Tsung-Hsuan Tsai 蔡宗軒
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Research Interests
My research interests are in geometric group theory, focusing on the Gromov density model of random finitely generated groups. My works on random groups are related to Gromov hyperbolic groups, van Kampen diagrams, small cancellation theory, random graph theory and combinatorial probability.
Here is my Research Statement.
Here is 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.
Published online first in Mathematische Zeitschrift, 303, 65 (2023). SharedIt link. DOI: 10.1007/s00209-022-03186-2.
Accepted
- Phase transition for the existence of van Kampen 2-complexes in random groups, arXiv: 2210.08234.
Accepted by Algebraic & Geometric Topology.
Preprints
- Parallel geodesics and minimal stable length of random groups, arXiv: 2210.07859.
Links
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!, 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)
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.