The left-orderable vonNeumann-Day problem

The left-orderable vonNeumann-Day problem

Markus Oliver Steenbock (ORCID: 0000-0002-0473-9940)

Disciplines

Mathematics (100%)

Keywords

    Geometric Group Theory, Small Cancellation Theory, Left-Orderable Groups, Simple Groups, Tarski monsters, Unique Product Property

Abstract

In this project, we are interested in dynamical, algebraic and geometric properties of groups. A group is an abstract mathematical object that encodes the symmetries of an underlying space. For example, the rotations and translations in the Euclidean plane generate a group. We will in particular work on so-called left-ordered groups. These groups consist of symmetries of the real line that preserve the natural order "larger", "equal", "smaller" on the real line. We plan to study and find such groups with particularly surprising properties. Like this we want to contribute to important open question on left-ordered groups.
Research institution(s)
International project participants

Research Output

  • 6 Publications
  • 1 Scientific Awards
  • 1 Fundings
Publications
  • 2025
    Title On what finitely generated (left-orderable) simple groups can know about their subgroups; In: Séminaires & Congrès 34, Geometric Methods in Group Theory - Papers dedicated to Ruth Charney
    Type Book Chapter
    Publisher Société Mathématique de France
    Pages 59-68
    Link Publication
  • 2025
    Title Random quotients of free products
    Type Other
    Author Einstein E
    Link Publication
  • 2024
    Title Uniform growth in small cancellation groups
    Type Other
    Author Legaspi X
    Link Publication
  • 2022
    Title Product set growth in Burnside groups
    DOI 10.5802/jep.187
    Type Journal Article
    Author Coulon R
    Journal Journal de l’École polytechnique — Mathématiques
    Pages 463-504
    Link Publication
  • 2021
    Title Product set growth in Burnside groups
    DOI 10.48550/arxiv.2102.10885
    Type Preprint
    Author Coulon R
  • 2023
    Title Subgroups and diversity of left-orderable small cancellation groups
    DOI 10.48550/arxiv.2312.12120
    Type Preprint
    Author Steenbock M
    Link Publication
Scientific Awards
  • 2023
    Title Workshop on orderings and groups, ICMAT, Spain
    Type Personally asked as a key note speaker to a conference
    Level of Recognition Continental/International
Fundings
  • 2024
    Title Research in Pairs
    Type Travel/small personal
    Start of Funding 2024
    Funder University of Vienna