Talks for Spring 2026.

Tuesday 3 February 2026

Speaker: Ujan Chakraborty (University of Glasgow)

Tuesday 10 February 2026

Speaker: Sanaz Pooya (University of Potsdam)

Tuesday 17 February 2026

Speaker: Shintaro Nishikawa (University of Southampton)

Tuesday 24 February 2026

Speaker: Safoura Zadeh (University of Bristol)

Tuesday 3 March 2026

Speaker: Nóra Szakács (University of Manchester)

Tuesday 10 March 2026

Speaker: Greg Patchell (University of Oxford)

Tuesday 17 March 2026

Speaker: Joachim Zacharias (University of Glasgow)

Tuesday 21 April 2026

Speaker: Michael Dritschel (Newcastle University)

Tuesday 28 April 2026

Speaker: Rachid El Harti (Hassan I University)

Speaker:Talks for Autumn 2025.

Tuesday 23 September 2025

Speaker: Christian Bönicke (Newcastle University)

Title: Nuclear dimension of groupoid C*-algebras

Abstract: Nuclear dimension is a noncommutative generalisation of Lebesgue covering dimension for compact Hausdorff spaces. Finiteness of this dimension plays an important role in the classification programme for simple nuclear C*-algebras. In this talk I give a brief introduction to this dimension theory and explain some results estimating the nuclear dimension for étale groupoid C*-algebras.

Tuesday 30 September 2025

Speaker: Niels Laustsen (Lancaster University)

Title: Equivalence after extension and Schur coupling for Fredholm operators on Banach spaces

Abstract: I shall report on joint work with Sanne ter Horst (North-West University, South Africa), in which we study two relations for bounded operators on Banach spaces: equivalence after extension (EAE) and Schur coupling (SC). They originate in the study of integral equations and have found numerous applications, often relying on a proof that they coincide in the case at hand.
More precisely, it has been known for 30 years that SC implies EAE, but only recently Ter Horst, Messerschmidt, Ran and Roelands disproved the converse by constructing a pair of Fredholm operators which are EAE, but not SC.
Motivated by this result, we investigate when EAE and SC coincide for Fredholm operators. Fredholm operators which are EAE have the same Fredholm index. Surprisingly, we find that for each integer n and every pair of Banach spaces (X,Y), either no pair of Fredholm operators of index n acting on X and Y, respectively, is SC, or every pair of this kind which is EAE is also SC.
Consequently, whether EAE and SC coincide for Fredholm operators of index n depends only on the geometry of the underlying Banach spaces X and Y, not on the properties of the operators themselves.
I intend to make the talk accessible to a broad audience of analysts; in particular, I shall not assume any prior knowledge of EAE and SC or specialist knowledge of Banach space theory.

Tuesday 7 October 2025

Speaker: Francesca Tripaldi (University of Leeds)

Title: Extracting subcomplexes in the subRiemannian setting

Abstract: On subRiemannian manifolds, the de Rham complex is not the ideal candidate to use to carry out geometric analysis. However, special subcomplexes have successfully been applied in very specific settings, such as Heisenberg groups and the Cartan group. I will give an overview of different techniques used to obtain such subcomplexes, as well as point out their limitations when used on arbitrary Carnot groups, and a possible way to overcome them.

Tuesday 14 October 2025

Speaker: Rhiannon Dougall (Durham University)

Title: From the thermodynamic formalism to convolution of probability in discrete groups 

Abstract: This talk will involve analysis on a discrete countable group. The analysis we are interested in is to describe limiting quantities associated to self-convolution of a probability function. (Quantities associated to a random walks on the group.) This is well-studied in the case where the probability is symmetric (whence one also benefits from self-adjointness of related operators). I’ll motivate the topic with how fundamental quantities associated to the group often appear in the limit. I’ll also explain a new result: a ratio limit theorem for amenable groups, and highlight the role (and novelty) of a thermodynamic mindset in this area.

