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COMBINEPIC SIGNED

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

Total Cost €

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EC-Contrib. €

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Partnership

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Project "COMBINEPIC" data sheet

The following table provides information about the project.

Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 

Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794
website: www.cnrs.fr

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 1˙242˙400 €
 EC max contribution 1˙242˙400 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-STG
 Funding Scheme ERC-STG
 Starting year 2018
 Duration (year-month-day) from 2018-02-01   to  2023-01-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) coordinator 1˙242˙400.00

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 Project objective

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).

 Publications

year authors and title journal last update
List of publications.
2019 Cédric Boutillier, Béatrice de Tilière, Kilian Raschel
The Z-invariant Ising model via dimers
published pages: 235-305, ISSN: 0178-8051, DOI: 10.1007/s00440-018-0861-x
Probability Theory and Related Fields 174/1-2 2020-04-07
2019 Gerold Alsmeyer, Kilian Raschel
The extinction problem for a distylous plant population with sporophytic self-incompatibility
published pages: 1841-1874, ISSN: 0303-6812, DOI: 10.1007/s00285-019-01328-5
Journal of Mathematical Biology 78/6 2020-04-07
2019 Alin Bostan, Alexander Marynych, Kilian Raschel
On the least common multiple of several random integers
published pages: 113-133, ISSN: 0022-314X, DOI: 10.1016/j.jnt.2019.03.017
Journal of Number Theory 204 2020-04-07

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The information about "COMBINEPIC" are provided by the European Opendata Portal: CORDIS opendata.

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