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Audiovisual Mathematics Library

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Multi angle

Authors : Shmerkin, Pablo (Author of the conference)
CIRM (Publisher )

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Abstract : In the last few years ideas from additive combinatorics were applied to problems in fractal geometry and led to progress on some classical problems, particularly on the smoothness of Bernoulli convolutions and other self-similar measures. We will introduce some of these tools from additive combinatorics and present some of the main applications, including the smoothness of Bernoulli convolutions outside of a small set of exceptions, and for explicit values of the parameter.

Keywords : self-similarity; Bernouilli convolutions; intersection of cantor sets

MSC Codes :
28A80 - Fractals
37C45 - Dimension theory of dynamical systems

Additional resources :
https://www.cirm-math.fr/RepOrga/1947/Slides/shmerkin-luminy1.pdf

Information on the Video

Film maker :

Hennenfent, Guillaume

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Download :

https://videos.cirm-math.fr/2019-05-13_Shmerkin_Part1.mp4

Information on the Event

Event Title : Dynamique au-delà de l'hyperbolicité uniforme / Dynamics Beyond Uniform Hyperbolicity
Event Organizers : Bonatti, Christian ; Buzzi, Jérôme ; Crovisier, Sylvain ; Gan, Shaobo ; Pacifico, Maria José
Dates : 13/05/2019 - 24/05/2019
Event Year : 2019
Event URL : https://conferences.cirm-math.fr/1947.html

Citation Data

DOI : 10.24350/CIRM.V.19524403
Cite this video as: Shmerkin, Pablo (2019). Additive combinatorics methods in fractal geometry - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19524403
URI : http://dx.doi.org/10.24350/CIRM.V.19524403

See Also

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[Multi angle] Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 3 / Author of the conference Burguet, David.
[Multi angle] Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 2 / Author of the conference Burguet, David.
[Multi angle] Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 1 / Author of the conference Burguet, David.
[Multi angle] Rigidity in rank one: dynamics and geometry - lecture 3 / Author of the conference Gogolev, Andrey.
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[Multi angle] Big mapping class groups - lecture 5 / Author of the conference Calegari, Danny.
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[Multi angle] Additive combinatorics methods in fractal geometry - lecture 3 / Author of the conference Varju, Peter.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 2 / Author of the conference Varju, Peter.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 1 / Author of the conference Varju, Peter.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 3 / Author of the conference Shmerkin, Pablo.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 2 / Author of the conference Shmerkin, Pablo.
[Multi angle] Transfer operators for Anosov flows - lecture 3 / Author of the conference Tsuijii, Masato.
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[Multi angle] Transfer operators for Anosov flows - lecture 1 / Author of the conference Tsuijii, Masato.
[Multi angle] Transfer operators for Sinai billiards - lecture 3 / Author of the conference Baladi, Viviane.
[Multi angle] Transfer operators for Sinai billiards - lecture 2 / Author of the conference Baladi, Viviane.
[Multi angle] Transfer operators for Sinai billiards - lecture 1 / Author of the conference Baladi, Viviane.

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