Post-edited Dense subgroups in simple groups - Lecture 2
Auteurs : Benoist, Yves (Auteur de la Conférence)
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.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.