SDU Operator Algebras Seminar

Title: Classification of simple C*-algebras from singular graphs

Abstract: There is a rich classification theory for unital simple C*-algebras associated to finite graphs with no sinks, allowing to decide by invariants when two such C*-algebras are isomorphic, not just in their own right, but equipped with their natural diagonals (Cartan subalgebras) or their natural circle actions. All of these results were proved by involving results from symbolic dynamics, even though some now are special cases of much more general results.

When one allows singular vertices — sinks or infinite emitters — the connection to the rich theory of shifts of finite type is lost, but the classical classification results have natural generalizations which one may aspire to show by other means. I will discuss and compare different notions of sameness of such graph C*-algebras; all fully understood in the regular case, both only half resolved in general. All work presented is joint with Efren Ruiz, and some also with Aidan Sims.

Title: The Levi-Civita connection on noncommutative differential forms

Abstract: I will discuss the main results and consequences of recent work with Bram Mesland. Using mostly algebraic techniques, with just a little Hilbert module analysis, we present necessary and sufficient conditions for the existence of Hermitian torsion-free connections on noncommutative  one-forms, such as those arising from spectral triples. Various consequences and examples will be discussed also.

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