Research
Interests
I am interested in geometry, and more specifically in questions involving one or several of the following keywords :
Discrete groups of isometries (in particular, Coxeter groups), and their fundamental polytopes and invariants
Combinatorial and computational methods in geometry and group theory
Applications of geometry and/or combinatorics, for instance to complex networks (electrical networks, foodwebs, etc), or to (computational) social sciences.
I am also currently working on educational and outreach projects in mathematics and science, especially for prospective students as well as students in science.
Publications
In preparation
Fundamental hyperbolic polygons of minimal area (with Simon Zürcher).
Published
On the robustness of democratic electoral processes to computational propaganda (with Glory Givi, Robin Delabays and Philippe Jacquod). Scientific Reports 14, 193 (2024). Supplementary information included.
All hyperbolic Coxeter n-cubes (with Steve Tschantz). Journal of Combinatorial Theory, Series A 158, 387-406 (2018). The arXiv preprint contains as an Appendix the explicit classification of all hyperbolic Coxeter 3-cubes.
Commensurability of hyperbolic Coxeter groups : theory and computation (with Rafael Guglielmetti and Ruth Kellerhals). RIMS Kôkyûroku Bessatsu B66 (2017), 57-113.
On hyperbolic Coxeter n-cubes. European Journal of Combinatorics 59 (2017), 192–203.
On commensurable hyperbolic Coxeter groups (with Rafael Guglielmetti and Ruth Kellerhals). Geometriae Dedicata 183(1), 143-167 (2016).
The inradius of a hyperbolic truncated n-simplex. Discrete and Computational Geometry 51 (4), 997-1016 (2014).
Popularization
Tout le monde a déjà vu de la géométrie non euclidienne, Interview given to Hémisphères - Revue suisse de la recherche et de ses applications, No 20, 2020.
Polyèdres et commensurabilité (with Rafael Guglielmetti), Quadrature - Magazine des mathématiques pures et épicées No. 108, 2018. (French adaptation of the MFO Snapshot below).
Polyhedra and commensurability (with Rafael Guglielmetti), Snapshots of Modern Mathematics from Oberwolfach No. 9/2016, 2016.
PhD Thesis
New contributions to hyperbolic polyhedra, reflection groups, and their commensurability. Thesis No 1929, University of Fribourg (2015). DOI 10.13140/RG.2.1.2418.8248.
Other documents
The inradius of a hyperbolic truncated simplex, Poster Session of the Workshop Exotic Geometric Structures, ICERM (Providence RI), 2013.
Distinctions
“Early Postdoc.Mobility” Fellowship from the Swiss National Science Foundation (2016-2017)
Prize for the best talk, 9th Graduate Colloquium, Neuchâtel 2012