Scandinavian Operator Algebra Workshop

Information about the Scandinavian Operator Algebra Workshop,

June 8-9, 2026 in Lund

This meeting of the Scandinavian noncommutative geometers and operator algebraists is going take place at Lund University during 8th to 9th of June 2026.

The talks will be in the seminar room MH:333, located on the third floor of the Centre for Mathematical Sciences at Lund University.

The workshop dinner (at your own expense) is at Ölkällaren, close to the train station.

Registration closed on may 25. If you want to attend but have not registered, please send an email to one of the organizers (see below). This is so we know how much coffee to order and tables to reserve for dinner.

Possible hotels to choose from in Lund are Elite Hotel Ideon (close to department), Hotel Lundia and Hotel Bishops Arms (close to train/tram).

Travelling in Lund: Inside Lund there are buses and a tram system, with only one tram line. The trams starting from the train station in Lund takes 5 minutes to the stop LTH (just next to the mathematics department). The trams run every 10-20 minutes until midnight. You can buy tickets on the tram/bus with a credit card or the Skånetrafiken app. For time tables, see the following link.

Monday, June 8

Room: MH:333

13.30-14.15: Kang Li (Lund University)

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 G0, and are actually independent of Σ. The essential flaw 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 (C0(G0)⊆ Cr*(G,Σ)) is indeed consistent with dynamic asymptotic dimension of G and the covering dimension of G0. Moreover, we compute the diagonal dimension and the dynamic asymptotic dimension for Xin Li's groupoid model. This is joint work with Christian Bönicke, as well as Zehong Huang and Hang Wang.

14.15-15.00 Coffee break

15.00-15.45: David Jekel (University of Copenhagen)

Title: Applications of free probability to W*-bundles
Abstract: Click to expand →

Abstract:

We consider bundles of tracial von Neumann algebras over compact Hausdorff spaces, first studied by Ozawa. We establish C*-algebraic properties such as stable rank one, real rank zero, Dixmier averaging, and strict comparison for a class of W*-bundles that includes all locally trivial bundles. Inspired by Popa's theorem on approximate free independence and Robert's notion of selflessness for C*-algebras, we introduce the class of selfless W*-bundles for which there exist elements in M that are, in each fiber, approximately freely independent from a given finite subset of M with the respect to the trace, with uniform error bounds over all the fibers. This allows us to apply results from free probability to the bundle M , in a uniform way over the fibers.

For instance, to prove stable rank one (that invertible elements are dense), we use that any x in a von Neumann algebra can be perturbed to have trivial kernel by adding a freely independent circular operator. In a selfless W*-bundle M , we can carry this perturbation out approximately, and argue that operators that have trivial kernel are generic, and such operators admit a unitary polar decomposition in M .

This is based on joint work in progress with Maxwell Ryder and Stuart White.

16.15-17.00: Makoto Yamashita (University of Oslo)

Title: Higher sheaves behind representable KK-theory and the Chern character
Abstract: Click to expand →

Abstract:

The triangulated category whose objects are C*-algebras over a locally compact space X, and morphism spaces are Kasparov’s representable KK-groups, can be upgraded to a stable infinity category. The map spaces from this construction form a spectrum-valued sheaf on X. This fits into the six-functor formalism for étale groupoids G when we take X to be the nerves of G. When G is a torsion-free étale groupoid satisfying the Baum-Connes conjecture with coefficients, this correspondence leads to a rational isomorphism between the K-groups of crossed product C*-algebras A x G and the groupoid hyperhomology over G (a variation of Matui's “HK conjecture”). This specializes to the classical Chern character isomorphism if G = X, a space as a groupoid, and A = C_0(X). Based on a joint work in progress with Valerio Proietti.

18.30 Dinner

Tuesday, June 9

Room : MH:333

9.00-9.45: Olof Giselsson (Chalmers and University of Gothenburg)

Title: Quantum SU(3) as a 2-graph
Abstract: Click to expand →

Abstract:

It is well known that Woronowics quantum SU(2), as a C*-algebra, is isomorphic to a graph C*-algebra, for a fixed directed graph of two vertex and three arrows.

This talk concerns a generalization of this result for quantum SU(3). However, higher dimensional quantized compact semi-simple Lie groups does not admit a description as a Graph-C*-algebra. Therefore, Instead of a directed graph, we use a higher dimensional generalization introduced by Pask and Kumijan, called a higher rank graph (or n-graph), and its associated C*-algebra.

