ERC credits brownian 3-torus. credit to Jeremie Bettinelli

ERC Starting Grant

New Interactions of Combinatorics
Through Topological Expansions

a C-decorated treemobile branchesvoronoiConjecture

    The 5-year project CombiTop, funded by the ERC (Starting Grant 2016) started in 2017. It is centered around, but not limited to, the combinatorics of maps on surfaces, and more precisely the combinatorics arising in topological expansions (roughly speaking, 2D counting problems where the dependence on the genus invariant plays a central role).

    The main goal is to study the interactions between:

  • the bijective approach to maps;
  • random maps and Brownian maps;
  • the "combinatorics of fermions", tau functions, symmetric group algebra and algebraic combinatorics;
  • the combinatorics of the topological recursion.

Each of these topics features some remarkable integrability properties as well as some beautiful combinatorial constructions, and the main goal of the project is to seek for a greater unification of these theories, including their combinatorial aspects.

A plucker relation

Project members or ex-members

News: Journée de l'ERC CombiTop le 15 février 2019 à l'IRIF: quatre orateur·trice·s aborderont les cartes dans leurs aspects combinatoires, probabilistes, et physiques. Inscription obligatoire avant le 1er février, voir ici.

                    We're hiring:

Third call for postdoc applications -- deadline December 15th 2019

  • Theme: Combinatorics of Maps and their interactions (random maps, combinatorial aspects of mathematical physics, algebraic combinatorics)
  • More precise subject: something that both you and I find interesting to think about
  • Location: IRIF, Université Paris-Diderot, in Paris 13th district.
  • Duration: 12 months, with possible extension to two years.
  • Starting date: flexible, in 2020.
  • Salary: determined by academic experience (starts at around 30000 euros net per year).
  • Deadline for application: December 15th, 2019.
The project offers one (or more) postdoctoral position of one year with a possible extension to two years. The starting date is not fixed. The successful applicant will join the Combinatorics group of the IRIF department. There is no teaching duty.

The salary offered will be approximately between 30000 and 40000 euros per year (net), depending of years of academic research since PhD (non negotiable, determined by CNRS scales). We will also provide the postdoc with a generous amount of travel money (up to 8keur/year if justified) and a laptop if necessary.

The candidate should have a strong background in at least one of the following subjects: enumerative combinatorics, probability theory, mathematical physics, algebraic combinatorics. His/her research interests should be related to the themes of the project. Possible research themes include: random maps, random trees, map enumeration, algebraic combinatorics, integrable systems.

Université Paris Diderot is located downtown Paris and interacts with many other research institutions, in particular CEA, École Polytechnique, École Normale Supérieure, Orsay, Marne-La-Vallée. Many research seminars make the working environment very stimulating.

Applications (including CV, list of publications and short description of research interests), as well as the names of two people who can submit letters of recommendation, should be sent before December 15th, 2019 by e-mail to Applicants are expected to have a PhD in computer science, mathematics or theoretical physics when the position starts.

Feel free to contact me if you have questions. Applications must be sent to Please also include a few words explaining why you are interested and what we could do together.

Please include "CombiTop2019" in the subject of your mail for application or for any question.

a random genus 0 map

Credit for the (purple) genus-3 Brownian map image at the top of this page: Jérémie Bettinelli.

The project CombiTop receives funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. ERC-2016-STG 716083).