Title: Classification and regularity properties of C*-algebras

Speaker: Shanshan Hua（University of Oxford）

Time: Monday, Sept 15, 2:30PM-5:30PM 

Venue: Mingde Building 201-1

Abstract ：The Elliott classification program, initiated in the 1990s, emerged as the C*-algebraic analogue to the successful classification results in von Neumann algebras. In 2015, a landmark result provided a complete classification theorem for a wide class of simple and amenable C*-algebras, using K-theoretical and tracial data. This series of three talks focuses on foundational concepts and recent advancements in the field, while also highlighting several important open problems in the field.

The first talk offers an overview of the classification program's history, tracing its origins and major milestones. Particular attention will be given to the most recent developments, especially the abstract classification framework that has become a cornerstone of current research.

In the second part, the discussion shifts to Z-stability, a central regularity property within the classification program. The Toms-Winter conjecture, one of the major open conjectures in the field, will also be explored. This conjecture plays a pivotal role in understanding and verifying Z-stability in various examples of C*-algebras.

The final talk will focus on the K-theoretical properties of classifiable C*-algebras, with an emphasis on K-stability. A brief proof will be provided, demonstrating that the K-theory of Z-stable C*-algebras can be computed using higher homotopy of the unitary group, without needing to take matrix amplifications.