Locally compact groups acting on discrete structures - WinSum School  14 - 18 December 2020

08:00 - 17:00
Room : GA 3 21

Organisers

Alejandra Garrido, Universidad Autónoma de Madrid

Colin Reid, The University of Newcastle, Australia

Stephan Tornier, The University of Newcastle, Australia

George Willis, The University of Newcastle, Australia

This WinSum School is intended as an introduction to the main themes of the program, focusing on key topics of the subsequent workshops: automorphism groups of graphs, dynamics on totally disconnected locally compact groups and their relation to self-similar groups, local structure of totally disconnected locally compact groups, and geometry and dynamics. Speakers include:
  • Waltraud Lederle (UCLouvain)
  • Colin Reid (University of Newcastle, Australia)
  • Zoran Šunić (Hofstra University)
  • George Willis (University of Newcastle, Australia)

The school will consist of mini-courses complemented by problem and discussion sessions.

Topics include:

  1. Automorphism groups of trees and graphs by Waltraud Lederle.
  2. It is a classical fact going back to Abels that every compactly generated, totally disconnected, locally compact group acts vertex-transitively and with compact open vetex stabilizers on some connected, locally finite graph. Such a graph is called a Cayley-Abels graph of the group. Many concepts and results known for the Cayley graph of a finitely generated group find their analogies in Cayley-Abels graphs. But in addition, Cayley-Abels graphs can also give information about the local structure of the group.

    In this mini-course we will give several constructions of Cayley-Abels graphs and prove basic properties. We will show connections between the action on a Cayley-Abels graph and the modular function or the scale function. Particular emphasis will be given to the case where a Cayley-Abels graph is a tree.

  3. Local structure of totally disconnected locally compact groups by Colin Reid.
  4. In a topological group, the local structure is the structure that is present in every neighbourhood of the identity. For totally disconnected locally compact groups, the connection between local and global structure is more subtle than it is for Lie groups, but still gives important information. I will be giving an overview of the local structure theory of totally disconnected locally compact groups, including the existence of arbitrarily small profinite open subgroups (Van Dantzig's Theorem); the universal group of a given local isomorphism type; and the consequences of local decomposition properties.

  5. Self-similar groups by Zoran Šunić.
  6. The set of automorphisms of a regular rooted tree carries three structures: group, metric, and self-similarity. A natural approach then, in the study of groups of tree automorphisms, is to simultaneously employ algebraic, topological, and symbolic dynamics methods. The interplay gives rise to deep and beautiful theory and produces important examples contributing to our understanding of groups and their actions from different points of view.

    Natural sources of finitely generated self-similar groups, such as iterated monodromy groups and, more generally, groups generated by finite self-similar sets (often called automaton groups) will be presented. The usual suspects, adding machine, dihedral, lamplighter, Grigorchuk, Basilica, Hanoi, ... along with a few new examples, will be introduced in sufficient depth to allow understanding of the properties that make them so interesting/significant.

    We will also discuss topologically finitely generated, compact, self-similar groups that arise as closures of self-similar groups. In particular, finitely constrained groups, that is, groups that are tree-shifts of finite type, will be considered.

    The theory of closed self-similar groups fits in the more general framework of the theory of totally disconnected locally compact groups both as an important special case and as a tool that can help in the understanding of the bigger picture.

