Please join us for the Distinguished Lecture Series with Professor Tatiana Shulman.

Bio: Tatiana Shulman obtained master's degree from Moscow Institute of Physics and Technology and PhD from Moscow Institute of Electronics and Mathematics in 2006. After PhD, Shulman held two postdoc positions at the University of Copenhagen, worked at the Institute of Mathematics of Polish Academy of Sciences from 2014 to 2020, and is Associate Professor at the University of Gothenburg from 2021.

Shulman's main research interests and results are in Operator Algebras, in particular, structure theory of C*-algebras, group C*-algebras with emphasis on stability and representation theory, connections with Operator Theory.

Shulman is an awarded member of AcademiaNet in 2022 (nominated by Swedish Research Council).

Lecture Series: Stability and lifting properties for C*-algebras and groups

Abstract: Group-theoretical stability requires that approximate representations of a group are close to actual representations, where closeness is measured using a chosen metric (e.g., the Hilbert-Schmidt distance). In recent years, there has been a surge of interest in group stability. This is motivated in part by the fact that group stability provides a promising new angle to attack appoximation conjectures (e.g. Connes embedding problem for groups).

Operator algebraic methods come up naturally in the study of stability for groups. In fact stability can be reformulated as a certain lifting property for full group C*-algebras and therefore is related with other important lifting properties of C*-algebras. In particular we will discuss Blackadar's projectivity and semiprojectivity (the latter can be considered as a very strong form of stability) that arise in the area of noncommutative topology and play an important role in structure theory of C*-algebras. We will also consider a somewhat related property of a C*-algebra of being residually finite-dimensional. This notion can be found at the heart of some of the most important questions in operator algebras and has subtle connections to residual finiteness properties of groups.

You can find all lecture recordings here: https://www.youtube.com/playlist?list=PLArBKNfJxuullSBdHx0mjIIVvaZhvJ9gg