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Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem
Multi angle
Authors : Kleinbock, Dmitry (Author of the conference)
CIRM (Publisher )
11J04 - Homogeneous approximation to one number
11J70 - Continued fractions and generalizations
22F30 - Homogeneous spaces
37A17 - Homogeneous flows
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 11J04 - Homogeneous approximation to one number
11J70 - Continued fractions and generalizations
22F30 - Homogeneous spaces
37A17 - Homogeneous flows
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/02/17 Conference Date : 08/02/17 Subseries : Research School arXiv category : Number Theory ; Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:05:27 Targeted Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2017-02-08_Kleinbock.mp4 
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Information on the Event
Event Title : Homogeneous spaces, diophantine approximation and stationary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnairesEvent Organizers : Adamczewski, Boris ; Athreya, Jayadev ; Mercat, Paul ; Palesi, Frédéric Dates : 06/02/17 - 10/02/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1712.html
Citation Data
DOI : 10.24350/CIRM.V.19118903Cite this video as: Kleinbock, Dmitry (2017). Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19118903 URI : http://dx.doi.org/10.24350/CIRM.V.19118903 |
See Also
- [Multi angle] Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic? / Author of the conference Paulin, Frédéric.
- [Multi angle] Dynamics on quotients of SL(2,C) by discrete subgroups - Lecture 2 / Author of the conference Schapira, Barbara.
- [Multi angle] Dynamics on homogeneous spaces and Diophantine approximation / Author of the conference Ghosh, Anish.
- [Post-edited] Dense subgroups in simple groups - Lecture 2 / Author of the conference Benoist, Yves.
Bibliography
- Kleinbock, D., & Wadleigh, N. (2017). A zero-one Law for improvements to Dirichlet's Theorem.
