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Projet H2020 "PACCAP"

REVEAL : Problems in Algebraic Complexity and Complexity of Algebraic Problems

Recherche : Mathématiques


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Description du projet

Porteur : ENS de Lyon

The P=NP? problem is widely recognized as one of the most important and challenging open problems in contemporary mathematics and computer science. The general belief is that P differs from NP. Unfortunately, this intuition is still not supported by a proof in spite of 35 years of intensive research. Given the difficulty of this problem, algebraic versions of P=NP? have been proposed. The hope is that these algebraic versions of the problem should be easier to solve than the original one. The two main algebraic versions of P=NP? are due to Valiant and to Blum-Shub-Smale. The Blum-Shub-Smale's model deals with computation over the ordered ring of the real numbers whereas the Valiant's model does not deal with decision problems but with polynomial evaluation. In algebraic complexity theory the main focus of this project will be on the study of the relations between Valiant's model, the Blum-Shub-Smale model, and the discrete model of computation. Another focus will be on the complexity of problems from algebraic geometry and from combinatorial optimization, such as linear programming. This research will begin in 2009 in Toronto. A program on Foundational of Computational Mathematics should be held at the Fields Institute in Toronto during the Fall semester. This program should attract many of the best specialists of this research area. Participation in this program is a major contribution to the Training component of the PACCAP project. The project will continue at the computer science department of the University of Toronto, which has a very strong Theory Group. The returning institution is Ecole Normale Supérieure de Lyon, where many of the future French theoretical computer scientist are studying. The skills developped in the PACCAP project will be used there both forresearch and teaching.

Budget global :

173 415,80 

Durée :

Du 1er août 2009 au 31 juillet 2012

Horizon 2020

Horizon 2020 est le plus grand programme de recherche et d'innovation de l'UE avec près de 80 milliards d'euros de financement disponibles sur 7 ans (2014 à 2020) - en plus des investissements privés que cette somme mobilisera. Ce programme est la promesse de nouvelles percées, de découvertes et d'innovations mondiales en faisant passer les grandes idées des laboratoire au monde du marché.

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