Instructor: Prof. Ilijas Farah
Email: ifarah@yorku.ca

Registration Fee: Free for all students

Course Description

Ultraproducts were discovered independently by operator algebraists and logicians in 1950s.This course will cover major basic applications of ultraproducts to the structure of von Neumann algebras and to C*-algebras. It would emphasize the unity of the subject: analogies between von Neumann algebras and C*-algebras, and analogies between ultraproducts and asyptotic sequence algebras in case of C*-algebras. We will start by covering McDuff’s analysis of II_1 factors, and proceed to Connes’s and Effros-Rosenberg results. More recent topics, such as tracially complete C*-algebras and their applications to classification of C*-algebras, will be covered as well. Prof. Aaron Tikuisis’ "Introduction to Operator Algebras" course (Fields Academy, Winter 2023) will provide sufficient background for this course.