Symmetry in Newcastle, Monday 21st June 2021

Symmetry in Newcastle seminar is here again!

The confirmed speakers for next Monday are Yves Stadler, Université Clermont Auvergne, and Ilaria Castellano, University of Milan–Bicoca.
Feel free to grab a beverage appropriate for your respective timezone and join us for a friendly chat after the talk!

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:

• 16:30–17:30 AEST (06:30–07:30  UTC) Yves Stadler
• 17:30–18:00 AEST (07:30–08:00  UTC) Break and chat
• 18:00–19:00 AEST (08:00–09:00  UTC) Ilaria Castellano

Date: 21 June 2021       Time: 16:30–17:30 AEST (06:30–07:30  UTC)
Speaker: Yves Stadler (Univ. Clermont Auvergne, France)
Title: Highly transitive groups among groups acting on trees

Abstract: Highly transitive groups; i.e., groups admitting an embedding in Sym(N) with dense image, form a wide class of groups. For instance, M. Hull and D. Osin proved that it contains all countable acylindrically hyperbolic groups with trivial finite radical. After an introduction to high transitiviy, I will present a theorem (from joint work with P. Fima, F. Le Maître and S. Moon) showing that many groups acting on trees are highly transitive. On the one hand, this theorem gives new examples of highly transitive groups. On the other hand, it is sharp because of results by A. Le Boudec and N. Matte Bon.

Date: 21 June 2021       Time: 18:00–19:00 AEST (08:00–09:00  UTC)
Speaker: Ilaria Castellano (Univ. Milan–Bicoca, Italy)
Title: The Euler characteristic and the ζ-functions of a totally disconnected locally compact group

Abstract: The Euler–Poincaré characteristic of a discrete group is an important (but also quite mysterious) invariant. It is usually just an integer or a rational number and reflects many quite significant properties. The realm of totally disconnected locally compact groups admits an analogue of the Euler–Poincaré characteristic which surprisingly is no longer just an integer, or a rational number, but a rational multiple of a Haar measure. Warning: in order to gain such an invariant the group has to be unimodular and satisfy some cohomological finiteness conditions. Examples of groups satisfying these additional conditions are the fundamental groups of finite trees of profinite groups. What arouses our curiosity is the fact that, in some cases, the Euler–Poincaré characteristic turns out to be miraculously related to a ζ-function. A large part of the talk will be devoted to the introduction of the just-cited objects. We aim at concluding the presentation by facing the concrete example of the group of -points of a split semisimple simply connected algebraic group G over (where denotes a non-archimedean locally compact field of residue characteristic p).

Joint work with Gianmarco Chinello and Thomas Weigel.

 

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

 

Hope to see some of you on Monday!

Michal