A course on Massive C*-algebras, January-April 2021

Course description:

The route to understanding separable C*-algebras frequently involves a detour via nonseparable C*-algebras, such as the Calkin algebra, the asymptotic sequence algebras, ultrapowers, and ultraproducts. Some basic ideas from logic can be used to analyze these massive C*-algebras. Among other things, we will see that the existence of outer automorphisms of the Calkin algebra depends on the set-theoretic axioms.

Text: Combinatorial Set Theory of C*-algebras, Ilijas Farah, Springer Monographs in Mathematics, 2019, ISBN 978-3-030-27093-3

As I mentioned in class, in spite of having been lovingly prepared with utmost care, this book contains a few typos and such. All the ones known to me can be found here:

Combinatorial Set Theory of C*-algebras Errata.

We will cover parts of Chapter 8, Chapter 9, and most of Part III.

Prerequisites: The first course in functional analysis, with some acquaintance with operator theory and C*-algebras.

No set-theoretic assumptions will be imposed on the students.

Lecture times: Monday and Friday, 9--10:30 (EST, or Eastern Standard Time, aka `Toronto time'); you need to register here in order to attend the course.

Recordings of all of the lectures are available at the Fields YouTube and at the Fields Institute webpage.

Saeed Ghasemi will be holding tutorials for this course on Mondays 1pm-3pm (EST).

Meeting ID: 940 6387 0029

Email me or Saeed for the passcode.

The first homework, due February 1.

Homework 3, due March 19 (Exercise 4 corrected March 12)

(Thanks to Luciano Salvetti for pointing out that the statement of Exercise 4 was incorrect.)

Topic: Massive C*-algebras

Start Time : Mar 19, 2021 08:54 AM

Since the Fields Institute is closed today (March 19), I am posting the recording and the slides here:

Class 21 recording (March 19).

Also, the example of a *-homomorphism with a sigma-narrow lifting but no Borel lifting that I wanted to give today is more interesting than I thought - I'll say a few words about it the next time.