Analytic aspects of locally compact groups acting on Euclidean buildings
(2014)
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- Authors
- Supervisors
- Caprace, Pierre-Emmanuel
- Abstract
- The research topic of my doctoral thesis explores the world of totally disconnected locally compact (t.d.l.c.) groups through the interaction with several geometric and harmonic analytic concepts. When investigating the existence of various properties of t.d.l.c groups, this interplay is far from being well understood. For example, this is the case when studying what are the necessary conditions of a t.d.l.c. group to enjoy the Howe--Moore property. Even for specific t.d.l.c. groups acting on d-regular trees, this problem remains widely open and only partials results have been obtained in this thesis. In consequence, new notions and techniques need to be discovered and exploited. Such a notion, namely, strongly regular hyperbolic elements, already emerged as a necessity to solve in full generality one of the questions proposed in my PhD project. This question was to characterize locally compact groups acting on Euclidean buildings and admitting a Gelfand pair. The particular dynamical properties of strongly regular hyperbolic elements beautifully link geometry with harmonic analysis. Additionally, these elements appear to have several other applications, for example, answering the flat closing problem for general buildings.
- Affiliations
Citations
Ciobotaru, C. G. (2014). Analytic aspects of locally compact groups acting on Euclidean buildings. https://hdl.handle.net/2078.5/54464