# Participants

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

Name | Talk name (if applicable) |
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Gernot Akemann | Universality of random matrices: from Coulomb gases to quantum systems Random matrices represent mathematical models that are simple enough to be analytically tractable, while being rich enough to describe universal features in many applications in Physics, Mathematics, and beyond. In this talk I will focus on Gaussian random matrices with complex eigenvalues representing a two-dimensional, static Coulomb gas at a certain temperature, the Ginibre ensembles. While being partly simpler than their Hermitian counterparts, they still pose interesting open mathematical problems. Some examples will be presented where they successfully describe complex spectra in quantum field theories with chemical potential and in dissipative open quantum systems. |

Tamara Davis | Adventures on the dark side of the universe Astrophysicists study phenomena that occur on time scales, length scales, and energy scales that we can’t even in principle achieve here on Earth — and our modern telescopes are giving us an unprecedented view of this rich laboratory. We can now see the universe as it was before galaxies even existed. We have found thousands of planets orbiting other stars. We regularly detect supernovae that went off billions of years before the earth even formed. We’ve even detected gravitational waves — ripples in space itself. And most enigmatically, we’ve discovered some kind of “dark energy” that is making the expansion of the universe speed up, contrary to our expectation that gravity should slow it down. In this talk you’ll hear about some of the latest news in astrophysics, including Tamara’s work with the Dark Energy Survey. |

Benjamin Doyon | Hydrodynamics for integrable systems Hydrodynamics is a powerful framework for large-wavelength phenomena in many-body systems. At its basis, it is the assumption that one can reduce the description of the system to that of long-lived, effective degrees of freedom obtained from the available conservation laws. Using this fundamental idea, it was extended recently to include integrable models, where an infinite number of conservation laws exist. This gave “generalised hydrodynamics”. In this talk, I will review the basic aspects of the hydrodynamics of integrable systems. I will take the simple examples of the quantum Lieb-Liniger model, describing cold atom gases, and the classical Toda model, a paradigmatic model of integrable classical gases. I will discuss a recent cold-atom experiment that confirmed the theory, and, if time permits, show some of the exact results that can be obtained with this formalism, such as exact nonequilibrium steady states and correlation functions. |

Lucile Savary | Quantum physics of rocks Rocks are not only for construction, paving, and mosaics. They are also a playground to explore quantum many body physics. Crystalline materials host highly quantum electrons that can exhibit amazing emergent properties with technological promise and which possess fundamental beauty. To study them theoretically requires a synergy of materials chemistry, physics, and mathematics, borrowing from quantum field theory, statistical mechanics, topology and more. I’ll discuss examples involving gauge fields, topological edge modes, and Weyl fermions. |

Masahito Yamazaki | Integrability and four-dimensional Chern-Simons theory Recently a new approach to integrable models has been developed based on a novel mixed topological/holomorphic four-dimensional Chern-Simons-type gauge theory. This gives conceptual explanations for the integrability both in integrable lattice models and integrable field theories, and moreover generates a class of new integrable models. In this talk I am planning to give an overview of the recent developments in this area, based partly on the speaker’s works with Kevin Costello and Edward Witten. |

Alhanouf Almutairi | Colour Lie algebras and quantum groups at roots of unity We discuss the limit of q as a root of unity of a quantum group Uq(g) corresponding to a simple Lie algebra g, and consider the presence of colour Lie algebras occurring as subalgebras in this limit. This will largely be a survey of the relevant literature, and a presentation of some preliminary results relating to certain colour Lie algebras. |

Murray Batchelor | |

Peter Bouwknegt | |

Tony Bracken | The quantum bus and its classical limit The counter-intuitive quantum effect of probability backflow is characterised by a dimensionless quantum number $lambda$, known after various studies to have the value $0.03847…$. This quantum number is peculiar in being independent of the value of Planck’s constant $hbar$. How then can one understand the classical limit, in which the phenomenon ceases to exist? A resolution is obtained by extending the setting of the phenomenon, enabling the classical limit to be understood while preserving the value and significance of the remarkable constant $lambda$. |

