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Dense subgroups in simple groups - Lecture 2
Post-edited
Authors : Benoist, Yves (Author of the conference)
CIRM (Publisher )
22E30 - Analysis on real and complex Lie groups
28A78 - Hausdorff and packing measures
43A65 - Representations of groups, semigroups, etc.
CIRM (Publisher )
Abstract :
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.
MSC Codes : 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.
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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 : Representation Theory ; Group Theory Mathematical Area(s) : Lie Theory and Generalizations Format : MP4 (.mp4) - HD Video Time : 01:13:06 Targeted Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2017-02-08_Benoist.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 : 06/02/2017 - 10/02/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1712.html
Citation Data
DOI : 10.24350/CIRM.V.19118103Cite 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 |
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] Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem / Author of the conference Kleinbock, Dmitry.
- [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.
Bibliography
- 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
