Speaker: Yusuke Isono (RIMS, Kyoto University)

Title: Introduction to Tomita--Takesaki theory

Time/Date: July 21 (Tue), 2026, 4:45-6:15pm

Room: 126 Math. Sci. Building

Abstract: In this talk, we give an introduction to Tomita--Takesaki theory, which plays a central role in the study of type III von Neumann algebras. The talk assumes no prior knowledge of the theory and begins with tracial von Neumann algebras. We discuss the difficulties that arise in the non-tracial setting and introduce the modular automorphism group and modular conjugation associated with a faithful normal state. As a concrete class of examples, we consider Powers--Araki--Woods factors and illustrate how the abstract definitions can be made explicit. Finally, we briefly touch on more structural notions such as the KMS condition, the continuous core, and Connes' invariants, and explain the importance of Tomita--Takesaki theory in the study of type III factors.