Richard Brak | |

Joshua Capel | |

Nathan Clisby | |

Jaklyn Crilly | Mathematical aspects of T-duality In this talk we review the ideas behind T-duality and explore how T-duality extends to certain mathematical objects such as invariant differential forms and Courant algebroids defined over principal circle bundles. We will then introduce some previous and ongoing works into extending these duality mappings and detail some of the benefits that such an extension has on the underlying physics. |

Jean-Pierre Derendinger | On quaternion-Kähler metrics and partial breaking of N=2 supergravity The partial supersymmetry breaking in N = 2 supergravity coupled to a single vector and a single hypermultiplet is in principle possible if the quaternion-Kähler space of the hypermultiplet admits (at least) one pair of commuting isometries. For this class of manifolds, various explicit metrics exist, allowing an analysis of a generic electromagnetic (dyonic) gauging of the isometries. An example of partial breaking in Minkowski spacetime has been found long ago and we demonstrate that no other example exists. Arriving at this result requires a careful use, and a minor correction, of the literature on quaternion-Kähler metrics. |

Holger Dullin | The Spheroidal Harmonics integrable system Separation of variables of the Laplace equation (or the free Schrodinger equation) in spheroidal coordinates leads to the spheroidal wave equation. This is a confluent Fuchsian equation which is the confluent Heun equation and it is well known how to compute eigenvalues and eigenfunctions in this case. We show that the spectrum of the spheroidal wave equation has quantum monodromy, which means that the joint spectrum of the two commuting operators cannot be globally uniquely labelled by quantum numbers. We suspect that the spheroidal wave equation is the simples (confluent) Fuchsian equation that shows this defect. We analyse the corresponding classical Liouville integrable system and show that it is a semi-toric system with a non-degenerate focus-focus singularity, which causes the defect. Finally we show that this spheroidal harmonics integrable system is symplectically equivalent to the C. Neumman system of a particle moving on sphere under the influence of a harmonic potential. |

Clare Dunning | On the exceptional spectrum of the asymmetric quantum Rabi model The Hamiltonian of the asymmetric quantum Rabi model couples a two-level atom and a single-mode bosonic field with tunnelling allowed between the two atomic states. I shall discuss the exceptional part of the spectrum by mapping the problem to a quasi-exactly solvable generalisation of the Poschl-Teller potential. |

Zachary Fehily | W-algebras related to sl(3) In this talk, I will present some general features of the representation theory of vertex operator algebras (VOAs) and the construction of W-algebras by quantum Hamiltonian reduction. Of particular interest are fractional-level WZW models and how the corresponding VOAs relate to their reductions. With admissible-level sl(3) WZW models in mind, I will describe some of my recent progress in understanding the representations of the admissible-level Bershadsky-Polyakov algebras. This includes a class of non-rational vertex operator algebras where characters and modular transformations are now within reach. |

Alexander Garbali | An integrable model for the quantum toroidal gl_1 The quantum toroidal gl_1 algebra has an exciting representation theory and multiple connections to various problems in mathematical physics. An interesting direction is the study of the integrable model given on the Fock representation of this algebra. In my talk I will focus on the problem of calculation of the R-matrix for this integrable model. |

Tim Garoni | Critical speeding up in dynamical percolation We study the integrated autocorrelation time of the size of the cluster at the origin in critical dynamical percolation. We consider trees, high-dimensional tori, and boxes on the triangular lattice, and in each case show that the autocorrelation time is bounded above by a strictly sublinear function of the graph size. It follows that the cluster size at the origin in these models exhibits critical speeding-up, and noise sensitivity. The main tool used in the proofs is a theorem of Schramm and Steif bounding Fourier coefficients of functions on the discrete hypercube via properties of certain randomised algorithms. The resulting randomised algorithms may also be of direct practical use for Monte Carlo sampling. |

