FP6Обмен на изследователи2004–2008

QUANTUM GEOMETRY · Noncommutative geometry and quantum groups

6РП — Действия „Мария Кюри“

Период: 2004-10-01 → 2008-09-30
Финансиране от ЕС: 502 462 €
Участници: 1
Схема: TOK

Линиите свързват координатора с партньорите.

Накратко на български

Некомутативната геометрия и квантовите групи изследват математически структури, при които редът на операциите променя крайния резултат. Тези абстрактни модели помагат за по-доброто разбиране на фундаменталните закони в чистата математика.

Този кратък обзор е генериран от изкуствен интелект

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

Резултати накратко

Final Activity Report Summary - QUANTUM GEOMETRY (Noncommutative geometry and quantum groups)

This transfer of knowledge programme was focused around eight full-scale lecture courses delivered by top experts from all over the world. They were devoted to the state-of-the-art mathematics, and unique due to their high level of expertise and quality of exposition. The courses were attended by faculty and students from many different places in Poland as well as France, Italy and United Kingdom. The notes taken from the lectures resulted in an about 1000-page long book to be published by the European mathematical society publishing house. The 20 guest scientists combined with 11 local team members formed an intellectual force reaching the majority of the initially planned research objectives and a number of new ones. The quantity of obtained results per the amount person months (more than one paper for each four person months) is commonly regarded as excellent in the area of pure mathematics.

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

Цел на проекта

Noncommutative geometry is a relatively new branch of mathematics that grew out of a fusion of operator algebras and differential geometry. Among most important motivations for the first formalism is quantum mechanics. For the second one, it is the general theory of relativity. The concept of noncommutative or quantum spaces provides a new paradigm in bothmathematics and physics. Due to its significantly new perspective, noncommutative geometry requires the development of a number of tools that are motivat ed by and tested on important examples of quantum groups and spaces.The long-term research aim of this project is twofold. Our first objective is to develop the formalism of topological quantum groups and principal bundles and apply it to crucial problems in mathematics, such as the Baum-Connes conjecture, and in mathematical models of physics, such as Yang-Mills or gauge theory. The second objective concerns the construction of cyclic theory that would both serve as a tool in computing K-theoretical invari ants and be adapted to the symmetry of given examples. In particular, this should address the dimensional drop occurring in quantum-group examples. The success in achieving the aforementioned goals hinges greatly on our ability to import knowledge and skil ls in areas such as spectral triples, graph C*-algebras and factors, Poisson geometry, foliations, multiplier Hopf algebras, Yetter-Drinfeld modules, q-special functions, KK-theory and the Baum-Connes conjecture. To this end, it is necessary to establish n ew collaboration links with experts in these areas of mathematics. This is what the transfer of knowledge programme is aimed to achieve.

Оригинален текст от CORDIS (на английски).

Участници

WARSAW UNIVERSITY · WARSZAWAКоординаторПолша