Until October Mireia Taus Nebot does a summer research internship supported by the DAAD in our working group. During her internship she'll work together with Marco Lotz on computer generated geometric realizations of Coxeter groups.
Welcome Mireia, we wish you a great stay in Magdeburg!
As of August 2021 Petra Schwer has joined the Editorial board of Innovations in Incidence Geometry - Algebraic, topological and combinatorial.
IIG publishes carefully selected and peer-reviewed original research papers of the highest quality about all aspects of incidence geometry and its applications. These include
- finite and combinatorial geometry,
- rank-2 geometries,
- geometry of groups,
- Tits-buildings and diagram geometries,
- incidence geometric aspects of algebraic geometry,
- incidence geometric aspects of algebraic combinatorics,
- computational aspects,
- arrangements of hyperplanes,
- abstract polytopes and convex polytopes,
- tropical and F1 geometry,
- Coxeter groups and root systems,
- topological geometry,
- applications of incidence geometry (including coding theory, cryptography, quantum information theory).
The preprint "Automatic continuity for groups whose torsion subgroups are small" by Daniel Keppeler, Philip Möller and Olga Varghese has been recently uploaded to the arXiv!
Link to the paper: arXiv:2106.12547
We prove that a group homomorphism φ:L→G from a locally compact Hausdorff group L into a discrete group G either is continuous, or there exists a normal open subgroup N⊆L such that φ(N) is a torsion group provided that G does not include Q or the p-adic integers Zp or the Prüfer p-group Z(p∞) for any prime p as a subgroup, and if the torsion subgroups of G are small in the sense that any torsion subgroup of G is artinian. In particular, if φ is surjective and G additionaly does not have non-trivial normal torsion subgroups, then φ is continuous.
As an application we obtain results concerning the continuity of group homomorphisms from locally compact Hausdorff groups to many groups from geometric group theory, in particular to automorphism groups of right-angled Artin groups and to Helly groups.