Attendees of the meeting are listed below. For attendees giving a talk, click on their talk title to see the abstract.

Name Talk title (if applicable)
Nina Holden
Rei Inoue
Johanna Knapp
Zhengwei Liu

Quantum Fourier Analysis is a subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory and TQFT) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. In this talk, we will introduce its background, development and outlook, based on representative examples, results and applications.

James Tener
Alhanouf Almutairi
Ibrahim Alotaibi
Leighton Arnold
Michael Assis
Sahil Balak
Murray Batchelor
Nicholas Beaton
Lachlan Bennett
For this talk, we will be discussing a particular quantum integrable four-site Bose-Hubbard model — a model which describes the physics of interacting bosons on a four-site lattice. Using the Bethe Ansatz technique, we will find exact expressions for leading order terms of the eigenvalues and eigenstates of the Hamiltonian. This enables us to find formulae describing the quantum dynamics of the system. With what we derive, we can show that given specific initial conditions, there exists a time when we have a quantum entangled state that approximates a NOON state. NOON states are used for parameter estimation that can outperform any classical interferometer. We will quantify exactly how close we come to creating a NOON state and compare the results of our analytic formulae to what we expect from numerical calculations.
Jean-Emile Bourgine
Peter Bouwknegt
Tony Bracken
Joshua Capel
Ming Chen
Eve Cheng
Nathan Clisby
Jan de Gier
Holger Dullin
Zachary Fehily
Tyler Franke
Ethan Fursman
Alexandr Garbali
Tim Garoni
Gregory Gold
Joshua Graham
Weiying Guo
Tony Guttmann
Bolin Han
Pedram Hekmati
Robert Henry
Md Fazlul Hoque
Robin Hu
Daniel Hutchings

Given a tensor field which satisfies the massive Klein-Gordon equation on four-dimensional Minkowski space, it decomposes into a sum of constrained fields describing irreducible representations of the Poincaré group with varying spin. Over sixty years ago, Behrends and Fronsdal derived spin projection operators which extract the component of this decomposition corresponding to the representation with the highest spin. Since then, numerous applications have been found for these projectors within the landscape of theoretical physics. For example, they were vital in the original formulation of conformal higher-spin gauge actions. In this talk, I will detail how these operators can be constructed on three-dimensional anti-de Sitter space and study several novel applications. I will then discuss the supersymmetric generalisations of these results.

Jessica Hutomo
Phillip Isaac

We discuss recent results on the construction of quantum (super)group invariants and explain some details in the context of historical results. The methods involved employ the characteristic identities. One of the aims of the talk is to share insights into these techniques.

Aleesha Isaacs
Iwan Jensen
Sam Jeralds
Nalini Joshi
Jonathan Kress
James La Fontaine
Conformal higher-spin gauge (CHS) theories and their supersymmetric extensions have recently attracted considerable interest. CHS theories are higher-spin extensions (s > 2) of Maxwell’s electrodynamics (s = 1) and conformal gravity (s = 2). Formally, CHS theories can be identified as the logarithmically UV divergent part of the effective action (called the induced action) for a complex scalar field coupled to a higher-spin background. However, this induced action has never been computed in closed form. In 2017, linearised superconformal higher-spin gauge (SCHS) theories were constructed and a question arose of whether these models and their non-linear completions can be obtained as an induced action. This talk will give a pedagogical review of our method for computing SCHS actions as induced ones.
Danilo Latini
The rank-1 Racah algebra R(3) plays a pivotal role in the theory of superintegrable systems. It appears as the symmetry algebra of the generic 3-parameter model on the 2-sphere, from which all second-order conformally flat superintegrable systems in 2D can be obtained as limiting cases. A higher rank generalization of R(3) has been considered and showed to be the symmetry algebra of the generic superintegrable model on the (n−1)-sphere. It has recently been shown that it also characterizes the symmetry algebra of generic superintegrable systems defined on pseudo-spheres.

In this talk, I will discuss how such a higher rank generalization of the Racah algebra naturally emerges for a class of nD quasi-maximally superintegrable systems endowed with sl(2,R) coalgebra symmetry.

