Symmetry in Newcastle, 9 August 2021

The state of New South Wales might be in lockdown, but that won’t stop our seminar:
     Symmetry in Newcastle seminar!!

The confirmed speakers for next Monday are (i) Sven Raum, Stockholm University, and (ii) James Parkinson, University of Sydney. Feel free to grab a beverage appropriate for your respective timezone and join us for a friendly chat during the break!

The talks will be recorded and made available on our YouTube channel https://tinyurl.com/zerodimensionalgroup and our website https://zerodimensional.group/. The running time of the talk, title and abstract are as follows:

The zoom link is https://uonewcastle.zoom.us/j/82596235512.

 

Date: 9 August 2021       Time: 16:30–17:30 AEST, (06:30–07:30  UTC)
Speaker: Sven Raum (Stockholm Univ.)
Title: Locally compact groups acting on trees, the type I conjecture and non-amenable von Neumann algebra

Abstract: In the 90s, Nebbia conjectured that a group of tree automorphisms acting transitively on the tree’s boundary must be of type I, that is, its unitary representations can in principal be classified. For key examples, such as Burger-Mozes groups, this conjecture is verified. Aiming for a better understanding of Nebbia’s conjecture and a better understanding of representation theory of groups acting on trees, it is natural to ask whether there is a characterisation of type I groups acting on trees. In 2016, we introduced in collaboration with Cyril Houdayer a refinement of Nebbia’s conjecture to a trichotomy, opposing type I groups with groups whose von Neumann algebra is non-amenable. For large classes of groups, including Burger-Mozes groups, we could verify this trichotomy.

In this talk, I will motivate and introduce the conjecture trichotomy for groups acting on tress and explain how von Neumann algebraic techniques enter the picture.

 

Date: 9 August 2021       Time: 17:30–18:00 AEST, (07:30–08:00  UTC)
Break and chat

Date: 9 August 2021       Time: 18:00–19:00 AEST,  (08:00–09:00  UTC)
Speaker: James Parkinson (U. Sydney)
Title: Automata for Coxeter groups

Abstract: In 1993 Brink and Howlett proved that finitely generated Coxeter groups are automatic. In particular, they constructed a finite state automaton recognising the language of reduced words in the Coxeter group. This automaton is constructed in terms of the remarkable set of “elementary roots” in the associated root system.
In this talk we outline the construction of Brink and Howlett. We also describe the minimal automaton recognising the language of reduced words, and prove necessary and sufficient conditions for the Brink–Howlett automaton to coincide with this minimal automaton. This resolves a conjecture of Hohlweg, Nadeau, and Williams, and is joint work with Yeeka Yau.

 

Hope to see some of you on Monday!

Michal

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