English
Dense subgroups in simple groups - Lecture 2
Post-edited
Auteurs : Benoist, Yves (Auteur de la Conférence)
CIRM (Editeur )
22E30 - Analysis on real and complex Lie groups
28A78 - Hausdorff and packing measures
43A65 - Representations of groups, semigroups, etc.
CIRM (Editeur )
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 : 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.
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, GuillaumeLangue : Anglais Date de publication : 15/02/17 Date de captation : 08/02/17 Sous collection : Research School arXiv category : Representation Theory ; Group Theory Domaine : Lie Theory and Generalizations Format : MP4 (.mp4) - HD Durée : 01:13:06 Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2017-02-08_Benoist.mp4 
|
Informations sur la Rencontre
Nom de la rencontre : Homogeneous Spaces, diophantine approximation and stationary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnairesOrganisateurs de la rencontre : 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
Données de citation
DOI : 10.24350/CIRM.V.19118103Citer cette vidéo: 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
- [Multi angle] Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic? / Auteur de la Conférence Paulin, Frédéric.
- [Multi angle] Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem / Auteur de la Conférence Kleinbock, Dmitry.
- [Multi angle] Dynamics on quotients of SL(2,C) by discrete subgroups - Lecture 2 / Auteur de la Conférence Schapira, Barbara.
- [Multi angle] Dynamics on homogeneous spaces and Diophantine approximation / Auteur de la Conférence Ghosh, Anish.
Bibliographie
- 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
