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Post-edited Dense subgroups in simple groups - Lecture 2

Auteurs : Benoist, Yves (Auteur de la Conférence)
CIRM (Editeur )

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convolution of Frostman measures Hausdorff dimension of subgroups convolution of functions on Lie groups Plancherel formula in compact groups Decay of Fourier coefficients coefficients in high frequencies convolution inequality questions of the audience

Résumé : In this series of lectures, we will focus on simple Lie groups, their dense subgroups and the convolution powers of their measures. In particular, we will dicuss the following two questions.
Let G be a Lie group. Is every Borel measurable subgroup of G with maximal Hausdorff dimension equal to the group G?
Is the convolution of sufficiently many compactly supported continuous functions on G always continuously differentiable?
Even though the answer to these questions is no when G is abelian, the answer is yes when G is simple. This is a joint work with N. de Saxce. First, I will explain the history of these two questions and their interaction. Then, I will relate these questions to spectral gap properties. Finally, I will discuss these spectral gap properties.

Codes MSC :
22E30 - Analysis on real and complex Lie groups
28A78 - Hausdorff and packing measures
43A65 - Representations of groups, semigroups, etc.

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 15/02/17
    Date de captation : 08/02/17
    Collection : Research schools
    Format : MP4 (.mp4) - HD
    Durée : 01:13:06
    Domaine : Lie Theory and Generalizations
    Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-02-08_Benoist.mp4

Informations sur la rencontre

Nom du congrès : Homogeneous Spaces, diophantine approximation and stationnary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnaires
Organisteurs Congrès : Adamczewski, Boris ; Athreya, Jayadev ; Mercat, Paul ; Palesi, Frédéric
Dates : 06/02/2017 - 10/02/2017
Année de la rencontre : 2017
URL Congrès : http://conferences.cirm-math.fr/1712.html

Citation Data

DOI : 10.24350/CIRM.V.19118103
Cite this video as: Benoist, Yves (2017). Dense subgroups in simple groups - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19118103
URI : http://dx.doi.org/10.24350/CIRM.V.19118103

Voir aussi

Bibliographie

  1. Benoist, Y., & de Saxcé, N. (2016). Convolution in perfect Lie groups. Mathematical Proceedings of the Cambridge Philosophical Society, 161(1), 31-45 - https://doi.org/10.1017/S0305004116000074



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