Wollongong OANCG Seminar

A weekly research seminar hosted at the University of Wollongong on the topics of operator algebras, noncommutative geometry, and related fields. The seminar has been running continuously since 2011.

Key Info

• Regular time: Thursday 3:30 pm Wollongong time (this may vary occasionally and will be noted on the talks below)
• Regular location: 39C.174 - Campus map
• Zoom: Link - Meeting ID: 861 2230 0349 (password provided on request)
• Organisers: Alexander Mundey & Alex Paviour

If you are interested in either giving a talk or being added to the mailing list, please contact the organisers at wollongong.oancg[at]gmail.com.

Talks typically run for around 55 minutes. We welcome speakers ranging from seasoned researchers to graduate students. We hold talks on campus and host remote speakers via Zoom.

Talks from previous years

Talk Schedule - 2025

Click on "Abstract" to reveal the abstract.

Upcoming talks

• March 6: Adam Rennie (University of Wollongong)
  Conformal transformations and equivariance in unbounded KK-theory
  Abstract

  I will give (at least) the third talk on this material, the two previous being by Ada, as is the bulk of this work. In this talk I will focus on the novel structures unveiled by probing conformality and equivariance. These include the essential appearance of ternary rings of operators, and the more general spectral-triple-like objects that result.
  
  Joint work with Ada Masters, arXiv:2412.17220.
• March 13: Dilshan Wijesena (University of New South Wales)
  A tensor product for representations of the Cuntz algebra
  Abstract

  In this talk we introduce a tensor product \(\boxtimes\) for a large class of representations of the Cuntz algebra \(O_2\), providing the first explicit notion of fusion for such representations. We do this by using our previous work on the classification of \(Rep(O_2)\) via Jones' technology and Pythagorean representations. We demonstrate many interesting applications of \(\boxtimes\). For example, we are able to produce many interesting tensor categories consisting of representations of \(O_2\) with computable fusion rules which is rather rare in the literature. Moreover, using \(\boxtimes\) we deduce Lie group actions that define smooth deformations of representations of the Thomspon groups \(F,T,V\) and \(O_2\), which recover many previously known representations. This is a joint work with Arnaud Brothier.
• March 20: Shay Tobin (Macquarie University)
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• March 27: Dani Czapski (University of New South Wales)
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• April 3: Jamieson Bell (University of Münster)
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• April 10: TBA
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• April 17: Murray Elder (University of Technology Sydney)
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Recent talks

• February 27: Alexander Mundey (University of Wollongong)
  Fibrewise compactifications and generalised limits (non)commutative topology
  Abstract

  The category of compact spaces and continuous maps is "nice". The category of locally compact spaces and continuous maps is less "nice"—infinite products and projective limits of locally compact spaces are not necessarily locally compact. To address this, I will introduce fibrewise compactifications, a family of constructions that extend continuous maps between locally compact spaces to proper maps. These provide a systematic way to construct limits of locally compact spaces, with examples including the boundary path space of a directed graph. I will also discuss how these constructions translate into the C*-algebraic setting via extensions, providing a new entry in the noncommutative topology dictionary.
• February 20: Chris Bourne (Nagoya University)
  A C*-module framework for interfaces of discrete quantum systems
  Abstract

  Loosely speaking, an interface describes a spatial mixing of several systems described by a C*-algebra of observables such that these mixed dynamics are not felt 'at infinity'. I will introduce work-in-progress to adapt work by Măntoiu to formalise a mathematical description of (discrete) interfaces using C*-modules and (discrete) crossed products. Several examples will be given as well as spectral and index-theoretic properties.
• February 13: Astrid an Huef (Victoria University of Wellington)
  Nuclear dimension of \(C^*\)-algebras of groupoids with large isotropy subgroups, and applications to \(C^*\)-algebras of graphs
  Abstract

  Let \(G\) be a locally compact, Hausdorff groupoid. Guentner, Willet and Yu defined a notion of dynamic asymptotic dimension (dad) for étale groupoids, and used it to find a bound on the nuclear dimension of \(C^*\)-algebras of principal groupoids with finite dad. To have finite dad, a groupoid must have locally finite isotropy subgroups which rules out, for example, the graph groupoids and twists of étale groupoids by trivial circle bundles. I will discuss how the techniques of Guentner, Willett and Yu can be adjusted to include some groupoids with large isotropy subgroups, including an applications to \(C^*\)-algebras of directed graphs that are AF-embeddable. This is joint work with Dana Williams.
• Talks from previous years