Schedule

Invited Talks (sorted alphabetically by last name):

• Patrick DeBonis (Purdue University) - The W* and C*-algebras of Similarity Structure Groups
  
  Abstract:
  Countable Similarity Structure (CSS) groups are groups of homeomorphisms that can be understood as generalizations of the Thompson groups. We identify a subclass referred to as CSS* groups that contains the Higman-Thompson groups $V_{d,r}$, the countable Röver-Nekrashevych groups $V_d(G)$, and the topological full groups of subshifts of finite type of Matui. I will highlight several new properties of both the group von Neumann algebra and reduced group C*-algebra of CSS* groups. These include primeness of many CSS* group von Neumann algebras and C*-simplicity in certain cases. This is joint work with Eli Bashwinger.

• Julian Gonzales (University of Glasgow) - On dense subalgebras of the singular ideal in groupoid C*-algebras
  
  Abstract:
  The `singular ideal' is an ideal in the reduced C*-algebra of a non-Hausdorff groupoid that has historically been an obstacle to understanding structural properties of the C*-algebra. This talk will discuss strategies for describing this ideal. In certain cases,  we will describe an explicit family of functions whose linear span is dense in this ideal. This is based on joint work with J. B. Hume.

• Mehrdad Kalantar (University of Oxford) - On C*-algebras of generalized normal subgroups
  
  Abstract:
  The study of invariant measures and minimal components of the space ${\rm Sub}(G)$ of subgroups of a discrete group $G$ (called IRS’s and URS’s, respectively) is a fast-developing topic in dynamics and ergodic theory. These are important generalizations of normal subgroups: while normal subgroups are kernels of group actions, those generalizations correspond to point stabilizer of measurable and topological group actions. In this talk we discuss some structural properties of C*-algebras generated by subgroups in an IRS or a URS of a given discrete group $G$. This is joint work with Yair Hartman.

• Christian Le Merdy (Laboratoire de Mathematiques de Besancon) - Isometric dilations on non-commutative Lp-spaces and Schur multipliers
  
  Abstract:
  Let T be a bounded operator on some Banach space X. We say that U : Y -- > Y  is an isometric dilation of T (on another Banach space Y) if U is an isometry (of course) and T^n=QU^nJ for all nonnegative integers n, where J : X -- >Y and Q : Y -->X are bounded operators. The interest of this notion depends on the link between X and Y, and sometimes on the specific properties of J and Q. In this talk, we will be mostly interested in the case where X and Y are non-commutative Lp spaces. I will present the context, a method for obtaining isometric dilations on non-commutative Lp spaces, and its significance. Then, I will focus more specifically on the case where T is a Schur multiplier.

• Xiao-Qi Lu (University of Glasgow) - Hilbert transforms on graph products of finite von Neumann algebras
  
  Abstract:
  The boundedness of Fourier multipliers on non-commutative $L_p$-spaces ($1 < p < \infty$) is a fundamental problem in non-commutative analysis. Building on the non-commutative Cotlar identity introduced by Mei and Ricard (2017), which yields $L_p$-boundedness ($1 < p < \infty$) of Hilbert transforms on amalgamated free products of finite von Neumann algebras, their approach relies heavily on freeness in the underlying free product structure.
  
  In this talk, we introduce a new strategy that overcomes this limitation. Our approach combines a generalized Cotlar identity, which holds on suitable subspaces and captures non-freeness information, with the property of Rapid Decay to control the remaining components. From this framework, we establish the $L_p$-boundedness ($1 < p < \infty$) of Rademacher-type Hilbert transforms on graph products of finite von Neumann algebras. This unified framework extends earlier results for free products of finite von Neumann algebras and for graph products of groups acting on right-angled buildings. This is a joint work with Runlian Xia.

• Brita Nucinkis (Royal Holloway) - On normal forms in Thompson’s group F and its generalisations
  
  Abstract:
  I will discuss normal forms both in Thompson’s group F and in certain submonoids. These prove useful when studying properties of their semigroup C*-algebras. I will then give an overview on how to find normal forms in the Golden Mean Thompson group.

• Kasia Rejzner (University of York) - Quantum reference frames and crossed products of von Neumann algebras
  
  Abstract:
  Quantum reference frames (QRFs) are a tool that is gaining increasing attention in quantum information theory and mathematical physics. In this talk I will explain how crossed products arise naturally when solving the physical problem of finding the algebra of invariants for a system consisting of quantum fields and an observer realized as a QRF. This is based on a joint work with Fewster, Janssen, Loveridge and Waldron [CMP 406, 19 (2025)], which generalizes the earlier paper of Chandrasekaran, Longo, Penington and Witten [JHEP 2023, 82 (2023)].

• Robert Yuncken (Institut Élie Cartan de Lorraine) - Harish-Chandra’s philosophy of cusp forms via Lie groupoids
  
  Abstract:
  Harish-Chandra spent his career understanding the unitary representations of real reductive Lie groups like SL(n,R).  One of the crucial points in this theory is his "philosophy of cusp forms", which says that any tempered unitary representation of a real reductive group (with compact centre) is either discrete series, meaning it is a subrepresentation of the regular representation, or it is induced from a parabolic subgroup, such as the block upper-triangular subgroup in SL(n,R).  This sets up an inductive argument over ever smaller subgroups.  I will describe how Harish-Chandra’s principal follows from a Lie groupoid construction due to Omar Mohsen plus some C*-algebra theory.