Wednesday 15 October 2025, 3-4pm, (HERB.4.TR2) 

Speaker: Tirthankar Bhattacharyya (Indian Institute of Science, Bangalore)

Tuesday 21 October 2025

Speaker: Andrew S. Toms (University of Oxford and Purdue University)

Title:  Homotopy groups of Cuntz classes in C*-algebras

Abstract:  The Cuntz semigroup of a C*-algebra A consists of equivalence classes of positive elements, where equivalence means roughly that two positive elements have the same rank relative to A.  It can be thought of as a generalization of the Murray von Neumann semigroup to positive elements and is an incredibly sensitive invariant.  We give a brief introduction to this object and its relevance to the classification theory of separable nuclear C*-algebras.  We then present a calculation of the homotopy groups of these Cuntz classes as topological subspaces of A when A is classifiable in the sense of Elliott.

Tuesday 28 October 2025

Speaker: Julian Gonzales (University of Glasgow)

Title: On dense subalgebras of the singular ideal in groupoid C*-algebras

Abstract: Groupoids provide a rich supply of C-algebras, and there are many results describing the structure of these C-algebras using properties of the underlying groupoid. For non-Hausdorff groupoids, less is known, largely due to the existence of ‘singular’ functions in the reduced C-algebra. This talk will discuss two approaches to studying ideals in non-Hausdorff groupoid C-algebras. The first uses Timmermann’s Hausdorff cover to reduce certain problems to the setting of Hausdorff groupoids. The second will restrict to isotropy groups. For amenable second-countable étale groupoids, these techniques allow us to characterise when the ideal of singular functions has dense intersection with the underlying groupoid *-algebra. This is based on joint work with K. A. Brix, J. B. Hume, and X. Li, as well as upcoming work with J. B. Hume.

Tuesday 4 November 2025 - 3:00-4:00pm in HERB.4.TR4 (NOTE THE UNUSUAL TIME AND ROOM!)

Speaker: Ali Wehbe (Lebanese University)

Title: Geometric conditions for the stability of some singular transmission problems

Abstract: We study an elastic/viscoelastic transmission problem governed by coupled partial differential equations in a bounded domain. The stability of the system is strongly influenced by the regularity of the coupling coefficients at the interface and by the geometry of the damping region. By employing a frequency-domain approach combined with a novel multiplier technique, we derive a polynomial energy decay rate under significantly weakened geometric assumptions and without required smoothness of the interface coefficient.

Tuesday 11 November 2025

No talk this week.

Tuesday 18 November 2025

Speaker: Christian Voigt (University of Glasgow)

Title: Equivariant cyclic homology for ample groupoids

Abstract. In this talk I’ll first review how (periodic) cyclic homology, developed by Connes and Tsygan in the 1980’s, can be viewed as an analogue of de Rham cohomology in the realm of noncommutative geometry. Then I’ll explain the construction of an equivariant version of periodic cyclic homology for actions of Hausdorff ample groupoids, and indicate why this theory should be a natural receptacle for an equivariant Chern character from groupoid equivariant bivariant KK-theory.  (Based on joint work with F. Pagliuca) 

Tuesday 25 November 2025

Speaker: Connor Evans

Tuesday 2 December 2025

Speaker: Connor Gauntlett (Newcastle University)

Tuesday 9 December 2025

Speaker: Kasia Rejzner (University of York)

Title: Algebraic Structures in QFT in the Presence of a Quantum Reference Frame

Abstract: I will start with introducing the framework of algebraic quantum field theory (also on curved spacetimes) and explain how to understand measurement in this framework using the approach of Fewster and Verch. In particular, I will demonstrate that in the presence of symmetries one needs to use a quantum reference frame to be able distinguish between measurements related by symmetry transformations. This leads to interesting consequences regarding the type of relevant observable algebras, as observed by Chandrasekaran, Longo, Penington and Witten in the context of QFT on de Sitter. This talk will be mostly based on my joint paper with Fewster, Janssen, Loveridge and Waldron, “Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory.”

