximation.

Keywords : Diophantine approximation; exponents of approximation

Codes MSC :
11J06 - Markov and Lagrange spectra and generalizations
11J13 - Simultaneous homogeneous approximation, linear forms
11J70 - Continued fractions and generalizations

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-11-23_Moshchevitin.mp4

Informations sur la Rencontre

Nom de la rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire
Organisateurs de la rencontre : Rivat, Joël ; Tichy, Robert
Dates : 23/11/2020 - 27/11/2020
Année de la rencontre : 2020
URL Congrès : https://www.chairejeanmorlet.com/2256.html

Données de citation

DOI : 10.24350/CIRM.V.19688203
Citer cette vidéo: Moshchevitin, Nikolay (2020). Diophantine exponents, best approximation and badly approximable numbers. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19688203
URI : http://dx.doi.org/10.24350/CIRM.V.19688203

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Bibliographie

MARNAT, Antoine et MOSHCHEVITIN, Nikolay G. An optimal bound for the ratio between ordinary and uniform exponents of Diophantine approximation. Mathematika, 2020, vol. 66, no 3, p. 818-854. - https://doi.org/10.1112/mtk.12045

AKHUNZHANOV, Renat et MOSHCHEVITIN, Nikolay. On badly approximable numbers. arXiv preprint arXiv:2002.00433, 2020. - https://arxiv.org/abs/2002.00433

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