Organisers:
Lisa Orloff Clark (Wellington University, New Zealand)
Anna Duwenig (UNSW, Australia)
Roozbeh Hazrat (Western Sydney University, Australia)
Huanhuan Li (Hefei University, China)
Aidan Sims (Wollongong University, Australia)

Program Description: Algebras constructed from combinatorial data are central in C*-algebra theory, symbolic dynamics and noncommutative algebra. There is a long history of researchers from two or more of these fields independently arriving at similar questions, and obtaining similar results, but via completely different techniques. An important example is the question of indecomposability for C*-algebras, algebras and dynamics coming from directed graphs: indecomposability has a natural meaning in each case; researchers in each area independently discovered a characterisation in terms of exactly the same property of the graph; but the proofs of these characterisations seemed completely unrelated, and shed no light on why indecomposability of one object should be related to that of either of the others. Discovering the underlying link between these three notions of indecomposability brought the algebra and C*-algebra communities together across a 10-year program of research. The synergy that this engendered energised both fields.

This research program on combinatorial combinatorial *-algebras will gather international and Australian researchers working at the cutting edge of the nexus between C*-algebras and abstract algebras, along with the emerging next generation of researchers in these areas. Its scientific focus will be to identify further meta-properties with natural interpretations across the two areas, and to understand the underlying mathematical connections between them. At the same time, it will explore emerging interrelation with geometric group theory via topological full groups. Specifically, we will focus on recent developments in non-Hausdorff groupoid algebras and Roe algebras, as well as open problems such as the algebraic Kirchberg-Phillips problem, Matui’s conjectures relating K-theory of groupoid algebras and groupoid homology, and Williams’ SSE-SE problem and its connections to Hazrat’s graded classification conjectures. This will strengthen ties and foster collaborations between the communities working on combinatorial *-algebras, including coarse geometers, C*-algebraists, pure algebraists and dynamicists.

Program Structure:
TBD

Registration:

• Deadline: TBD
• Registration is by invitation only. If you are interested to participate in this program, please contact one of the organisers with your CV and research background.
• Arrival date: 1 March 2026

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 3 March 2026
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.