(Joint work with Jacob Bradd and Nigel Higson)

Contributed Talks:

• Brian Chan (University of Oxford) - The Cuntz-Krieger relations in the context of the Cuntz semigroup
  
  Abstract:
  A major source of the appeal of graph C*-algebras is the ability to explicitly compute various invariants associated to C*-algebras, such as the Murray-von Neumann semigroup and the primitive ideal space. This is possible because of the Cuntz-Krieger relations, which completely define graph C*-algebras. With examples, we will discuss for a finite graph the natural question of how the Cuntz-Krieger relations behave in the Cuntz semigroup.

• Ujan Chakraborty (University of Glasgow) - Ergodic Average Dominance for Unimodular Amenable Groups
  
  Abstract:
  We show that the ergodic averages of the action of any unimodular amenable group along certain Følner sequences can be dominated by the Cesàro means of a suitably constructed Markov operator, that is, the ergodic averages of an integer action. Moreover, the restriction on these Følner sequences are mild enough so that every two-sided Følner sequence has a subsequence satisfying these conditions. As a consequence of this inequality, we obtain the maximal and pointwise (individual) ergodic theorems for actions of unimodular amenable groups directly from the corresponding ergodic theorems for integer actions. This allows us to deal with the commutative and noncommutative ergodic theorems on an equal footing. This is based on joint work with Joachim Zacharias and Runlian Xia.

• Lucas Hataishi (University of Oxford) - Abstract spin systems, DHR-bimodules and unitary Drinfeld centers
  
  Abstract:
  The term abstract spin systems refers to a formulation of spin systems using nets of finite dimensional operator algebras on discrete metric spaces, in contrast to the more traditional Hilbert space approach. It is analogous to the algebraic approach to quantum field theory in many ways, and by exploring these analogies C. Jones introduced the category of DHR-bimodules as a fundamental invariant of both spin chains and nets of operator algebras. Since early it was realized that DHR-bimodules capture the information of topological quantum field theories associated to spin chains.
  
  In this talk I will report in joint work with D. Jaklitsch, C. Jones and M. Yamashita on the theory of DHR-bimodules for locally infinite 1-dimensional abstract spin systems, model as nets of infinite dimensional von Neumann algebras on a discrete 1-dimensional metric space. This allows the contemplation of new examples associated for instance to the representation theory of compact quantum groups, and makes viable a renormalization procedure on such 1-dimensional systems.
  
  

Lightning Talks:

• Max Clarke (University of Southampton) - On symmetries of UHF algebras and the Jiang-Su algebra
  
  Abstract:
  In 1990, Blackadar constructed a period-2 automorphism (symmetry) of the CAR algebra for which the associated crossed product has non-trivial K_1. This construction generalises to yield many K-theoretically non-trivial symmetries of UHF algebras. In this lightning talk, we will discuss Blackadar's result and outline a possible strategy of using the generalised construction to realise symmetries of the Jiang-Su algebra.

• Alexander Gjelsvik Ravnanger (University of Copenhagen) - The largest AF-ideal in certain crossed products
  
  Abstract:
  We present a dynamical description of the largest AF-ideal in certain crossed products by the integers. In the case of the uniform Roe algebra of the integers, this reveals an interesting connection to a well-studied object in topological semigroup theory.

• Rodrigo Samuel Roemig (University of Glasgow) - Non-Hausdorff groupoids and foliations
  
  Abstract:
  The theory of groupoids has drawn the attention of operator algebraists since the '80s, often with the assumption that the groupoid is Hausdorff. However, several examples of groupoids that arise from the theory of foliations do not satisfy this condition. In this talk, I will explain how recent techniques, such as the Hausdorff cover, can shed light on these examples of non-Hausdorff groupoids. Furthermore, I will also briefly mention a possible connection with orbifolds.

• Maxwell Ryder (University of Oxford) - Classifying Continuous Families of Projections in II_1-Factors
  
  Abstract:
  It is well known that the projections in a $\mathrm{II}_1$-factor are classified by their trace, up to Murray-von Neumann equivalence. More recently, considerable progress was made in the classification programme for $C^*$-algebras using techniques to access such historic von Neumann algebraic results through the consideration of continuous bundles of $\mathrm{II}_1$-factors. In this setting, it is natural to ask whether the trace may analogously classify continuous families of projections, up to continuously varying Murray-von Neumann equivalence.
  
  In my talk, I will summarise the brief history of partial answers to this question, before discussing a new result from joint work with David Jekel which provides a positive answer in full generality. This is obtained via a novel approach, utilising free probability theory in a uniform manner across such $\mathrm{II}_1$-factor bundles, which also provides a number of other regularity properties for these objects.

• Austin Shiner (University of Oxford) - Classifying Certain W-Stable Extensions
  
  Abstract:
  In 2015, unital, simple, separable, nuclear stably finite C*-algebras satisfying certain regularity properties, were fully classified by K-theory and traces. A natural question to ask is if one can push the classification to the non-simple setting. The simplest case is that of a C*-algebra with exactly one proper non-zero ideal, such that the ideal and quotient have trivial K-theory. We give examples of such algebras and show that, in the case of a unique trace, these algebras can be completely classified.

• George Tridimas (Cardiff University) - Cocycle actions on C*-algebras and infinite loop spaces
  
  Abstract:
  A cocycle action on a C*-algebra is a generalisation of a group action on a C*-algebra. It is closely related to the notion of a G-kernel. Girón Pacheco, Izumi and Pennig developed a unified approach to handle lifting obstructions for these actions.

In this talk, I will give an overview of their construction in the context of cocycle actions. The construction naturally associates to each (unital) C*-algebra and to each notion of action a topological space, called its classifying space. One is then interested in when this space is an infinite loop space. If the C*-algebra is strongly self-absorbing, all these classifying spaces are always infinite loop spaces. I will briefly sketch how this is achieved to conclude the presentation.

The latter is joint work with my supervisor Ulrich Pennig.