In the case of SU(3), the graph will have dimension 2. A description of the 2-graph whose C*-algebra is isomorphic to SU(3) will be concretely given, and we’ll discuss aspects of it’s construction. We will further give an outline of what the appropriate generalization should be for quantum SU(n) (the graph will be of dimension n-1), as well as the framework and technical obstacles for proving these types of results. This result is related to similar research by M. Matassa and R. Yuncken.

10.00-10.45: Matteo Pagliero (University of Southern Denmark)

Title: Selflessness for reduced free products and reduced graph products of C*-algebras
Abstract: Click to expand →

Abstract:

Motivated by results of Ken Dykema, Mikael Rørdam, and Sorin Popa, Leonel Robert introduced the notion of selfless C*-algebras. These C*-algebras contain a copy of themselves in their ultrapower that is free from the diagonal copy with respect to a fixed state. Apart from being an interesting property on its own right, selflessness yields a number of regularity properties, such as strict comparison of positive elements (in the tracial case). In this talk I will present recent work with Felipe Flores, Mario Klisse, and Micheal Ó Cobhthaigh, in which we show that reduced free products satisfying the so called Avitzour condition, as well as certain reduced graph products, are selfless. The preprint of our article can be found on arxiv.

10.45-11.15 Coffee break

11.15-12.00: Ada Masters (Lund University)

Title: Whither twisted spectral triples?
Abstract: Click to expand →

Abstract:

Twenty years after the appearance of twisted spectral triples in a preprint of Connes and Moscovici, I will discuss the new framework of 'conformally generated cycles', which incorporates every known example of twisted spectral triple with nontrivial index theory, while, at the same time, extending in a well-defined way the unbounded picture of KK-theory. Distinctive features of this framework are the use of conformal factors instead of twists and the appearance of ternary rings of operators. I will also mention the notion of 'matched' operator on a Hilbert module, relying on the Pedersen ideal, which gives conformally generated cycles their dynamical quality, reminiscent of Woronowicz's C*-algebras generated by unbounded elements. In considering descent for conformally group- and quantum-group-equivariant spectral triples, we obtain a number of novel examples.

This is joint work with Adam Rennie (arXiv:2412.17220).

Current organizers and contact:

Chalmers/University of Gothenburg

Lyudmila Turowska

University of Copenhagen:

Søren Eilers

Lund University:

Magnus Goffeng [magnus dot goffeng (at) math dot lth dot se (responsible for the homepage)]

University of Southern Denmark (Odense):

Kevin Aguyar Brix

Information about the Scandinavian Operator Algebra Workshop,

June 8-9, 2026 in Lund

Monday, June 8

Room: MH:333

13.30-14.15: Kang Li (Lund University)

Title: Dimension theories from groupoids to classifiable C*-algebras, and back again

Abstract:

14.15-15.00 Coffee break

15.00-15.45: David Jekel (University of Copenhagen)

Title: Applications of free probability to W*-bundlesAbstract: Click to expand →

Abstract:

16.15-17.00: Makoto Yamashita (University of Oslo)

Title: Higher sheaves behind representable KK-theory and the Chern characterAbstract: Click to expand →

Abstract:

18.30 Dinner

Tuesday, June 9

Room : MH:333

9.00-9.45: Olof Giselsson (Chalmers and University of Gothenburg)

Title: Quantum SU(3) as a 2-graphAbstract: Click to expand →

Abstract:

10.00-10.45: Matteo Pagliero (University of Southern Denmark)

Title: Selflessness for reduced free products and reduced graph products of C*-algebrasAbstract: Click to expand →

Abstract:

10.45-11.15 Coffee break

11.15-12.00: Ada Masters (Lund University)

Title: Whither twisted spectral triples?Abstract: Click to expand →

Abstract:

Current organizers and contact:

Chalmers/University of Gothenburg

University of Copenhagen:

Lund University:

University of Southern Denmark (Odense):

Title: Applications of free probability to W*-bundles
Abstract: Click to expand →

Title: Higher sheaves behind representable KK-theory and the Chern character
Abstract: Click to expand →

Title: Quantum SU(3) as a 2-graph
Abstract: Click to expand →

Title: Selflessness for reduced free products and reduced graph products of C*-algebras
Abstract: Click to expand →

Title: Whither twisted spectral triples?
Abstract: Click to expand →