# Operator Algebras and Non-commutative Geometry

### Overview

The subject of operator algebras has its origins in the work of Murray and von Neumann concerning mathematical models for quantum mechanical systems. During the last thirty years, the scope of the subject has broadened in a spectacular way and now has serious and deep interactions with many other branches of mathematics: geometry, topology, number theory, harmonic analysis and dynamical systems.

Alain Connes' program of non-commutative geometry is based on the fact that any commutative C*-algebra is isomorphic to an algebra of continuous functions on some space. The aim of the program is to develop the tools of geometry in the setting where a commutative algebra of functions is replaced by a non-commutative algebra of operators.

Operator algebras has a strong history in Canada, but the establishment of substantial groups of researchers in the west (particularly Victoria, Regina and Alberta) is more recent. The proposed period of concentration will be part of the development of this group and its profile worldwide. The participation of people like Cuntz, Arveson, Higson, Rieffel and Connes is a result of the collaborative efforts of the group and attests to its standing. The program of activities demonstrates that the group is involved in the latest developments in the field and will, in turn, establish western Canada as a world leader.

### CRG Leaders:

- Douglas Farenick, University of Regina
- Marcelo Laca, University of Victoria
- Anthony Lau, University of Alberta
- Ian Putnam, University of Victoria

### Scientific Activities:

**Year 2009**

- 37th Canadian Operator Symposium, University of Regina, May 26-30, 2009
- KMS States and Non-Commutative Geometry, University of Victoria, June 29-July 10, 2009
- 2009 Northwest Functional Analysis Seminar, Banff, Alberta, October 16-18, 2009

**Year 2010**

- Workshop on Non-commutative Dynamics and Quantum Probability, University of Regina, May 14-17, 2010
- Summer School on Operator Algebras and Non-commutative Geometry, University of Victoria, June 14-25, 2010
- Conference on Selected Topics in Non-commutative Geometry, University of Victoria, June 27-July 2, 2010

**Year 2011**

- Canadian Operator Symposium (COSY) 2011, University of Victoria, May 24-28, 2011

### Visitors:

**Year 2009**

- Adam Rennie, Australian National University, June 23 - July 10, 2009
- Alan Carey, Australian National University, June 23 - July 10, 2009
- Fyodor Sukochev, University of New South Wales, June 26 - July 9, 2009
- Christian Skau, Norwegian University of Science and Technology, Aug. 10 - 14, 2009

**Year 2010**

- Astrid an Huef, University of Otago, June 26 - July 9, 2010
- Iain Raeburn, University of Otago, June 26 - July 9, 2010
- Jerry Kaminker, Indiana University- Purdue University Indianapolis, June 26- July 9, 2010
- Joachim Cuntz, Universitat Munster, Oct. 1 - 30, 2010 (PIMS Distinguished Chair)

**Year 2011**

TBA

### Postdoctoral Fellows

- Bodgan Nica, September 2009 - August 2011
- Antoine Julien, September 2010 - August 2012