| Date: | Thursday, 5th February 2026 |
| Speaker: | Dr Anna Duwenig (University of New South Wales, Australia) |
| Title: | The Zappa–Szép product of groupoid twists |
| Abstract: | The Zappa–Szép (ZS) product of two groupoids is a generalisation of the semi-direct product: instead of encoding one groupoid action by homomorphisms, the ZS product groupoid encodes two (non-homomorphic, but "compatible") actions of the groupoids on each other. Together with my collaborator Boyu Li, I have been working on various ways of generalising this construction to the world of C*-algebras. In this talk, I will introduce you to our generalisation of the ZS product to two twists over groupoids and, if time permits, I will show how our construction ties in with Weyl twists from Cartan pairs arising from Kumjian–Renault theory. (Based on joint work with Boyu Li, New Mexico State University.) |
| — [No seminar on 12th February 2026.] — | |
| Date: | Thursday, 19th February 2026 |
| Speaker: | Dr Aleksa Vujičić (University of Waterloo, Canada) |
| Title: | The Fourier spine of Fell groups |
| Abstract: | For a locally compact group G, one can define the Fourier and Fourier–Stieltjes algebras A(G) and B(G), which in the abelian case are isomorphic to L1(Ĝ) and M(Ĝ) respectively. While there is no direct analogue in the general case, they do share similar properties, so typically A(G) is more "tractable" than B(G) and often easier to describe. The notable exception is when G is compact, in which case these algebras coincide. The Fell group, defined as G = Qp ⋊ Op* (where Qp and Op denote the p-adic numbers and integers respectively), has very compact-like behaviour in many regards. In particular, B(G) is small: it can be written as the direct sum B(G) = A(G) ⊕ A(Op*). The combination of all direct sums of this form is known as the "spine" of B(G), and the Fell group is one of a few known non-compact examples of a group where the spine of B(G) is B(G) itself. Based on joint work with Nico Spronk, we investigate the structure of B(G) for higher dimensional analogues of the Fell group. Although B(G) is larger than its spine in these groups, we find that this difference is rather small in some sense. |
| — [No seminar on 26th February 2026.] — | |
| — [No seminar on 5th or 12th March 2026 due to MATRIX Workshop.] — | |
| Date: | Thursday, 19th March 2026 |
| Speaker: | Dr Adam Dor-On (Haifa University, Israel) |
| Title: | Distance to commuting unitary matrices |
| Abstract: |
A question going back to Halmos asks when two approximately commuting matrices of a certain kind are close to genuinely commuting matrices of the same kind. It was quickly realised that dimension-independent results were far more difficult to obtain, and in work of Lin the result was settled for self-adjoint matrices. Estimates for the distance to commuting self-adjoint matrices were sought out by many authors until optimal bounds were established by Kachkovskiy and Safarov. On the other hand, it has long been known, since the work of Voiculescu, that there is an obstruction for dimension-independent approximately commuting unitary matrices to be close to commuting unitary matrices. However, in work of Gong and Lin, and of Eilers, Loring and Pedersen, it was shown that when this obstruction vanishes a positive result still holds. Despite this, quantitative bounds for the distance in terms of the commutator of the unitary matrices were still unknown.
In this talk I will report on joint work with Hall and Kachkovskiy where we show that under the vanishing of said obstruction, we can find bounds for the distance to commuting unitary matrices in terms of the commutator of the original pair of unitary matrices. |
| — [No seminar on 26th March 2026 due to unavailability of the originally scheduled speaker.] — | |
| Date: | Thursday, 2nd April 2026 |
| Speaker: | Ryan Thompson (Victoria University of Wellington, New Zealand) |
| Title: | Groupoid Isotropy, the Baire Category Theorem, and Choice |
| Abstract: | We take a look at three seemingly-unrelated mathematical ideas – isotropy conditions in étale groupoids, the Baire Category Theorem, and the Axiom of Choice. It is known that the full strength of choice can be used to establish a number of Baire Category theorems, but often you only need a weaker form of choice to show that a particular class of spaces are Baire. In 2014, Brown and Clark established an equivalence between the axiom of dependent choice and a condition about étale groupoid isotropy. We build on this, with a focus on the groupoid condition of topological freeness. This is based on recent joint work with Clark and Tolich. |
| — [No seminar on 9th or 16th April 2026 due to Mid-Trimester Break.] — | |
| Date: | Thursday, 23rd April 2026 |
| Speaker: | Dr Becky Armstrong (Victoria University of Wellington, New Zealand) |
| Title: | Learning Seminar: The Functional Calculus, Part 1 |
| Abstract: | TBA |
| Date: | Thursday, 30th April 2026 |
| Speaker: | Dr Becky Armstrong (Victoria University of Wellington, New Zealand) |
| Title: | Learning Seminar: The Functional Calculus, Part 2 |
| Abstract: | TBA |
| Date: | Thursday, 7th May 2026 |
| Speaker: | Professor Astrid an Huef (Victoria University of Wellington, New Zealand) |
| Title: | Learning Seminar: Induction of Representations, Part 1 |
| Abstract: | TBA |
| Date: | Thursday, 14th May 2026 |
| Speaker: | Professor Astrid an Huef (Victoria University of Wellington, New Zealand) |
| Title: | Learning Seminar: Induction of Representations, Part 2 |
| Abstract: | TBA |
| Date: | Thursday, 21st May 2026 |
| Speaker: | TBA |
| Title: | TBA |
| Abstract: | TBA |
| Date: | Thursday, 28th May 2026 |
| Speaker: | TBA |
| Title: | TBA |
| Abstract: | TBA |