ANR project
CartesEtPlus
–
Combinatorics of maps, meanders and multicurves,
and its interactions

CartesEtPlus (French for MapsAndMore) is a 5-year project funded by the French Agence Nationale de la recherche, project number ANR-23-CE48-0018, call AAPG 2023. It is centered in combinatorics but has many interactions, in particular with probability, algebra, or mathematical physics.

The main objective of the project is to structure the effervescence that took place in recent years around the combinatorics of two-dimensional topological objects, and in particular maps and related objects such as meanders or multicurves. Even if these themes are well established, new directions are emerging at the boundaries of the subject. Several new questions at the interface with fundamental physics and geometry have not yet been studied in detail according to the combinatorial approach, even though they bring new insights, and raise profound challenges.

The project will seek out a greater unification of these emerging themes, in order to bring out new directions, share new tools between the different fields addressed, and solve important problems by combining these viewpoints and approaches.

Kick-off meeting at the University of Bordeaux

Our first meeting will take place in LaBRI (CNRS and University of Bordeaux), from June 4 to June 5. It will be dedicated to open problems presented by the researchers involved in the project. The goal is to create a dynamics between the experts of the various themes emerging in the project. We will ask our members to present problems from their field that they think will benefit from the expertise of our other project members. After the presentations of those open problems, we propose that our members form groups to approach them and turn them into some concrete projects in the fields of map combinatorics, analytic combinatorics, geometry and probability.

List of project members by site :

Site IRIF – Center Paris
Scientific manager: Guillaume Chapuy
- Marie Albenque (IRIF)
- Jérémie Bouttier (IMJ-PRG)
- Guillaume Chapuy (IRIF)
- Enrica Duchi (IRIF)
- Elba Garcia-Failde (IMJ-PRG)


SITE LIGM - Paris East/South
Scientific manager: Valentin Bonzom
Valentin Bonzom (LIGM)
Jérémie Bettinelli (LIX)
Linxiao Chen (LAGA)
Wenjie Fang (LIGM)
Éric Fusy (LIGM)
Emmanuel Guitter (IPhT)
Gilles Schaeffer (LIX)

Site Bordeaux
Scientific manager: Mireille Bousquet-Mélou
Mireille Bousquet-Mélou (LaBRI)
Vincent Delecroix (LaBRI)
Andrew Elvey-Price (IDP)
Élise Goujard (IMB)
Baptiste Louf (IMB)
Jean-François Marckert (LaBRI)

The project CartesEtPlus is funded by the ANR (Agence Nationale de la Recherche), grant number ANR-23-CE48-0018). Project coordinator: Guillaume Chapuy.