## General information.

### Organizing comittee:

**Pere Ara**, Universitat Autònoma de Barcelona (coordinator).

**Fernando Lledó**, Universidad Carlos III de Madrid, RWTH-Aachen University.

**Francesc Perera**, Universitat Autònoma de Barcelona.

### Contact address:

oalgebras(at)mat.uab.cat

### Official webpage:

Universidad Internacional Menéndez Pelayo

### Place and dates:

Santander, 21-25 of July, 2008.

### Description:

This school is divided in three parts:Part A: K-theory for operator algebras. Classification of C*-algebras.

Part B: Modular theory for von Neumann algebras and applications to quantum field theory.

Part C: Amenability, hyperbolic groups and operator algebras Part C provides connections between part A (C*-algebras) and part B (von Neumann algebras).

The theory of operator algebras introduced in the thirties by J. von Neumann was developed in close relationship with fundamental aspects of functional analysis, ergodic theory, harmonic analysis and quantum physics. More recently this field has shown many further fruitful interrelations with other areas of mathematics and mathematical physics.

This school addresses two fundamental aspects of the theory of operator algebras which are interesting in themselves and important in applications: K-Theory for C*-algebras and Modular Theory for von Neumann algebras.

This school aims to train PHD students and young researchers with interdisciplinary interests in mathematics or mathematical physics in some fundamental aspects of operator algebras. Background: Rudiments of functional analysis, algebra or quantum theory.

Bibliography (some background text books; more specific references will be distributed during the course)

[1] H. Baumgaertel, Operatoralgebraic methods in quantum field theory, Akademie Verlag, 1995.

[2] B. Blackadar, K-Theory for Operator Algebras, Spinger Verlag, 1986.

[3] A. Connes (et al. eds),"Noncommutative Geometry, Springer Verlag, 2004.

[4] M. Rordam, Classifications of nuclear C*-algebras, Springer Verlag 2002.

[5] M. Rørdam, F. Larsen, N. Laustsen, An introduction to K-theory for C*-algebras. London Mathematical Society Student Texts, 49. Cambridge University Press, Cambridge, 2000.

[6] S. Stratila, Modular Theory in Operator Algebras, Abacus Press, 1981.

[7] V.S. Sunder, An Invitation to von Neumann algebras, Springer Verlag, 1987.

[8] M. Takesaki, Theory of operator algebras. Vols I,II and III, Springer-Verlag, 2002.

[9] N.E. Wegge-Olsen, K-Theory and C*-Algebras. An Introduction, Oxford University Press, 1993.