Steffen Kionke

activity

20122025

most citedZeta functions associated to admissible representations of compact p-adic Lie groups

5 citations · 49 across the 28 of their papers we have counts for

collaborators

30 papers

math.GR2025

Infinite groups from the profinite point of view

Holger Kammeyer, Steffen Kionke

We survey recent work ranging around the question in how far a group, or a property of a group, is determined by the set of finite quotient groups. Our focus lies on $S$ -arithmetic…

math.GR2024

Asymptotic invariants of residually finite just infinite groups

Andrei Jaikin-Zapirain, Steffen Kionke

Recently, Eduard Schesler and the second author constructed examples of finitely generated residually finite, hereditarily just infinite groups with positive first $L^{2}$ -Betti numb…

math.GR2024

Profiniteness of higher rank volume

Holger Kammeyer, Steffen Kionke, Ralf Köhl

We show that the covolume of an irreducible lattice in a higher rank semisimple Lie group with the congruence subgroup property is determined by the profinite completion. Without r…

math.GR2024

Hereditarily just-infinite torsion groups with positive first $ℓ^{2}$ -Betti number

Steffen Kionke, Eduard Schesler

We present a new method to construct finitely generated, residually finite, infinite torsion groups. In contrast to known constructions, a profinite perspective enables us to contr…

math.GR2023

Gassmann triples with special cycle types and applications

Holger Kammeyer, Steffen Kionke

We show that if one of various cycle types occurs in the permutation action of a finite group on the cosets of a given subgroup, then every almost conjugate subgroup is conjugate.…

math.GR2023

From telescopes to frames and simple groups

Steffen Kionke, Eduard Schesler

We introduce the notion of a telescope of groups. Very roughly a telescope is a directed system of groups that contains various commuting images of some fixed group $B$ . Telescopes…

math.GR2023

On representations of direct products and the bounded generation property of branch groups

Steffen Kionke, Eduard Schesler

We prove that the minimal representation dimension of a direct product $G$ of non-abelian groups $G_{1}, \dots, G_{n}$ is bounded below by $n + 1$ and thereby answer a question of Abért.…

math.GR2022★ 2 cited

Realizing residually finite groups as subgroups of branch groups

Steffen Kionke, Eduard Schesler

We prove that every finitely generated, residually finite group $G$ embeds into a finitely generated perfect branch group $Γ$ such that many properties of $G$ are preserved under t…

math.GR2022

Weil zeta functions of group representations over finite fields

Ged Corob Cook, Steffen Kionke, Matteo Vannacci

In this article we define and study a zeta function $ζ_{G}$ - similar to the Hasse-Weil zeta function - which enumerates absolutely irreducible representations over finite fields of…

math.GR2022★ 3 cited

On absolutely profinitely solitary lattices in higher rank Lie groups

Holger Kammeyer

We establish conditions under which lattices in certain simple Lie groups are profinitely solitary in the absolute sense, so that the commensurability class of the profinite comple…

math.GR2022

On upper bounds for the first $ℓ^{2}$ -Betti number

Carsten Feldkamp, Steffen Kionke

This article presents a method for proving upper bounds for the first $ℓ^{2}$ -Betti number of groups using only the geometry of the Cayley graph. As an application we prove that B…

math.GR2021

Counting irreducible modules for profinite groups

Ged Corob Cook, Steffen Kionke, Matteo Vannacci

This article is concerned with the representation growth of profinite groups over finite fields. We investigate the structure of groups with uniformly bounded exponential represent…

math.GR2021★ 3 cited

Amenability and profinite completions of finitely generated groups

Steffen Kionke, Eduard Schesler

This article explores the interplay between the finite quotients of finitely generated residually finite groups and the concept of amenability. We construct a finitely generated, r…

math.GR2020★ 5 cited

Adelic superrigidity and profinitely solitary lattices

Holger Kammeyer, Steffen Kionke

By arithmeticity and superrigidity, a commensurability class of lattices in a higher rank Lie group is defined by a unique algebraic group over a unique number subfield of $\mathbb…

math.GR2020★ 1 cited

On the profinite rigidity of lattices in higher rank Lie groups

Holger Kammeyer, Steffen Kionke

We investigate which higher rank simple Lie groups admit profinitely but not abstractly commensurable lattices. We show that no such examples exist for the complex forms of type $E…

math.GT2020★ 1 cited

A note on $p$ -adic simplicial volumes

Steffen Kionke, Clara Loeh

We define and study generalizations of simplicial volume over arbitrary seminormed rings with a focus on $p$ -adic simplicial volumes. We investigate the dependence on the prime and…

math.AT2019

Equivariant Benjamini-Schramm Convergence of Simplicial Complexes and $ℓ^{2}$ -Multiplicities

