ERC starting grant - 2018/2024 - COMBINEPIC - 759702


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


Andrew Elvey Price (Researcher, Feb 2019/Jan 2024)
Dan Betea (Postdoctoral researcher, Nov 2021/Oct 2022)
Matthieu Dussaule (Postdoctoral researcher, Nov 2020/Oct 2022)
Helen Jenne (Postdoctoral researcher, Sep 2020/Aug 2021)
Viet Hung Hoang (PhD student, Oct 2019/May 2023)
Andreas Nessmann (PhD student, Oct 2020/Nov 2023)
Kilian Raschel (Principal Investigator)
Harriet Walsh (Postdoctoral researcher, Nov 2022/Jan 2024)

Working group

International conferences funded by the ERC project

Other events supported by the ERC project

Books edited


They have been visiting the project

Gerold Alsmeyer, Beniamin Bogosel, Alin Bostan, Manfred Buchacher, Elisabetta Candellero, François Chapon, Thomas Dreyfus, Matthieu Dussaule, Andrew Elvey Price, Sandro Franceschi, Éric Fusy, Olga Izyumtseva, Helen Jenne, Alexander Marynych, James Mcredmond, Marni Mishna, Stjepan Šebek, Samuel Simon, Pierre Tarrago, Amélie Trotignon, Wolfgang Woess, Yiqiang Q. Zhao

Summary of the ERC project

This 6-year project is devoted to the use of special functions in combinatorics, probability theory and statistical mechanics. The term "special functions" is understood here in a broad sense, including algebraic, differentially finite, (hyper)elliptic, hypergeometric functions, etc. In this project we focus on two major examples emanating from combinatorics and probability: Though deeply different, these domains have two points in common. First, they are fundamental research domains in combinatorics and probability: random walks in cones appear in the theory of quantum random walks, non-colliding random walks, planar maps, population biology, finance, etc.; integrable models of two-dimensional statistical mechanics (including the dimer model, the Ising model and spanning trees/forests) consist of the few models of the field which are exactly solvable, thus opening the way for remarkable exact formulas. Further, in both domains, the last ten years have seen the development of promising techniques to understand these exactly solvable models: functional equations, special functions and boundary value problems, to cite a few. We also propose applications in population biology.


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