Instructor: Prof. Aaron Tikuisis
Email: aaron.tikuisis@uottawa.ca

Course Dates: January 9th - April 5th, 2023
Mid-Semester Break: February 20th - 24th, 2023
Lecture Times: Monday 1:00 - 2:20 PM (ET) | Wednesday 11:30 AM - 12:50 PM (ET)
Office Hours: Tuesday | 12:00 - 2:00 PM (ET)

Registration Fee: PSU Students - Free | Other Students - $500 CAD

Prerequisites: Students should have taken a course in functional analysis, which includes Hilbert spaces, the Hahn-Banach theorems (both extending functionals and the separation theorem), the Open Mapping theorem, Goldstine’s theorem, and the Krein-Milman theorem.

Evaluation: Students will be required to submit 5 assignments during the term.

Capacity Limit: 35 students (auditing is allowed beyond the capacity limit)

Format: Online

Course Description

This course will introduce students to operator algebras (C*-algebras and von Neumann algebras) and some of their diverse connections to other areas of mathematics. We will begin with the basics: definitions of operator algebras, representations, functional calculus, traces and comparison theory. We will see some interesting examples such as: group operator algebras, the hyperfinte II1 factor, AF algebras, the irrational rotation algebras. Time-permitting, we will explore connections to fields such as amenability, knot theory, quantum information, and/or random matrix theory.