Previous talks from Spring 2025

Tuesday 4 February 2025

Speaker: Kevin Aguyar Brix (University of Southern Denmark)

Title: A meditation on flow

Abstract: I will discuss the notion of flow equivalence for several examples of homeomorphisms on 0-dimensional compact Hausdorff spaces, e.g. shifts of finite type, and how it connects to flows on 1-dimensional spaces. It is an ongoing problem to extend this to higher dimensional dynamical systems, and I will explain one approach to this (joint with Elizabeth Gillaspy and David Pask).

Thursday 6 February 2025, 4-5pm, HERB.4.TR2 (note the unusual day and time!)

Speaker: Taro Sogabe (Kyoto University)*

Title: Cuntz–Krieger algebras their Toeplitz extensions and reciprocal algebras

Abstract: The Cuntz–Krieger algebras are typical examples of classifiable C* algebras and have many interesting structures including the gauge action, computable K-theory and the associated Fock space.
In this talk, I would like to focus on so-called Toeplitz extensions of the Cuntz–Krieger algebras introduced by Fujii–Enomoto–Watatani and Evans, and will explain the strong K-theoretic duality discussed in the joint works with Ulrich Pennig (published) and Kengo Matsumoto (unpublished ongoing joint work).
If time permits, I will explain the reciprocal algebras and a construction of reciprocal algebras of the Cuntz–Krueger algebras.

11 February 2025

Speaker: Lucas Hataishi (University of Oxford)

Title: Discrete C*-algebraic inclusions as quantum symmetries.

Abstract: Building on the philosophy started in the theory of subfactors, I will discuss how a class of C-algebraic inclusions can be described in terms of representations of abstract algebraic and combinatorial objects, known as unitary tensor categories. A particular instance of that description encloses representations of groups, and also of quantum groups, motivating the terminology ‘quantum symmetries’ in the general framework. We call the C-algebraic inclusions fitting in this framework discrete, since structurally
they are similar to crossed products by discrete groups. The main analytical tool used in the characterization of discrete inclusions is
a collection of Pimsner-Popa inequalities, explored to construct faithful conditional expectations.

This talk will be based on joint work with Roberto Hernandez Palomares.

Monday, 17 February 2025, 4-5pm, HERB.4.TR1 (note the unusual day, time, and room!)

Speaker: Alistair Miller (University of Southern Denmark)

Title: Homology and K-theory for self-similar group actions

Abstract:  Self-similar groups are groups of automorphisms of infinite rooted trees obeying a simple but powerful rule. Under this rule, groups with exotic properties can be generated from very basic starting data, most famously the Grigorchuk group which was the first example of a group with intermediate growth.

Nekrashevych introduced a groupoid and a C*-algebra for a self-similar group action on a tree as models for some underlying noncommutative space for the system. Our goal is to compute the K-theory of the C*-algebra and the homology of the groupoid. Our main theorem provides long exact sequences which reduce the problems to group theory. I will demonstrate how to apply this theorem to fully compute homology and K-theory through the example of the Grigorchuk group.

This is joint work with Benjamin Steinberg.

18 February 2025

Speaker: Sihan Wei (University of Glasgow)

Title: Groupoid approach of Cuntz-Pimsner C*-algebras of subshifts and their nuclear dimension

Abstract: During the last decades, attempts to associate C-algebras to arbitrary subshifts have been made to extend and generalize Cuntz-Krieger algebras associated to shifts of finite type. This finally gives the class of Cuntz-Pimsner algebras using C-correspondence. Among many of its equivalent definitions, a groupoid approach was established by T. Carlsen, i.e., by associating a second countable etale groupoid to every subshift where the Cuntz-Pimsner algebra is isomorphic to the corresponding full groupoid C*-algebra.

In this talk, I will make an overall review of this groupoid approach. A description to the groupoid of a particular class of subshifts will also be given, which allows us to compute the nuclear dimension of their Cuntz-Pimsner algebras upon use of the dynamic asymptotic dimension. The talk is based on a joint work with Z. He, and the previous result of K. Brix.

