Diagonals in classifiable C*-algebras

Wilhelm Winter (Universität Münster)

14:00-15:00, July 31th, 2024   

上海数学与交叉学科研究院

摘要：

Cartan and diagonal subalgebras encode underlying dynamical structures of C*-algebras via their associated groupoids.

The existence of Cartan subalgebras in separable, simple, nuclear C*-algebras is closely related to the UCT problem, but even for well-known classifiable ambient C*-algebras, we have only limited knowledge of the range of examples. A long-term goal is it to explore structural properties of Cartan subalgebras and diagonals of classifiable C*-algebras,and pave the grounds to eventually classifiy suitable classes of such subalgebras.

In this talk I will describe new examples of diagonals of classifiable C*-algebras such as the Cuntz algebra O_2, the CAR algebra, and the Jiang-Su algebra Z.

About the speaker:

Wilhelm Winter is currently a Professor at the University of Münster. Due to his exceptional scholarly achievements, Professor Winter was invited to give a 45-minute talk at the 2018 International Congress of Mathematicians (ICM). He was awarded the G. de B. Robinson Prize in 2010 and the European Research Council Prize in 2019. His research interests are mainly in noncommutative topology; more specifically in the structure and classification of nuclear C*-algebras and in the interplay with dynamical systems. He also has an interest in connections to coarse geometry and logic. His research has been published in top-tier mathematical journals such as Annals of Mathematics, Inventiones Mathematicae, Acta Mathematica, and PNAS.