The left-orderable vonNeumann-Day problem
The left-orderable vonNeumann-Day problem
Markus Oliver Steenbock
(ORCID: 0000-0002-0473-9940)
Disciplines
Mathematics (100%)
Keywords
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Geometric Group Theory,
Small Cancellation Theory,
Left-Orderable Groups,
Simple Groups,
Tarski monsters,
Unique Product Property
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)
- Universität Wien - 100%
International project participants
Research Output
- 6 Publications
- 1 Scientific Awards
- 1 Fundings
Publications
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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
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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
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2024
Title Research in Pairs Type Travel/small personal Start of Funding 2024 Funder University of Vienna