25 February 2025 - MOVED TO ROOM KGVI.1.12.

Speaker: David Kimsey (Newcastle University)

Title: Multivariate moment indeterminateness: separating functions and bounded point evaluations

Abstract: The discrete data encoded in the power moments of a positive measure fast decaying at infinity on Euclidean space is incomplete for recovery leading to the concept of moment indeterminateness.On the other hand classical integral transforms (Fourier-Laplace, Fantappiè, Poisson) of such measures are complete often invertible via an effective inverse operation. The gap between the two non-uniqueness/uniqueness phenomena is manifest in the dual picture when trying to extend the measure regarded as a positive linear functional from the polynomial algebra to the full space of continuous functions. This point of view was advocated by Marcel Riesz a century ago in the single real variable setting. Notable advances in functional analysis have root in Riesz’ celebrated four notes devoted to the moment problem. A key technical ingredient being there the monotone approximation by polynomials of kernels of integral transforms. With inherent new obstacles we reappraise in the context of several real variables M. Riesz’ variational principle. The result is an array of necessary and sufficient moment indeterminateness criteria some raising real algebra questions others involving intriguing analytic problems all gravitating around the concept of moment separating function.

This talk is based on joint work with Mihai Putinar.

14 March 2025, 3-4pm, HERB.4.TR1 (note the unusual day, time, and room!)

Speaker: Sophie Emma Zegers (Delft University of Technology)

Title: On the classification of quantum lens spaces

Abstract: In the study of noncommutative geometry, various of classical spaces have been given a quantum analogue. A class of examples are the quantum lens spaces described by Hong and Szymański as graph $C^*$-algebras. The graph $C^*$-algebraic description has made it possible to obtain important information about their structure and to work on classification. Moreover, every quantum lens space comes with a natural circle action, leading to an equivariant isomorphisms problem.

In this talk, I will give a brief introduction on how to classify quantum lens spaces and how to obtain a number theoretic invariant in low dimensions. Moreover, I will present my recent joint work with Søren Eilers on the existence and construction of equivariant isomorphisms of low dimensional quantum lens spaces.

29 April 2025

Speaker: Haluk Sengun (University of Sheffield)

Title: Unitary representations of groups and operator algebras

Abstract: The representation theory of locally compact groups and operator algebra theory had important interactions very early in their infant years but they began to move in separate directions afterwards. Recent years have seen efforts to bring the two theories back together in the fundamental case of reductive groups.

In this expository talk, we will touch upon some of these synergies; the interactions in the theory of unitary induction dating back to the 1970s and the recently discovered interactions in the theory of theta correspondence (aka Howe duality). This is based on joint works with Bram Mesland (Leiden) and with Magnus Goffeng (Lund).

6 May 2025

Speaker: Jennifer Pi (University of Oxford)

Title: A Logical Classification Theorem for C*-Algebras

Abstract: I discuss a logical variant of the classification program for C*-algebras, proving that a particular kind of logical equivalence of the Elliott invariant implies equivalence of C*-algebras. This answers a question posed in the paper “Games on AF-Algebras”, by de Bondt, Vaccaro, Velickovic, and Vignati. The proof uses some descriptive set theory and a novel way of representing KK-equivalence of C*-algebras in terms of first-order model theory. In particular, the key is proving that the set of separable C*-algebras satisfying the UCT is an analytic set, in the sense of descriptive set theory. This is work-in-progress with Michał Szachniewicz and Mira Tartarotti. 

22 July 2025

Speaker: Ilija Tolich (Victoria University of Wellington)

Title: Stably finite and purely infinite crossed products

Abstract: The C*-algebras associated to  \'{e}tale groupoids can be viewed as a crossed product: the inverse semigroup of bisections acting on the (commutative) continuous functions on the unit space. Using this as our model we can consider inverse semigroup crossed products of noncommutative C*-algebras.

For certain classes of groupoids there is a known dichotomy: the groupoid C*-algebra is either stably finite or purely infinite. This extends a dichotomy for classes of classifable C*-algebras. The key construction in these proofs is a type semigroup arising from the dynamics on the underlying Hausdorff unit space.

In order to accomodate arbitrary C*-algebras we use the Cuntz semigroup as a noncommutative replacement for the unit space to build a type semigroup.  We will outline the crossed product construction and present work towards the purely infinite-stably finite dichotomy.

