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CombiTop SIGNED

New Interactions of Combinatorics through Topological Expansions, at the crossroads of Probability, Graph theory, and Mathematical Physics

Total Cost €

EC-Contrib. €

Partnership

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CombiTop project word cloud

Explore the words cloud of the CombiTop project. It provides you a very rough idea of what is the project "CombiTop" about.

triple fruits interactions deep export tools genus theory eynard first geometry developped view fermions places toda describe tamari embedding methodology structured combinatorics probability unification algebraic unified enumerative integrable principal strategic viewpoints say directions framework recursion mathematical domains demonstrated purpose topological certain maps plays combinatorial dealing objects domain appear surface random invariant connect physics investigator lattices outcome expansions branch originality unify mathematics hierarchies school proposing coming nature connection natural graph rising pertinence orantin ubiquitous kp unveil underlying french connections

Project "CombiTop" 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˙086˙125 €
EC max contribution	1˙086˙125 € (100%)
Programme	1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
Code Call	ERC-2016-STG
Funding Scheme	ERC-STG
Starting year	2017
Duration (year-month-day)	from 2017-03-01 to 2022-02-28

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 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.	FR (PARIS)	coordinator	1˙086˙125.00

Map

Project objective

'The purpose of this project is to use the ubiquitous nature of certain combinatorial topological objects called maps in order to unveil deep connections between several areas of mathematics. Maps, that describe the embedding of a graph into a surface, appear in probability theory, mathematical physics, enumerative geometry or graph theory, and different combinatorial viewpoints on these objects have been developed in connection with each topic. The originality of our project will be to study these approaches together and to unify them.

The outcome will be triple, as we will: 1. build a new, well structured branch of combinatorics of which many existing results in different areas of enumerative and algebraic combinatorics are only first fruits; 2. connect and unify several aspects of the domains related to it, most importantly between probability and integrable hierarchies thus proposing new directions, new tools and new results for each of them; 3. export the tools of this unified framework to reach at new applications, especially in random graph theory and in a rising domain of algebraic combinatorics related to Tamari lattices.

The methodology to reach the unification will be the study of some strategic interactions at different places involving topological expansions, that is to say, places where enumerative problems dealing with maps appear and their genus invariant plays a natural role, in particular: 1. the combinatorial theory of maps developped by the 'French school' of combinatorics, and the study of random maps; 2. the combinatorics of Fermions underlying the theory of KP and 2-Toda hierarchies; 3; the Eynard-Orantin ``topological recursion' coming from mathematical physics.

We present some key set of tasks in view of relating these different topics together. The pertinence of the approach is demonstrated by recent research of the principal investigator.'

Publications

List of publications.
year	authors and title	journal	last update
2019	Guillaume Chapuy On tessellations of random maps and the $$t_g$$ t g -recurrence published pages: 477-500, ISSN: 0178-8051, DOI: 10.1007/s00440-018-0865-6	Probability Theory and Related Fields 174/1-2	2019-12-16
2019	Baptiste Louf A new family of bijections for planar maps published pages: 374-395, ISSN: 0097-3165, DOI: 10.1016/j.jcta.2019.06.006	Journal of Combinatorial Theory, Series A 168	2019-11-13
2018	A. Alexandrov, G. Chapuy, B. Eynard, J. Harnad Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion published pages: 777-826, ISSN: 0010-3616, DOI: 10.1007/s00220-017-3065-9	Communications in Mathematical Physics 360/2	2019-11-13

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