I am currently a PhD student at IMJ-PRG University of Paris, under the supervision of Romain Tessera (CNRS & IMJ-PRG, Paris) and Anthony Genevois (CNRS & IMAG, Montpellier). I completed my master degree at EPFL, working mainly under the guidance of Nicolas Monod. More details on my CV.
Interests
My main interests lie in group theory, especially in geometric, combinatorial, analytic and
probabilistic aspects.
Currently, I focus on the study of the asymptotic and large scale geometry of lamplighter-like groups.
Some key themes: quasi-isometric rigidity, large-scale geometry of halo products (see in particular this very nice paper), negative curvature,
amenability, random walks, (quantitative) orbit and measure equivalences etc.
Research
In preparation
4. On quantitative orbit equivalence for lamplighter-like groups, joint with Corentin Correia.
3. Isoperimetric profiles of lamplighter-like groups, joint with Corentin Correia.
Preprints
2. Quasi-isometric rigidity for lamplighters with lamps of polynomial growth, 21 pages, preprint arxiv, 2025.
1. On the quasi-isometric classification of permutational wreath products, 52 pages, preprint arxiv, 2024.
Talks
To come
June 2025: Ergodic theory seminar, IRMAR, Rennes, France.
May 2025: Geometries seminar, ICJ, Lyon, France.
April 2025: BGSU-TU Geometry and Topology seminar, online.
Past
March 2025: Darboux seminar, IMAG, Montpellier, France.
March 2025: Geometry and applications seminar, IRMA, Strasbourg, France.
February 2025: Working group on ergodic theory, IMJ-PRG, France. Recording of part I, and of part II.
January 2025: PhD seminar, LAREMA, Angers, France.
July 2024: Journées des doctorants de l'équipe AO, IMJ-PRG, Paris, France.
Activities
Since January 2025: Co-organizer (with Corentin Correia) of the working group Geometric group theory and its coarse neighborhood at IMJ-PRG.
Since October 2023: Co-organizer (with Francesca Rizzo and Sébastien Biebler) of the PhD students seminar at IMJ-PRG.
Teaching
Current semester
Free of charge.
Past semesters
Fall 2024: Mathematics I, Interactions between maths and physics.
Spring 2024: Oral interrogations in linear algebra and real analysis.
Fall 2023: Mathematics I, Interactions between maths and physics.
Theses
- Geometric approaches to amenability and unitarisability. Master thesis, EPFL. Click here for a quick overview of the project.
- Amenability of discrete groups through random walks: two major results. Semester project, EPFL.
Miscellaneous
Here you find several texts I wrote for different purposes, for instance when following in class, or just for fun! They are most likely incomplete and containing typos and mistakes, feel free to contact me if you spot any of those!
- Topological groups, coarse embeddings and quasi-isometry invariants
- Spectral theory: lecture notes, and exercises
- Ergodic theory: lecture notes
- Galois theory: lecture notes (in French), and exercises
- Amenability of groups and actions
- Basics from representation theory
Contact
Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris Cité.
Bâtiment Sophie Germain, 8, place Aurélie Nemours, 75205 Paris Cedex 13.
Bureau 752.
vincent.dumoncel@imj-prg.fr