Registration Deadline: TBA

Instructor: Professor Jesse Peterson, University of Waterloo
Course Date: TBA
Mid-Semester Break: TBA
Lecture Time: TBA

Office Hours: TBA

Registration Fee:

• Students from our Principal Sponsoring & Affiliate Universities: Free
• Other Students: CAD$500

Capacity Limit: TBA

Format: TBA

Course Description

This course will study von Neumann algebras, with an emphasis on modern techniques developed to study II${_1}$ factors. We will first go though some preliminary concepts such as the geometry of projections and classification into types. We will then focus on II${_1}$ factors, discussing the construction of the trace, group and group-measure space von Neumann algebras, amenability and other (non) approximation properties such as Haagerup’s property and property (T). We will then study deformation/rigidity results such as examples with trivial fundamental group, examples of (strongly) solid II${_1}$ factors, and examples of II${_1}$ factors with unique Cartan subalgebra.

Course resources:

Course notes will be available. The following textbook can provide additional context:

• Claire Anantharaman and Sorin Popa. An introduction to II${_1}$ factors, book preprint available at: https://www.math.ucla.edu/~popa/Books/IIunV15.pdf

Prerequisites: An introductory course in Operator Algebras or an advanced course in Functional Analysis. We will assume familiarity with concepts such as continuous functional calculus, the Gelfand transform, the GNS construction, and other topics that can be found in introductory books on operator algebras such as Gert Pedersen's book "Analysis Now (Graduate Texts in Mathematics, 118)", Springer New York, 1996, ISBN: 9780387967882

Evaluation: The grade will be determined from 5 homework assignments (50%) and one final written report (50%).