Project CoMTE

Presentation

CoMTE (COmbinatoire du groupe Modulaire et Triangulations Enracinées) is a project funded as part of the 2024 campaign of the "appel à projets Paris 8" and extended for another year during 2025. Broadly, the project aims to:

Explore the combinatorics of triangulations and their relation to (subgroups of) the modular group \(PSL(2,\mathbb{Z})\) and related objects such as triangle groups.
Explore the combinatorics of dessins d'enfants.
Explore spectral-theoretic properties of such objects, notably the Ihara zeta functions and their relation to Von Neumann algebras attached to congruence subgroups of the modular group.

The collaboration has resulted in a preprint and two workshops, as of October 2025.

Members:

The project was co-initiated by Alexandros Singh and Revekka Kyriakoglou, and currently involves researchers distributed across laboratories in France (LIX, LIASD) and Greece (AMMM). You can find the full listing of project members below.

Seminar

As part of this project, the following seminars have been given:

06/03/2024: Alexandros Singh "An introduction to the combinatorics of triangulations and trivalent maps"
27/03/2024: Revekka Kyriakoglou "Recognizable morphisms and a decision algorithm for substitutive languages"
17/04/2024: Prassidis Efstratios "Spectral theory of graphs"
05/06/2024: Vassilis Metaftsis "Constellations and maps, part 1"
12/06/2024: Alexandros Singh "Constellations and maps, part 2"
04/07/2024: Prassidis Efstratios "Dessins d’enfants, Constellations, Belyi Maps"

CoMTE Meetings

September 2024

The first international meeting of the CoMTE project took place during the first week of September 2024 at the Department of Mathematics, University of Aegean at Karlovasi, Samos.

November 2024

A second international meeting/workshop of the CoMTE project took place in Paris, Université Paris 8.