Mitglieder und Gäste der Arbeitsgruppe tragen über ihre laufenden Forschungsarbeiten vor.

Hier befindet sich eine Übersicht über die Vorträge in den vergangenen Semestern.

Hier befindet sich eine Übersicht über die Vorträge in den vergangenen Semestern.

- 3 April 2019Matteo Vannacci
**Pro-p groups with quadratic cohomology and generalised p-RAAGs** - 10 April 2019Patrick Wegener
**Diagrammatics of Reflection and Artin Groups** - 17 April 2019Leo Margolis
**Orders of units in integral group rings** - 24 April 2019Sarah Rees
**Rewriting in Artin groups** - 8 May 2019Volkmar Welker
**Higher dimensional connectivity versus minimal degree of random graphs and minimal free resolutions** - the minimal number of vertices that have to be deleted such that the clique complex of the remaining graph has homology in dimension \(i\)
- the minimal number of vertices that have to be deleted such that an \(i\)-simplex in the clique complex has empty link.
- 15 May 2019Xiaolei Wu
**On the homotopy of finite CW-complexes** - 15 May 2019Rachel Skipper
**Generating lamplighter groups with bireversible automata** - 29 May 2019Doryan Temmerman
**Property (FA) for low rank linear groups and applications to \({\mathcal U}({\mathbb Z} G)\)** - 5 June 2019Jonas Beyrer
**Marked length spectrum rigidity of actions on CAT(0) cube complexes** - 19 June 2019Giles Gardam
**Boundaries of hyperbolic and CAT(0) groups and Cannon-Thurston maps** - 19 June 2019Alan Logan
**The Post correspondence problem for free groups** - 26 June 2019Claudio Llosa Isenrich
**Lower bounds on Dehn functions of residually free groups** - 3 July 2019Michael Giudici
**Bases for permutation groups and the Saxl graph**

\( \langle x_1,x_2,\cdots,x_n \mid \overbrace{x_ix_jx_i\cdots}^{ m_{ij}}= \overbrace{x_jx_ix_j \cdots}^{m_{ij}}, i\neq j \in \{1,2,\ldots,n\}\rangle ,\, m_{ij} \in {\mathbb{N}} \cup \{ \infty\}, m_{ij} \geq 2. \)

But it contains a variety of groups with apparently quite different properties. For the class as a whole, many problems remain open, including the word problem; this is in contrast to the situation for Coxeter groups, which arise as quotients of Artin groups. I'll discuss what is known about rewrite systems for Artin groups, and evidence for the possibility of a general approach to rewriting in these groups. I'll give some general background, starting at work of Artin, then Garside, Deligne, Brieskorn-Saito, then move on, via Appel-Schupp, to very recent work, by myself and Derek Holt (and sometimes Laura Ciobanu), by Eddy Godelle and Patrick Dehornoy, also by Blasco, Huang-Osajda.

The main tool will be a natural cross ratio on some boundary of the cube complex. We show that, given two actions with the same marked length spectrum on X and Y, we find subsets of the boundaries of X and Y where the cross ratios coincide and then show that this subset together with the cross ratio already determines the isomorphism type of the cube complex. Similar as Culler-Morgans result can be used to compactify outer space of free groups, we show that this allows to compactify the Charney-Stambaugh-Vogtmann outer space for irreducible RAAGs.

Joint work with Elia Fioravanti.