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A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.
Sommario
Foreword George Willis; 1. On the role of totally disconnected groups in the structure of locally compact groups Marc Burger; 2. Locally compact groups as metric spaces Romain Tessera; 3. A short primer on profinite groups John S. Wilson; 4. Lectures on Lie groups over local fields Helge Gloeckner; 5. Abstract quotients of profinite groups, after Nikolov and Segal Benjamin Klopsch; 6. Automorphism groups of trees: generalities and prescribed local actions Alejandra Garrido, Yair Glasner and Stephan Tornier; 7. Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups Colin Reid and George Willis; 8. The Neretin groups ¿ukasz Garncarek and Nir Lazarovich; 9. The scale function and tidy subgroups Albrecht Brehm, Maxime Gheysens, Adrien Le Boudec and Rafaela Rollin; 10. Contraction groups and the scale Phillip Wesolek; 11. The Bader-Shalom normal subgroup theorem ¿wiatos¿aw Gal; 12. Burger-Mozes' simple lattices Laurent Bartholdi; 13. A lecture on invariant random subgroups Tsachik Gelander; 14. L2-Betti number of discrete and non-discrete groups Roman Sauer; 15. Minimal normal closed subgroups in compactly generated tdlc groups Thibaut Dumont and Dennis Gulko; 16. Elementary totally disconnected locally compact groups, after Wesolek Morgan Cesa and François Le Maître; 17. The structure lattice of a totally disconnected locally compact group John S. Wilson; 18. The centraliser lattice David Hume and Thierry Stulemeijer; 19. On the quasi-isometric classification of locally compact groups Yves de Cornulier; 20. Future directions in locally compact groups: a tentative problem list Pierre-Emmanuel Caprace and Nicolas Monod; Index.
Info autore
Pierre-Emmanuel Caprace is a member of the Institute of Research in Mathematics and Physics (IRMP) at the Catholic University of Leuven, Belgium. His joint work with his co-author, Nicolas Monod, received the Berwick Prize from the London Mathematical Society in 2015.Nicolas Monod is a professor and director of the research chair EGG at École Polytechnique Fédérale de Lausanne. He is also the Director of the Bernoulli Center (CIB). His joint work with his co-author, Pierre-Emmanuel Caprace, received the Berwick Prize from the London Mathematical Society in 2015.
Riassunto
This collection of expository articles provides an overview of the major renaissance happening today in the study of locally compact groups and their many connections to other areas of mathematics, including geometric group theory, measured group theory and rigidity of lattices. For researchers and graduate students.