  7. Endomorphisms and automorphisms of totally disconnected locally compact groups by George Willis.
  8. The dynamics of the action of an endomorphism on a t.d.l.c. group may be characterised through invariants such as the scale of the endomorphism, and described by structures in the group such as subgroups tidy for the endomorphism and its contraction subgroup. These invariants serve to analyse the group when calculated for inner automorphisms. I will illustrate these ideas with numerous examples before going on to say more about how they apply when several automorphisms are considered simultaneously. The key concept here is that of flatness of a group of automorphisms, and results about flat groups will be developed in more detail.
Name University Dates of visit
Faryad Ali Al Imam University (IMSIU), Riyadh 14/12/2020 - 18/12/2020
Laila Alqrafi Tabouk university 14/12/2020 - 18/12/2020
Raphael Appenzeller ETHZ 14/12/2020 - 18/12/2020
Shivam Arora Memorial University of Newfoundland 14/12/2020 - 18/12/2020
Amine Bahayou Kasdi Merbah University 14/12/2020 - 18/12/2020
Oussama Bensaid Paris Diderot 14/12/2020 - 18/12/2020
Federico Berlai University of the Basque Country 14/12/2020 - 18/12/2020
Lara Beßmann University of Münster 14/12/2020 - 18/12/2020
Sebastian Bischof Justus-Liebig Universität (Gießen) 14/12/2020 - 18/12/2020
Corentin Bodart Université de Genève 14/12/2020 - 18/12/2020
Henry Bradford University of Cambridge 14/12/2020 - 18/12/2020
Pierre-Emmanuel Caprace UCLouvain 14/12/2020 - 18/12/2020
Alex Carrazedo Dantas Universidade de Brasília 14/12/2020 - 18/12/2020
Sean Carroll The University of Auckland 14/12/2020 - 18/12/2020
Max Carter University of Newcastle 14/12/2020 - 18/12/2020
Ilaria Castellano Universitá di Udine 14/12/2020 - 18/12/2020
Tal Cohen Weizmann Institute of Science 14/12/2020 - 18/12/2020
Matthew Conder University of Cambridge 14/12/2020 - 18/12/2020
Michelle Daher University of florida 14/12/2020 - 18/12/2020
Kajal Das Institute of Mathematics of Polish Academy of Sciences 14/12/2020 - 18/12/2020
Alexander Dranishnikov University of Florida 14/12/2020 - 18/12/2020
Thibaut Dumont HEP Vaud 14/12/2020 - 18/12/2020
Amandine Escalier Université Paris Diderot 14/12/2020 - 18/12/2020
Gabriel Favre Stockholm University 14/12/2020 - 18/12/2020
Michal Ferov The University of Newcastle, Australia 14/12/2020 - 18/12/2020
Francesco Fournier Facio ETH Zurich 14/12/2020 - 18/12/2020
Dominik Francoeur ENS Lyon 14/12/2020 - 18/12/2020
Shintaro Fushida-Hardy Stanford University 14/12/2020 - 18/12/2020
Giles Gardam University of Münster 14/12/2020 - 18/12/2020
Alejandra Garrido Universidad Autónoma de Madrid 14/12/2020 - 18/12/2020
Max Gheorghiu University of British Colombia 14/12/2020 - 18/12/2020
Gil Goffer Weizmann Institute of Science 14/12/2020 - 18/12/2020
Roman Gorazd University of Newcastle 14/12/2020 - 18/12/2020
Armando W. Gutiérrez INRIA Saclay and Ecole Polytechnique 14/12/2020 - 18/12/2020
Stefan Hammer TU Graz 14/12/2020 - 18/12/2020
Anton Hase Technion Israel Institute of Technology 14/12/2020 - 18/12/2020
Sam Hughes University of Southampton 14/12/2020 - 18/12/2020
Colin Jahel Université Claude Bernard Lyon 1 14/12/2020 - 18/12/2020
S.M.B. Kashani Tarbiat Modares University 14/12/2020 - 18/12/2020
Daniel Keppeler Universität Münster 14/12/2020 - 18/12/2020
Alice Kerr Oxford University 14/12/2020 - 18/12/2020
Mile Krajcevski University of South Florida 14/12/2020 - 18/12/2020
Yannick Krifka ETH Zürich 14/12/2020 - 18/12/2020
Rishi Kumar Ben gurion university 14/12/2020 - 18/12/2020
Octave Lacourte Université Claude Bernard Lyon 1 14/12/2020 - 18/12/2020
Adrien Le Boudec CNRS - ENS Lyon 14/12/2020 - 18/12/2020
Waltraud Lederle UCLouvain 14/12/2020 - 18/12/2020
Florian Lehner TU Graz 14/12/2020 - 18/12/2020
Elyasheev Leibtag Weizmann Institute 14/12/2020 - 18/12/2020
Arkady Leiderman Ben-Gurion University of the Negev 14/12/2020 - 18/12/2020
Diego Liberati National research council of Italy 14/12/2020 - 18/12/2020
Christian Lindorfer Graz University of Technology 14/12/2020 - 18/12/2020
Arunava Mandal Indian Statistical Institute, Bangalore 14/12/2020 - 18/12/2020
Eduardo Martinez Pedroza Memorial University 14/12/2020 - 18/12/2020
Pratyush Mishra North Dakota State University 14/12/2020 - 18/12/2020
Bernhard Muehlerr Justus Liebig University Giessen 14/12/2020 - 18/12/2020
Philip Möller University of Münster 14/12/2020 - 18/12/2020
Mike Ogiugo University of Ibadan 14/12/2020 - 18/12/2020
Lluís Pastor Pérez EPFL 14/12/2020 - 18/12/2020
Jan Moritz Petschick Heinrich Heine Universität Düsseldorf 14/12/2020 - 18/12/2020
Joao Vitor Pinto e Silva University of Newcastle 14/12/2020 - 18/12/2020
Karthika Rajeev Heinrich Heine Universität Düsseldorf 14/12/2020 - 18/12/2020
Colin Reid The University of Newcastle, Australia 14/12/2020 - 18/12/2020
Anju Saini Graphic Era Deemed University Dehradun 14/12/2020 - 18/12/2020
Tulio Santos Universidade de Brasília 14/12/2020 - 18/12/2020
Mohammed Saqlain Khan Rheinische Friedrich-Wilhelms-Universität Bonn 14/12/2020 - 18/12/2020
Bakul Sathaye University of Münster 14/12/2020 - 18/12/2020
Lancelot Semal UCLouvain 14/12/2020 - 18/12/2020
Rachel Skipper The Ohio State University 14/12/2020 - 18/12/2020
Meisam Soleimani Malekan University of Isfahan 14/12/2020 - 18/12/2020
Nico Stucki Karlsruhe Institute of Technology 14/12/2020 - 18/12/2020
François Thilmany KU Leuven 14/12/2020 - 18/12/2020
Thomas Titz Mite Justus-Liebig-Universität Gießen 14/12/2020 - 18/12/2020
Stephan Tornier The University of Newcastle, Australia 14/12/2020 - 18/12/2020
Olga Varghese University of Münster 14/12/2020 - 18/12/2020
Torben Wiedemann Justus Liebig University Gießen 14/12/2020 - 18/12/2020
George Willis The University of Newcastle, Australia 14/12/2020 - 18/12/2020
Stefan Witzel Gießen University 14/12/2020 - 18/12/2020
Wolfgang Woess TU Graz 14/12/2020 - 18/12/2020
Zhiqiang Xiao Peking University 14/12/2020 - 18/12/2020
Zoran Šunić Hofstra University 14/12/2020 - 18/12/2020
Total Guests : 81
Name University Dates of visit
Waltraud Lederle UCLouvain 14/12/2020 - 18/12/2020
Colin Reid The University of Newcastle, Australia 14/12/2020 - 18/12/2020
George Willis The University of Newcastle, Australia 14/12/2020 - 18/12/2020
Zoran Šunić Hofstra University 14/12/2020 - 18/12/2020
Total Guests : 4
Conference in Honor of the 70th Birthday of Tudor Ratiu, 20 to 24 July 2020.
Registration fees of CHF 50.- are mandatory for visits from 1 day to full attendance of the conference.
Cancellations and no-shows are not eligible for a refund.
I hereby agree to the conditions of the registration fees and to settling the amount by 28 February 2020.

