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HEОбмен на изследователи2023–2026

Graph Algebras · Operator Algebras that One Can See

„Хоризонт Европа“ — Действия „Мария Склодовска-Кюри“

Период
2023-01-01 → 2026-12-31
Финансиране от ЕС
496 800 €
Участници
28
Схема
HORIZON-TMA-MSCA-SE

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Накратко на български

Графовите C-алгебри изследват структурата и симетрията на операторни алгебри чрез визуални модели като графи. Това помага за по-доброто разбиране на некомутативната метрична геометрия и класификацията на тези математически обекти.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Operator Algebras that One Can See

The main objectives of the project concern the classification, symmetry, structure and noncommutative metric geometry of operator algebras. The innovation in our approach comes from our emphasis on the ubiquitous class of graph C*-algebras, and through combination of ideas from many different fields of research.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

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.

Оригинален текст от CORDIS (на английски).

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Данни: CORDIS, © Европейски съюз