EXPLOREMAPS

"Combinatorial methods, from enumerative topology to random discrete structures and compact data representations."

Coordinatore	CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	France [FR]
Totale costo	750˙000 €
EC contributo	750˙000 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2007-StG
Funding Scheme	ERC-SG
Anno di inizio	2008
Periodo (anno-mese-giorno)	2008-07-01   -   2013-06-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE  Organization address address: Rue Michel -Ange 3 city: PARIS postcode: 75794 contact info Titolo: Dr. Nome: Gilles Cognome: Schaeffer Email: send email Telefono: -69334659 Fax: -69332982	FR (PARIS)	hostInstitution	0.00
2	CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE  Organization address address: Rue Michel -Ange 3 city: PARIS postcode: 75794 contact info Titolo: Ms. Nome: Julie Cognome: Zittel Email: send email Telefono: -45075672 Fax: -45075787	FR (PARIS)	hostInstitution	0.00

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 Obiettivo del progetto (Objective)

'Our aim is to built on recent combinatorial and algorithmic progress to attack a series of deeply connected problems that have independantly surfaced in enumerative topology, statistical physics, and data compression. The relation between these problems lies in the notion of 'combinatorial map', the natural discrete mathematical abstraction of objects with a 2-dimensional structures (like geographical maps, computer graphics' meshes, or 2d manifolds). A whole new set of properties of these maps has been uncovered in the last few years under the impulsion of the principal investigator. Rougly speaking, we have shown that classical graph exploration algorithms, when correctly applied to maps, lead to remarkable decompositions of the underlying surfaces. Our methods resort to algorithmic and enumerative combinatorics. In statistical physics, these decompositions offer an approach to the intrinsec geometry of discrete 2d quantum gravity: our method is here the first to outperform the celebrated 'topological expansion of matrix integrals' of Brezin-Itzykson-Parisi-Zuber. Exploring its implications for the continuum limit of these random geometries is our great challenge now. From a computational geometry perspective, our approach yields the first encoding schemes with asymptotically optimal garanteed compression rates for the connectivity of triangular or polygonal meshes. These schemes improve on a long series of heuristically efficient but non optimal algorithms, and open the way to optimally compact data structures. Finally we have deep indications that the properties we have uncovered extend to the realm of ramified coverings of the sphere. Intriguing computations on the fundamental Hurwitz's numbers have been obtained using the ELSV formula, famous for its use by Okounkov et al. to rederive Kontsevich's model. We believe that further combinatorial progress here could allow to bypass the formula and obtaine an elementary explanation of these results.'