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European Mathematical Society Publishing House
2016-09-19 17:05:17
Oberwolfach Reports
Oberwolfach Rep.
OWR
1660-8933
1660-8941
General
10.4171/OWR
http://www.ems-ph.org/doi/10.4171/OWR
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Mathematisches Forschungsinstitut Oberwolfach
1
2004
4
Nichtkommutative Geometrie
Alain
Connes
Le Bois-Marie, BURES-SUR-YVETTE, FRANCE
Joachim
Cuntz
Universität Münster, MÜNSTER, GERMANY
Marc
Rieffel
University of California, BERKELEY, UNITED STATES
Noncommutative geometry applies ideas from geometry to mathematical structures determined by noncommuting variables. Within mathematics, it is a highly interdisciplinary subject drawing ideas and methods from many areas of mathematics and physics. Natural questions involving noncommuting variables arise in abundance in many parts of mathematics and quantum mathematical physics. On the basis of ideas and methods from algebraic topology and Riemannian geometry, as well as from the theory of operator algebras and from homological algebra, an extensive machinery has been developed which permits the formulation and investigation of the geometric properties of noncommutative structures. Areas of intense research in recent years are related to topics such as index theory, K-theory, cyclic homology, quantum groups and Hopf algebras, the Novikov- and Baum-Connes conjectures as well as to the study of specific questions in other fields such as number theory, modular forms, topological dynamical systems, renormalization theory, theoretical high-energy physics and string theory. The meeting was attended by 45 participants, including a fair number of young mathematicians but also many of the leading experts in the field. The exchange of ideas was very lively and quite a few significant new results were presented in the talks, which covered many of the aspects of noncommutatve geometry mentioned above.
Global analysis, analysis on manifolds
General
2349
2418
10.4171/OWR/2004/45
http://www.ems-ph.org/doi/10.4171/OWR/2004/45