Title: An Introduction to Noncommutative Integration

Abstract: In the first of two talks, we introduce and discuss the theory of noncommutative integration. First made rigorous by Segal, it establishes a deep connection between the theory of von Neumann algebras and measure theory through functional analytic techniques, and allows us to study spectral theory through the lens of measures and integration. We will discuss the motivation and application for the study of von Neumann algebras and their associated operators in such a sense, and develop some of the fundamental tools and techniques of the field. This will provide background for a general audience for the second talk.

About the Speaker: Thomas Scheckter received his PhD  from the University of New South Wales, Sydney, Australia. He completed his thesis, Martingale convergence techniques in noncommutative integration, under the supervision of Fedor Sukochev in 2020, and for his efforts he won a UNSW Dean's Award for outstanding PhD Theses.   After graduation Dr. Schecter worked in the School of Mathematics and Statistics as a Research Associate alongside Professor Sukochev, Dr Dmitriy Zanin, and Dr Ed McDonald, studying Functional Analysis and Operator Theory. He has just finished a new position as a Research Fellow at the University of New Mexico. His work  with Professor Anna Skripka  focuses on Multilinear Operator Integration. In June 2021, Dr. Schechter was the keynote speaker for the Online Workshop in Sthocastic Analysis organized by Professor Skripka and supported by her NSF CAREER grant.