Orateur
Description
The solution to Hilbert’s fifth problem dictates that every connected locally compact group is an inverse limit of connected Lie groups, and thus Lie theoretic techniques can be used in the study of connected locally compact groups. In contrast, totally disconnected locally compact (tdlc) groups cannot be approximated by Lie groups or algebraic group over tdlc fields, and their structure is not well understood, generally speaking. Modern research in topological group theory is largely focussed on understanding the class of tdlc groups. Furthermore, our understanding of the (unitary) representation theory and harmonic analysis of tdlc groups lags far behind that of connected locally compact groups.
In this talk, I will discuss recent progress on the harmonic analysis of (tdlc) contraction groups. Contraction groups can be viewed, in some sense, as analogues / generalisations of unipotent groups in the theory of tdlc groups. The focus will be on discussing recent progress on the unitary representation theory of these groups, and time pending, I will say a bit about spectral synthesis of certain convolution algebras on these groups.
