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Operator Algebras that One Can See

Description du projet

Utiliser les C*-algèbres de graphes pour examiner les liens entre des domaines mathématiques apparemment sans rapport

Les C*-algèbres de graphes sont des C*-algèbres universelles construites à partir d’un graphe orienté. L’analyse des graphes orientés, notamment les graphes de rang supérieur ou les graphes quantiques, permet aux mathématiciens de visualiser et d’examiner ces objets analytiques de manière intuitive. Les C*-algèbres de graphes font office de modèles remarquablement efficaces pour des problèmes clés ouverts en géométrie non commutative, en topologie et dans les systèmes dynamiques C*. Elles fournissent également un point focal pour l’extension nécessaire du célèbre programme de classification d’Elliott aux C*-algèbres non simples. Financé par le programme Actions Marie Skłodowska-Curie, le projet Graph Algebras utilisera les C*-algèbres de graphes pour unifier des domaines des mathématiques jusqu’ici non connectés. Rassemblant environ 70 chercheurs de l’UE et d’ailleurs, Graph Algebras étendra également les applications des C*-algèbres de graphes à l’informatique quantique.

Objectif

Graph C*-algebras are analytical objects blessed with a tangible structure and classification theory derived from their combinatorial origins. Through the analysis of directed graphs, including higher-rank graphs or quantum graphs, one can visualize and explore them in intuitive ways lacking elsewhere. They serve as strikingly efficient models for key open problems in noncommutative geometry and topology, as well as in C*-dynamical systems. They also provide a focal point for the much-needed extension of the celebrated Elliott classification program to non-simple C*-algebras.

The main objective of the project is to achieve a critical mass for a successful attack on these problems by combining the weight of strong research groups inside and outside the EU, using graph algebras as a unifying vehicle for hitherto unconnected areas of mathematics. The synergy of these new and innovative connections should allow us to develop and apply brand new methods unavailable otherwise. Furthermore, researchers using graph C*-algebras for applications in adjacent fields are likely to provide groundbreaking insights making impact way beyond graph algebras themselves. In particular, we expect to develop an interdisciplinary dimension involving quantum computing.

We aim to achieve our objective through networking and transfer of knowledge. Between twenty six partners from the EU and North America participating in the network, there are worldwide leading scientific centers. Among about seventy researchers involved in the project, there are famous experts and extremely efficient mentors of young researchers. Combining them with student members of the network yields a top human-resource infrastructure. An important objective is to take advantage of that potential by creating new career opportunities. Another tremendous asset of the network is a unique opportunity it gives to tie new and lasting connections for successful transcontinental scientific collaboration.

Coordinateur

INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK
Contribution nette de l'UE
€ 110 400,00
Adresse
UL. SNIADECKICH 8
00-656 WARSZAWA
Pologne

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PME

L’entreprise s’est définie comme une PME (petite et moyenne entreprise) au moment de la signature de la convention de subvention.

Oui
Région
Makroregion województwo mazowieckie Warszawski stołeczny Miasto Warszawa
Type d’activité
Higher or Secondary Education Establishments
Liens
Coût total
Aucune donnée

Participants (10)

Partenaires (15)