Joint work with Becky Armstrong, Lisa Orloff Clark, Astrid an Huef and
Diego Martínez.

Previous talks.

27 September 2024

Speaker: Tirthankar Bhattacharyya (Indian Institute of Science, Bangalore)

Title: Herglotz and Caratheodory over the ages

Abstract: Herglotz’s representation of holomorphic functions with positive real part and Caratheodory’s theorem on approximation by inner functions are two well-known classical results in the theory of holomorphic functions on the unit disc. In this talk, we shall first see that they are equivalent. On a multi-connected domain Ω, a version of Heglotz’s representation is known. Caratheodory’s approximation was not known. This will be formulated. We then show that it is equivalent to the known form of Herglotz’s representation.
Additionally, it also enables us to prove a new Heglotz’s representation in the style of Koranyi and Pukanszky. Of particular interest is the fact that the scaling technique of the disc is replaced by Caratheodory’s approximation theorem while proving this new form of Herglotz’s representation. Caratheodory’s approximation theorem is also proved for matrix-valued functions on a multi-connected domain. The part of this talk which is new is joint work with Poornendu Kumar and Mainak Bhowmik.

1 October 2024

Speaker: Takuya Takeishi (Kyoto Institute of Technology)

Title: Groupoid homology and K-theory for algebraic actions from number theory

Abstract: By the work of Bruce and Li, the topological full group (TFG) of the groupoid associated to the ring C*-algebra for the ring of integers of a number field is known to be a complete invariant for number fields, but it is now clear how basic invariants of number fields are reflected in the TFG. For the first step to understand this TFG, we show that the extension degree over the rational field coincides with the smallest degree such that the group homology of the TFG does not vanish. We show it by the calculation of the groupoid homology. For another application of this computation, we give another proof of Li-Luck’s computation of the K-theory of the ring C*-algebras. We also compute the groupoid homology of Barlak–Omland–Stammeier groupoids and solve the conjecture for K-theory of their C*-algebras. This is a joint work with C. Bruce and Y. Kubota.

8 October 2024

Speaker: Zinaida Lykova (Newcastle University)

15 October 2024

Speaker: David Seifert (Newcastle University)

Title: A non-uniform stability result of Datko-Pazy type

Abstract: The Datko-Pazy theorem characterises uniform (exponential) stability of strongly continuous operator semigroups in terms of an integrability condition. It is a cornerstone of the classical stability theory of operator semigroups. More recent work, in some cases motivated by applications to evolution equations, has focussed on weaker quantitative notions of stability. After reviewing some background on the stability theory of operator semigroups I shall present a simple adaptation of the classical Datko-Pazy theorem for non-uniform (polynomial) stability of a bounded semigroup, and discuss some consequences of this result. The talk is based on joint work with Nicolas Vanspranghe and Lassi Paunonen.

22 October 2024

Speaker: Andrea Vaccaro (Universität Münster)

Title: Uniform property Gamma and the small boundary property
Abstract: Uniform property Gamma is an adaptation of the well-studied concept of property Gamma, from tracial von Neumann algebras, to the framework of tracial C-algebras. In this talk I will give an overview of the role played by uniform property Gamma in the study of simple nuclear C*-algebras, particularly in relation to the Toms-Winter conjecture, and I will discuss the connections and relations that this property has with the notion of small boundary property for topological dynamical systems.

29 October 2024

Speaker: Ben Bouwen (University of Southern Denmark)

Title: A unified approach for classifying simple nuclear C*-algebras

Abstract: The classification program of C-algebras aims to classify simple, separable, nuclear C-algebras by their K-theory and traces, inspired by analogous results obtained for von Neumann algebras. A landmark result in this project was obtained in 2015, building upon the work of numerous researchers over the preceding 20 years. More recently, Carrión, Gabe, Schafhauser, Tikuisis and White developed a new, more abstract approach to classification, which connects more explicitly to the von Neumann algebraic classification results. In their paper, they carry out this approach in the stably finite setting, while for the purely infinite case, they refer to the original result obtained by Kirchberg and Phillips. In this talk, I provide an overview of how the new approach can be adapted to classify purely infinite C*-algebras, recovering the Kirchberg-Phillips classification by K-theory and obtaining Kirchberg’s absorption theorems as corollaries of classification rather than (pivotal) ingredients. This is joint work with Jamie Gabe.

