Abstracts of Ghent Methusalem Junior Analysis

Effie Papageorgiou
(University of Crete, Greece)
 

An introduction to multipliers on non-compact symmetric spaces and locally symmetric spaces

The purpose of this talk is to give a brief introduction to Fourier multipliers on symmetric spaces of non-compact type, which are non-positively curved manifolds, including hyperbolic space. Their rich structure induces some remarkable phenomena related to multiplier theory. We also consider quotients of a symmetric space by good enough subgroups of its isometry group, that is, locally symmetric spaces. This talk intends to compare some of the results on settings above with their euclidean analogues. Finally, we examine a family of multipliers that falls outside the scope of standard theory.

Juan Pablo Velasquez Rodriguez
(Ghent University, Belgium) 

An introduction to Vilenkin groups

The purpose of this talk is to give a quick overview of the history and motivation of a particular class of topological groups called Vilenkin groups. Through the exposition of important particular examples, this talk intends to exhibit some of the similarities and differences between the analysis on these groups and the analysis on connected topological groups. Specially, we would like to describe the unitary dual of a Vilenkin group and show how the usual Fourier analysis looks like in this setting.

Hong-Wei Zhang
(Orleans University, France, and UGent) 

An introduction to spherical Fourier analysis on noncompact symmetric spaces

This introductory talk intends to present some preliminaires about the harmonic analysis on Riemannian symmetric spaces of non-compact type for the junior researchers who are interested in such nice negatively curved Riemannian manifolds. By comparing with real hyperbolic spaces (which are rank one symmetric spaces), this talk will focus on the higher rank analysis, I will also share some recent progress on this topic.