Projet COMBINEPIC (H2020)

Elliptic Combinatorics : Solving famous models from combinatorics, probability and statistical mechanics, via a transversal approach of special functions

Date de début de projet :

Domaine scientifique principal : Numérique & Data

Type de projet: prix

Résumé / Présentation

I am willing to solve several well-known models from combinatorics, probability theory and statistical mechanics: the Ising
model on isoradial graphs, dimer models, spanning forests, random walks in cones, occupation time problems. Although
completely unrelated a priori, these models have the common feature of being presumed “exactly solvable” models, for which
surprising and spectacular formulas should exist for quantities of interest. This is captured by the title “Elliptic Combinatorics”,
the wording elliptic referring to the use of special functions, in a broad sense: algebraic/differentially finite (or
holonomic)/diagonals/(hyper)elliptic/ hypergeometric/etc.
Besides the exciting nature of the models which we aim at solving, one main strength of our project lies in the variety of
modern methods and fields that we cover: combinatorics, probability, algebra (representation theory), computer algebra,
algebraic geometry, with a spectrum going from applied to pure mathematics.
We propose in addition two major applications, in finance (Markovian order books) and in population biology (evolution of
multitype populations). We plan to work in close collaborations with researchers from these fields, to eventually apply our
results (study of extinction probabilities for self-incompatible flower populations, for instance).

Responsable / porteur / P.I. : Kilian RASCHEL

Lieu principal : Orléans

Périmètre d'action : International

Tutelle : CNRS

Laboratoires impliqués : LMPT