12 November 2024

Speaker 1 (2:00-3:00): Malte Leimbach (Radboud University)

Title: Spectral truncations and convergence of compact quantum metric spaces

Abstract: A fundamental principle of noncommutative geometry is to encode geometric information by spectral data, formalised in the notion of spectral triples. In physical practice there are, however, always obstructions on the availability of such data, and one might be led to considering truncated versions of spectral triples instead. In this talk we will take a closer look at this formalism and explore it within the framework of compact quantum metric spaces. In particular, we will discuss how one might appropriately approximate spectral triples by their truncated versions. As concrete examples we will consider spectral truncations of tori and Peter–Weyl truncations of compact quantum groups.

Speaker 2 (3:30-4:30): Joan Bosa (Universidad de Zaragoza)

Title: Almost Elementary Dynamical Systems
Abstract: Motivated by recent work on dynamical analogues of the Toms-Winter conjecture, we propose an extension of Kerr’s notion of almost finiteness for actions of discrete groups on compact metric spaces to actions on general C*-algebras by generalising the concept of castle. We call such actions almost elementary and study these dynamical systems in different frameworks. For instance, we show that they lead to $\mathcal Z$-stable crossed products, if these are simple, and that for actions of the trivial group our condition is a weak form of being tracially AF or having tracial nuclear dimension 0.

19 November 2024

Speaker: Jeremy Hume (University of Glasgow) — CANCELLED

Title: Dynamical Covers

Abstract: A method to understand a dynamical system is to study simpler and better behaved systems that factor onto it, which we will call “covers”. For instance, this method can be successfully employed to prove the existence of unique measures of maximal entropy and provide combinatorial classifications for symbolic dynamical systems known as sofic sub-shifts.

The talk is based on the pre-print https://arxiv.org/abs/2408.11917 (joint work with Kevin Brix and Xin Li), where we construct covers that generalize the ones in symbolic dynamics responsible for the two mentioned successes. We will discuss the functorial and universal properties of the constructions which make the covers computable in practice. We will also describe some relationships between properties of the original systems and properties of their covers, and provide applications to C*-algebras of semi-etale groupoids.

26 November 2024

Speaker: Shanshan Hua (University of Oxford)

Title: Uniqueness theorems for maps into II1-factors and ultraproducts of matrices

Abstract: Over the past few decades, the classification results for C*-algebras have been built on those of morphisms. In the recent work of Carrión, Gabe, Schafhauser, Tikuisis and White, they recaptured the classification theorem for a large class of simple Z-stable C*-algebras by classifying maps into such C-*algebras. Following their abstract classification framework, we go beyond the range of currently existing classification results. For instance, as part of our results, uniqueness theorems for maps into II1-factors and ultraproducts of matrices are obtained, where codomain C*-algebras are either not known to admit Z-stability or are known to lack Z-stability.

3 December 2024

Speaker: Andrew Pritchard (Newcastle University)

Title: Semi-uniform stability of semigroups and their cogenerators

Abstract: Semi-uniform stability for a strongly continuous semigroup refers to the stability of classical solutions of a linear evolution equation. The cogenerator of a strongly continuous semigroup is a bounded linear operator defined as the Cayley transform of the generator. In this talk, I will present some results relating the (quantified) stability of strongly continuous semigroups with that of the discrete semigroup given by powers of the cogenerator. These results are obtained through two distinct approaches. The first approach is based on resolvent estimates and uses a quantified version of the Katznelson-Tzafriri theorem. The second approach is based on an integrability condition and the boundedness of a certain vector-valued integral transform.
This talk is based on joint work with David Seifert.

10 December 2024

Speaker: Apurva Seth (University of Oxford)