Speaker: Xuanlong Fu (Tongji University)
Abstract: In this talk, I will introduce the notion of tracial approximate oscillation zero. Tracial approximate oscillation zero is a useful tool for proving certain C-algebras have stable rank one. Let A be a separable (not necessarily unital) simple C-algebra with strict comparison. We show that if A has tracial approximate oscillation zero, then A has stable rank one and the canonical map Γ from the Cuntz semigroup of A to the corresponding lower-semicontinuous affine function space is surjective. The converse also holds. As a by-product, we find that a separable simple C*-algebra which has almost stable rank one must have stable rank one, provided it has strict comparison and the canonical map Γ is surjective.
Time: 2:30-3:30pm, Friday, Feb 21, 2025
Location: Room 1410
Host: Huaxin Lin
About the speaker: Xuanlong Fu is an assistant professor at Tonji University. From 2018-2021, Fu was a postdoc at Shanghai Center for Mathematical Sciences and from 21-24, he was a postdoc at University of Toronto/The Feilds Institute. His main research interest is in C*-algebra theory.
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