Homogeneous spaces, diophantine approximation and stationary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnaires

Collection Homogeneous spaces, diophantine approximation and stationary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnaires

Organizer(s) Adamczewski, Boris ; Athreya, Jayadev ; Mercat, Paul ; Palesi, Frédéric

Date(s) 06/02/2017 - 10/02/2017

linked URL http://conferences.cirm-math.fr/1712.html

00:00:00 / 00:00:00

3 6

Chapters

Dense subgroups in simple groups - Lecture 2

By Yves Benoist

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.

Information about the video

Date of recording 08/02/2017
Date of publication 15/02/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19118103
Cite this video Benoist, Yves (08/02/2017). Dense subgroups in simple groups - Lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19118103
URL https://dx.doi.org/10.24350/CIRM.V.19118103

Domain(s)

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

MSC codes

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