Adrien Abgrall's web page

PhD Candidate at IRMAR

Rennes 1 University, Beaulieu Site, Building 23, Office 334

adrien.abgrall _ univ-rennes1.fr

Cette page en français

Research

I study Geometric Group Theory, more precisely the geometry of CAT(0) cube complexes and the outer space of right-angled Artin groups, supervised by Vincent Guirardel. I am also interested in Baumslag-Solitar groups and general graphs of free groups.

Publications

Automorphisms of untwisted outer space for right-angled Artin groups, in preparation

Relative untwisted outer space for right-angled Artin groups, preprint, March 2025

Spatial cube complexes, preprint, November 2024

On residual finiteness in graphs of free groups with cyclic edge groups, with Zachary Munro, preprint, October 2024

Teaching

• Spring 2025 TA for Calculus II MIASHS: the course's webpage
• Spring 2024 TA for Calculus II MIASHS: the course's webpage
• Spring 2023 TA for Calculus II MIASHS: the course's webpage
• Fall 2022 TA for MAT1 SVE: the course's webpage

Archive

• My CV (last updated March 2025)
• Introduction to my research field (written 2022 for my ENS diploma): Géométries des groupes d’automorphismes extérieurs (in french)
• Master's thesis (2021): Outer space for right-angled Artin groups
• Bachelor Thesis, with Maxime Ramzi (2018) : Dynamique topologique et théorie de Ramsey (in french)
• A list of false theorems (find counterexamples!)

Mathematical Illustrations

Introductory video (in french) to the mathematics of origami:

The following images come from 3D models and can be rotated to see them from every angle.

Dupin's cyclide, a cubic surface obtained by inverting a torus at one of its points. It contains 4 real lines and each has complement fibered by circles. Flipping the object over corresponds to the automorphism exchanging the two coordinates of the torus.

More to come soon…