The next meeting of the Algebra and Logic Seminar will be held on February 21, 2025 (Friday) at 1:00 pm (UTC+2).

A talk on:

Classification of C*-algebras through the lens of Cartan subalgebras

will be delivered by

Ali Raad (American University in Bulgaria).

Abstract.C*-algebras were introduced in the last century following various attempts to mathematically formalize the foundations of quantum mechanics. As such they encapsulate the study of noncommutative topology, as every C*-algebra is an algebra of bounded operators on some Hilbert space. Over the years there has been a significant attempt to classify C*-algebras by an invariant consisting of K-theoretic and tracial data. A recent breakthrough result has shown that every classifiable C*-algebra has a distinguished Abelian subalgebra called a Cartan subalgebra. Cartan subalgebras are pivotal in realizing C*-algebras as being built from topological groupoids. This yields concrete tools with which one can study a C*-algebra. A natural open problem is to find the defining characteristics of the groupoids giving rise to classifiable C*-algebras. In this talk I will discuss this problem and highlight some recent results. I aim to give a gentle overview of the theory of C*-algebras, their classification, Cartan subalgebras and their corresponding groupoids. Then I will highlight some recent progress in this open problem. Some of the results I will mention constitute joint work between myself and Xin Li, as well as myself with Ward Bruyndonckx and Jonathan Taylor.

Everybody is invited.

Algebra and Logic Department, IMI – BAS
http://www.math.bas.bg/algebra/seminarAiL/
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