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Operator Algebras that One Can See

Project description

Using Graph C*-algebras to explore connections between seemingly unrelated mathematical areas

Graph C*-algebras are universal C*-algebras constructed from a directed graph. The analysis of directed graphs, including higher-rank graphs or quantum graphs, enables mathematicians to visualise and explore these analytical objects in intuitive ways. Graph C*-algebras serve as strikingly efficient models for key open problems in noncommutative geometry, topology, and C*-dynamical systems. They also provide a focal point for the much-needed extension of the celebrated Elliott classification programme to non-simple C*-algebras. Funded by the Marie Skłodowska-Curie Actions project, the Graph Algebras project will use graph C*-algebras to unify hitherto unconnected areas of mathematics. Bringing together around 70 researchers from across the EU and outside, Graph Algebras will also extend graph C*-algebra applications to quantum computing.

Objective

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.

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Coordinator

INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK
Net EU contribution
€ 110 400,00
Address
Ul. sniadeckich 8
00-656 Warszawa
Poland

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SME

The organization defined itself as SME (small and medium-sized enterprise) at the time the Grant Agreement was signed.

Yes
Region
Makroregion województwo mazowieckie Warszawski stołeczny Miasto Warszawa
Activity type
Higher or Secondary Education Establishments
Links
EU contribution
No data

Participants (10)

Partners (15)