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All videos are available here : https://tube.switch.ch/channels/ac9077a5?order=oldest-first&view=list

Monday 14 December
08:30 Local structure of totally disconnected locally compact groups I (Colin Reid)
10:00 Endomorphisms and automorphisms of totally disconnected locally compact groups I (George Willis)
11:30 Workshop
14:00 Automorphism groups of trees and graphs I (Waltraud Lederle)
15:30 Workshop
17:00 Self-similar groups I (Zoran Šunić)
18:30 Workshop

Tuesday 15 December
07:00 Workshop
08:30 Local structure of totally disconnected locally compact groups II (Colin Reid)
10:00 Endomorphisms and automorphisms of totally disconnected locally compact groups II (George Willis)
11:30 Workshop
14:00 Automorphism groups of trees and graphs II (Waltraud Lederle)
15:30 Workshop
17:00 Self-similar groups II (Zoran Šunić)
18:30 Workshop

Wednesday 16 December
07:00 Workshop
08:30 Local structure of totally disconnected locally compact groups III (Colin Reid)
10:00 Endomorphisms and automorphisms of totally disconnected locally compact groups III (George Willis)
11:30 Workshop
14:00 Automorphism groups of trees and graphs III (Waltraud Lederle)
15:30 Workshop
17:00 Self-similar groups III (Zoran Šunić)
18:30 Workshop

Thursday 17 December
07:00 Workshop
08:30 Local structure of totally disconnected locally compact groups IV (Colin Reid)
10:00 Endomorphisms and automorphisms of totally disconnected locally compact groups IV (George Willis)
11:30 Workshop
14:00 Automorphism groups of trees and graphs IV (Waltraud Lederle)
15:30 Workshop
17:00 Self-similar groups IV (Zoran Šunić)
18:30 Workshop

Friday 18 December
07:00 Workshop
08:30 Local structure of totally disconnected locally compact groups V (Colin Reid)
10:00 Endomorphisms and automorphisms of totally disconnected locally compact groups V (George Willis)
11:30 Workshop
14:00 Automorphism groups of trees and graphs V (Waltraud Lederle)
15:30 Workshop
17:00 Self-similar groups V (Zoran Šunić)
18:30 Workshop