Focus Programmes

Actions of totally disconnected locally compact groups on discrete structures

This Focus Programme aims to foster collaborations in the study of locally compact groups acting on infinite discrete structures such as graphs and buildings. Key themes include geometric and combinatorial approaches, local-to-global phenomena, self-similarity and topological dynamics. We encourage participation of researchers at any career stage in related fields.

Conferences and Workshops:

• 4 - 8 September 2023: Summer School
  Introduction to totally disconnected locally compact groups
  This summer school provides an introduction to various aspects of t.d.l.c. groups aimed at graduate students and postgraduate fellows. Topics include Cayley-Abels graphs, homological methods, p-adic Lie groups and self-similarity.

• 11 - 15 September 2023: Workshop 1
  Totally disconnected locally compact groups from a geometric perspective
  Many discrete geometric structures admit symmetries that are not determined by a finite substructure. This phenomenon is reflected in the non-discreteness of their automorphism group. Conversely, sufficiently non-discrete t.d.l.c. groups admit geometric actions on such structures. This workshop focuses on the above approaches and their interplay.
• 9 - 13 October 2023: Workshop 2
  Totally disconnected locally compact groups: local to global
  This workshop studies the relationship between local, or small-scale, and global, or large-scale, properties of t.d.l.c. groups, which is more subtle than for Lie groups. Small-scale structure, which manifests both in the topological group structure and the objects on which the groups act, interacts with large-scale properties such as simplicity, amenability and quasi-isometry type.

Organisers:

Simon André (Münster), Michal Ferov (Newcastle), Alejandra Garrido (Madrid), Shirly Geffen (Münster), David Kerr (Münster), Colin Reid (Newcastle), Katrin Tent (Münster), Stephan Tornier (Newcastle), George Willis (Newcastle)

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News 06/2023: Humboldt Research Awards for Prof. George Willis and Dr. Colin Reid

Effective and dynamic behaviour of random structures

This Focus Programme addresses probability theory and its interplay with analysis as well as mathematical physics. Topics include Gaussian multiplicative chaos, Liouville quantum gravity, renormalization theory, stochastic partial differential equations, stochastic approximation for neural networks, optimal transport, branching random walks, random polytopes and random graphs.

Conferences and Workshops:

• 20 - 24 June 2022: Quantum many body systems and interacting particles
• 23 - 29 September 2022: Stochastic analysis and applications
• 20 - 24 March 2023: Random discrete structures

Organisers:

Gerold Alsmeyer, Steffen Dereich, Anna Gusakova, Martin Huesmann, Arnulf Jentzen, Zakhar Kabluchko, Matthias Löwe, Chiranjib Mukherjee, André Schlichting, Christian Seis, Angela Stevens, Raimar Wulkenhaar, Caterina Zeppieri

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Previous Focus Programmes

Geometry and PDEs: from theory to applications

This Focus Programme aims to connect the fields of differential geometry, metric geometry, PDEs, calculus of variations, data science and numerics. We will study geometric flows, geometric viewpoints on PDEs and data, as well as measure-based generalizations of geometric notions.

Conferences and Workshops:

• 1-7 August 2021: Workshop on Curvature and Global Shape
• 20-24 September 2021: Analysis on singular spaces
• 1-5 November 2021: New Trends in Geometric PDEs

Organisers:

Christoph Böhm, Manuel Friedrich, Hans-Joachim Hein, Gustav Holzegel, Martin Huesmann, Joachim Lohkamp, Stephan Luckhaus, Christian Seis, Anna Siffert, Burkhard Wilking, Benedikt Wirth, Caterina Zeppieri

Coordinators:

Christoph Böhm
Benedikt Wirth

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Operator algebras and topological dynamics: amenability and beyond

This is a Focus Programme on operator algebras and their interplay with group actions. In this context we will be interested in amenable structures and their many incarnations, and in rigidity phenomena which typically arise as soon as one leaves the amenable setup.

Conferences and Workshops:

• 7-10 June 2021: Interactions between expanders, groups and operator algebras
• 28 June - 9 July 2021: Groups meet C*-algebras, in honour of Siegfried Echterhoff’s 60th birthday
• 12-16 July 2021: Cuntz semigroups Workshop
• 2-13 August 2021: Young Mathematicians in C*-Algebra

Organisers:

Kristin Courtney, Tim de Laat, Siegfried Echterhoff, Eusebio Gardella, Wilhelm Winter

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