Copenhagen
Groups and Operator Algebras Seminar
We meet on Wednesdays from 15:15 to 16:15. If you have any questions about the seminar or want to be added to the email list, please contact one of the organizers:
Pieter Spaas: pisp@math.ku.dk
Martín Blufstein: mabc@math.ku.dk
David Jekel: daj@math.ku.dk
Ian Thompson: ian@math.ku.dk
22/01/2025, TBA
Note: This seminar takes place at 14:00-15:00.
Srivatsav Kunnawalkam Elayavalli (UC San Diego)
Title: TBA
Abstract: TBA
22/01/2025, Aud 2.
Jennifer Pi (University of Oxford)
Title: Generic Central Sequence Algebras in II_1 Factors
Abstract: When does a tracial von Neumann algebra admit factorial relative commutant in its own ultrapower? Is there a special class of algebras with a distinguished object M so that every algebra of the class admits an embedding into an ultrapower of M with factorial relative commutant? We consider these questions and give some partial answers via a central sequence property we call "uniformly super McDuff". This is based on a joint work with Isaac Goldbring, David Jekel, and Srivatsav Kunnawalkam Elayavalli.
29/01/2025, Aud 8.
Kang Li (Friedrich-Alexander-Universität Erlangen-Nürnberg)
Title: Dimension theories from groupoids to classifiable C*-algebras, and back again
Abstract: The motivation comes from the spectacular breakthrough in the Elliott classification program for simple nuclear C*-algebras: the class of all separable, simple, finite nuclear dimensional C*-algebras satisfying the UCT is classified by their Elliott invariants. Shortly after, Xin Li proved that those classifiable C*-algebras have a twisted étale groupoid model (G, Σ). A natural question is which twisted étale groupoid C*-algebras have finite nuclear dimension. Very recently, Bönicke and I have extended the previous results to show that their nuclear dimensions are bounded by the dynamic asymptotic dimension of the underlying groupoid G and the covering dimension of its unit space G^0.
The problem is that dynamic asymptotic dimension cannot be consistent with nuclear dimension for simple C*-algebras because every simple C*-algebra with finite nuclear dimension has nuclear dimension either zero or one. Therefore, we (together with Liao and Winter) introduced the so-called diagonal dimension for an inclusion (D ⊆ A) of C*-algebras. In this talk, I will explain how the diagonal dimension of (C_0(G^0)⊆ C_r^*(G,Σ)) is indeed consistent with dynamic asymptotic dimension of G and the covering dimension of G^0. Moreover, we compute the diagonal dimension and the dynamic asymptotic dimension for Xin Li’s groupoid model.
05/02/2025, TBA.
Adam Dor-On (Haifa University)
Title: TBA
Abstract: TBA