Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem | Vidéo | Carmin.tv

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Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem

By Dmitry Kleinbock

Appears in collections : Homogeneous spaces, diophantine approximation and stationary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnaires, Ecoles de recherche

Optimal results on the improvements to Dirichlet's Theorem are obtained in the one-dimensional case. For simultaneous approximation the problem is open. I will describe reduction of the problem to dynamics both in one-dimensional case (via continued fractions) and for higher dimensions (via diagonal flows on the space of lattices). If time allows I'll mention an inhomogeneous version which is easier than the homogeneous one. Joint work with Nick Wadleigh.

Information about the video

Date of recording 08/02/2017
Date of publication 15/02/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19118903
Cite this video Kleinbock, Dmitry (08/02/2017). Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19118903
URL https://dx.doi.org/10.24350/CIRM.V.19118903

Domain(s)

Bibliography

Kleinbock, D., & Wadleigh, N. (2017). A zero-one Law for improvements to Dirichlet's Theorem. <arXiv:1609.06780> - https://arxiv.org/abs/1609.06780

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