Explore the words cloud of the COMBINEPIC project. It provides you a very rough idea of what is the project "COMBINEPIC" about.
The following table provides information about the project.
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
|Coordinator Country||France [FR]|
|Total cost||1˙242˙400 €|
|EC max contribution||1˙242˙400 € (100%)|
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
|Duration (year-month-day)||from 2018-02-01 to 2023-01-31|
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|1||CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS||FR (PARIS)||coordinator||1˙242˙400.00|
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).
|year||authors and title||journal||last update|
CÃ©dric Boutillier, BÃ©atrice de TiliÃ¨re, 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|
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|
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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