Noncommutative Geometry (EU-NCG)

Grunddaten zu diesem Projekt

Beschreibung

European scientists have played leading roles in many of the most exciting recent discoveries in the interaction between operator algebras, geometry, topology, algebraic geometry and quantum groups in pure mathematics and algebraic and conformal field theory, string theory, statistical mechanics in theoretical physics. The primary objective of this Research Training Network is to ensure that there is a new generation of young researchers in Europe with sufficient breadth of knowledge and training required for this interdisciplinary research. This will be achieved through bringing them to the cutting edge of research across a broad front including the following Research Objectives: 1. Operator-algebras - classification and structure 2. measure and isomorphism rigidity 3. free probability and random matrices 4. KK-theory and applications 5. cyclic theory and index theory 6. interplay between harmonic analysis and topology 7. quantum groups 8. applications to number theory 9. algebraic quantum field theory 10. fuzzy physics 11. strings and non-commutative geometry 12. quantum dynamics, quantum spin systems, quantum information The unifying mathematical concept behind the programme is the use of noncommutative operator algebras and noncommutative geometry to understand singular spaces or quantum spaces, replacing classical topological or measure spaces and the associated commutative algebras of continuous or measurable functions with noncommutative algebras of operators. Bringing together groups in Europe having a common goal in pursuing the deep connections between various branches of mathematics and physics we plan to address their conjectures and problems through a training network preparing young researchers equipped to work in operator algebras and noncommutative geometry. European scientists have played leading roles in many of the most exciting recent discoveries in the interaction between operator algebras, geometry, topology, algebraic geometry and quantum groups in pure mathematics and algebraic and conformal field the