Tsung-Hsuan Tsai 蔡宗軒
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Research Interests
I am interested in geometric group theory, in particular: random groups, hyperbolic groups, applications of small cancellation theory and van Kampen diagrams, random graphs and expander graphs, topological dynamics, uniformly recurrent subgroups.
Here is my Research Statement.
My PhD Thesis, "Phase transitions in random groups: free subgroups and van Kampen 2-complexes", and the slides of the defence.
Publications
- Density of random subsets and applications to group theory, arXiv: 2104.09192.
In Journal of Combinatorial Algebra, volume 6, number 3/4 (2022). DOI: 10.4171/JCA/63.
- Freiheitssatz and phase transition for the density model of random groups, arXiv: 2111.08958.
In Mathematische Zeitschrift, 303, 65 (2023). SharedIt link. DOI: 10.1007/s00209-022-03186-2.
- Phase transition for the existence of van Kampen 2-complexes in random groups, arXiv: 2210.08234.
In Algebraic & Geometric Topology, volume 24, issue 7 (2024) 3897–3917. DOI: 10.2140/agt.2024.24.3897
Preprints
- Parallel geodesics and minimal stable length of random groups, arXiv: 2410.07859.
Talks
- 02.2020, 10.2020, 09.2021 Séminaire Doctorant, IRMA, Strasbourg (France)
- 12.2021 Ergodic theory seminar, IRMAR, Rennes (France)
- 12.2021 ENS Group theory seminar, Paris (France, Online)
- 12.2021 Topology seminar, Institut Fourier, Grenoble (France)
- 10.2023 Group de travail Action! (two sessions), ENS Lyon (France)
- 11.2023 Groups and Actions seminar, Institut de Mathématique d'Orsay (France)
- 12.2023 Geometry seminar, Institut Camille Jardan, Lyon (France)
- 02.2024 GADT seminar, IMB, Dijon (France)
- 03.2024 Algebra and geometry seminar, LMNO, Caen (France)
- 03.2025 Geometry and analysis seminar, University of Bristol (UK)
Conferences attended
- Aspects of Geometric Group Theory, IHES summer school 2019 (France), July 2019.
- Frontiers in Analysis and Probability, 8th Strasbourg/Zurich Meeting, University of Zurich (Switzerland), November 2019.
- Young Geometric Group Theorey IX, Saint-Jacut-de-la-Mer (France), February 2020.
- Young Geometric Group Theorey X, Newcastle University (UK, Online), August 2021.
- Geometry in non-positive curvature and Kähler groups, IHES, Bures-sur-Yvette (France), September 2021.
- Hyperbolic groups and their generalisations, IHP, Paris (France), July 2022.
- Rigidity of isometric actions, CIRM, Marseille (France), Mars 2025.