Steffen Kionke, Michael Schrödl-Baumann

We define a variant of Benjamini-Schramm convergence for finite simplicial complexes with the action of a fixed finite group G which leads to the notion of random rooted simplicial…

math.GR2019

Profinite invariants of arithmetic groups

Holger Kammeyer, Steffen Kionke, Jean Raimbault +1

We prove that the sign of the Euler characteristic of arithmetic groups with CSP is determined by the profinite completion. In contrast, we construct examples showing that this is…

math.AT2018★ 5 cited

On $p$ -adic limits of topological invariants

Steffen Kionke

The purpose of this article is to define and study new invariants of topological spaces: the $p$ -adic Betti numbers and the $p$ -adic torsion. These invariants take values in the $p…

math.GR2018★ 4 cited

Groups acting on rooted trees and their representations on the boundary

Steffen Kionke

We consider groups that act on spherically symmetric rooted trees and study the associated representation of the group on the space of locally constant functions on the boundary of…

math.AT2017★ 2 cited

The growth of Betti numbers and approximation theorems

Steffen Kionke

These short lecture notes provide a brief introduction to the field of homology growth. They are composed out of two lectures, which I have given at the Borel seminar 2017 in Les D…

math.GR2017★ 5 cited

Zeta functions associated to admissible representations of compact p-adic Lie groups

Steffen Kionke, Benjamin Klopsch

Let $G$ be a profinite group. A strongly admissible smooth representation $ρ$ of $G$ over $C$ decomposes as a direct sum $ρ\cong \bigoplus_{π\in \mathrm{Irr}(G)} m_π(ρ) \,…

math.GR2017★ 5 cited

Characters, $L^{2}$ -Betti numbers and an equivariant approximation theorem

Steffen Kionke

Let $G$ be a group with a finite subgroup $H$ . We define the $L^{2}$ -multiplicity of an irreducible representation of $H$ in the $L^{2}$ -homology of a proper $G$ -CW-complex. These inva…

math.GR2016★ 5 cited

Positively finitely related profinite groups

Steffen Kionke, Matteo Vannacci

We define and study the class of positively finitely related (PFR) profinite groups. Positive finite relatedness is a probabilistic property of profinite groups which provides a fi…

Infinite groups from the profinite point of view

Asymptotic invariants of residually finite just infinite groups

Profiniteness of higher rank volume

Hereditarily just-infinite torsion groups with positive first ℓ2-Betti number

Gassmann triples with special cycle types and applications

From telescopes to frames and simple groups

On representations of direct products and the bounded generation property of branch groups

Realizing residually finite groups as subgroups of branch groups

Weil zeta functions of group representations over finite fields

On absolutely profinitely solitary lattices in higher rank Lie groups

On upper bounds for the first ℓ2-Betti number

Counting irreducible modules for profinite groups

Amenability and profinite completions of finitely generated groups

Adelic superrigidity and profinitely solitary lattices

On the profinite rigidity of lattices in higher rank Lie groups

A note on p-adic simplicial volumes

Equivariant Benjamini-Schramm Convergence of Simplicial Complexes and ℓ2-Multiplicities

Profinite invariants of arithmetic groups

On p-adic limits of topological invariants

Groups acting on rooted trees and their representations on the boundary

The growth of Betti numbers and approximation theorems

Zeta functions associated to admissible representations of compact p-adic Lie groups

Characters, L2-Betti numbers and an equivariant approximation theorem

Positively finitely related profinite groups

Hereditarily just-infinite torsion groups with positive first $ℓ^{2}$ -Betti number

On upper bounds for the first $ℓ^{2}$ -Betti number

A note on $p$ -adic simplicial volumes

Equivariant Benjamini-Schramm Convergence of Simplicial Complexes and $ℓ^{2}$ -Multiplicities

On $p$ -adic limits of topological invariants

Characters, $L^{2}$ -Betti numbers and an equivariant approximation theorem