Reference: D. Latini, I. Marquette and Y.-Z. Zhang. Annals of Physics 426, 168397 (2021)

Xueting Li
Jon Links
Xilin Lu
Inna Lukyanenko
Vladimir Mangazeev
Ian Marquette
William Mead
The asymmetric simple exclusion process (ASEP) is a stochastic model of indistinguishable particles with KPZ-like limiting behaviour. There are very few mathematically rigorous results for the limiting behaviour of multi-species models. In this talk we describe a method for evaluating transition probabilities for a multi-species version of the ASEP. This is performed via a reduction from a family of integrable stochastic vertex models. From this, we derive expressions for bulk crossing probabilities and discuss their implications. Based on joint work with Jan de Gier and Michael Wheeler.
Benjamin Morris
Makoto Narita
Paul Norbury
Jeremy Nugent
Madeline Nurcombe
The Temperley-Lieb algebra arises in many lattice models in statistical mechanics, from quantum spin chains to systems of polymers. It admits a useful diagrammatic presentation and has a rich and well-studied representation theory. In this talk, I will discuss a one-boundary generalisation of the algebra that depends on three complex parameters. Using a diagrammatic presentation, I will introduce a family of its representations and identify which of them are irreducible. I will also determine for what parameter values the algebra is semisimple, and discuss the structure of the representations when the algebra is non-semisimple.
Judy-anne Osborn
Xavier Poncini
Causal dynamical triangulations (CDT) is a non-perturbative approach to quantum gravity where the formal path integral is regularised by a triangulation. Of particular interest is the coupling of matter fields to the geometry of pure triangulations and the question whether the coupling influences the macroscopic features of the ensemble, such as the Hausdorff dimension. In this talk, I will present three models on 2D causal triangulations: a pure CDT model, a dense loop model, and a dilute loop model. The two loop models introduce a matter coupling to the pure CDT model, reminiscent respectively of the fully-packed and dilute loop models on regular lattices. After introducing correspondences with labelled planar trees and developing a transfer-matrix formalism, the critical behaviour of each model is analysed. The pure CDT and dense loop models are shown to exhibit similar behaviour — indicating the absence of a significant interaction between matter and geometry. The critical behaviour of the dilute loop model is found to be different, with evidence of a shift in Hausdorff dimension from 2 to 1.

Michael Ponds
Robert Pryor
Thomas Quella

We study $U_q(sl_2)$-invariant interpolations between even-spin $q$AKLT states and fully dimerized states and show that the associated transfer matrix has a spectral gap. This confirms an earlier suggestion by one of the authors that even-spin $q$AKLT states are topologically trivial, even if quantum group invariance is preserved. All computations are carried out analytically for general even-integer physical spin and arbitrary $q>0$. An analytical verification of earlier numerical results for even-spin AKLT states by Pollmann et al is included as a special case for $q=1$.

Milena Radnovic
Emmanouil Raptakis
The study of symmetries of a given field theory yields nontrivial information regarding its structure and often provides important insights into potential extensions or generalisations. In particular, a novel class of models for non-linear electrodynamics was recently discovered by Bandos et al. by requiring that they preserve the conformal and U(1) duality invariance obeyed by the free theory. Since such symmetries are also shared by the free theories of conformal higher-spin fields, it is an interesting question to determine what nonlinear deformations consistent with conformal and duality invariance the latter admit. In this presentation, I will present new families of nonlinear models for conformal fields of spins greater than 1.

Jorgen Rasmussen
Christopher Raymond
David Ridout
Pieter Roffelsen
Yang Shi
Benjamin Stone
Two-point and three-point correlation functions of primary operators are the main observables in conformal field theories. Of particular interest are correlation functions of conserved currents such as the vector current, the energy momentum tensor, and more generally, higher-spin conserved currents. An interesting feature of conformal field theories in three-dimensions is that correlation functions of conserved currents contain parity-violating structures which do not appear in four-dimensional theories. In superconformal field theories the vector current and energy-momentum tensor are contained within the flavour current and supercurrent multiplets respectively. In this talk I will discuss the properties of the three-point functions of the supercurrent and flavour current multiplets in three-dimensional superconformal field theories; in particular I will show that they do not-contain parity violating structures. Hence there is an apparent tension between supersymmetry and the existence of parity violating structures in conformal field theories.
Gabriele Tartaglino-Mazzucchelli
Jason Werry
Ben Wootton
Yao-Zhong Zhang
Zongzheng Zhou
Paul Zinn-Justin