Christina Giarmatzi | Witnessing quantum memory in non-Markovian processes TBA |

Mark Gould | |

Anthony Guttmann | The existence of the critical exponent for two-dimensional self-avoiding walks It remains unproved that the critical exponent exists for two- and three-dimensional self-avoiding walks. It has long been believed that the scaling limit of SAWs exists and is given by SLE_{8/3}, which would both prove the existence of the exponents and confirm the expected numerical values. We will present three alternative routes to a proof of the existence of the critical exponents (derived in conversation with the late J M Hammersley) and give numerical evidence for the validity of these routes. |

Bolin Han | |

Rebecca Haustein | |

Pedram Hekmati | A deformation of fusion rings I will discuss a certain deformation of the fusion rings for rational Wess-Zumino-Witten models, describe the associated fusion ideals and the geometric origin of this deformation. |

Robert Henry | Unusual properties of the free parafermion model The free parafermion model is a non-Hermitian but PT-symmetric 1D quantum model with a simple exact solution. It has some unusal properties not seen in any similar system, including a boundary condition-dependent bulk energy, and diverging values of some correlations. This talk will briefly introduce the model and its solution, as well as the broader notion of PT symmetry. The model’s unusual properties will then be examined, including new results on diverging correlations and an examination of the model’s phase diagram using a fidelity approach. Some comparisons will be made with similar quantum clock models such as the Potts model and superintegrable chiral Potts model. |

Daniel Hutchings | Superprojectors and higher-spin superconformal gravity Superprojectors are superspace projection operators which single out the irreducible representations of supersymmetry. These operators have proven to be an indispensable tool within the framework of supersymmetric field theories. For example, in three dimensions (3D) they can be used to construct the higher-spin super-Cotton tensor, which is intimately related to higher-spin extensions of linearised superconformal gravity. In this talk, I will present a systematic procedure to construct the N-extended transverse spin projection operators in 3D Minkowski superspace. These superprojectors will then be used to construct linearised rank-n super-Cotton tensors and off-shell N-extended superconformal actions. |

Phillip Isaac | |

Iwan Jensen | |

Andrew Kels | Yang-Baxter maps associated to discrete soliton equations and hypergeometric functions The Yang-Baxter maps are solutions to the set-theoretical Yang-Baxter equation. I will present a set of new Yang-Baxter maps for the mapping of 4-dimensional complex space to itself. These Yang-Baxter maps involve 2-component complex parameters, and the top level Yang-Baxter map also involves additional parameters associated to the Weierstrass elliptic curve. These Yang-Baxter maps are constructed using continuous-spin solutions of the star-triangle relation, which are associated to the hypergeometric beta-type integrals, such as the classical Euler Beta function and its recently discovered hyperbolic and elliptic generalisations. The derivation produces a counterpart Yang-Baxter map for each of the discrete integrable soliton equations in the ABS classification. |

Mario Kieburg | Limiting spectral statistics for products with the shifted Gaussian Unitary Ensemble Polynomials of random matrices have gained attention in recent years. One goal of that is to understand stochastic matrix difference equations. A first step in this direction is to consider products involving Hermitian matrices and understand their local spectral statistics. I will report on that for rather general products with the shifted Gaussian Unitary Ensemble. |

Andreas Kluemper | Correlation functions of the integrable SU(n) spin chain We study the correlation functions of $SU(n) n>2$ invariant spin chains in the thermodynamic limit. We formulate a consistent framework for the computation of short-range correlation functions via functional equations which hold even at finite temperature. We give the explicit solution for two- and three-site correlations for the $SU(3)$ case at zero temperature. The correlators do not seem to be of factorizable form. From the two-sites result we see that the correlation functions are given in terms of Hurwitz’ zeta function, which differs from the $SU(2)$ case where the correlations are expressed in terms of Riemann’s zeta function of odd arguments. |

Johanna Knapp | D-brane central charge and Landau-Ginzburg models We propose a universal expression for the (quantum) exact central charge of a D-brane in the context of Calabi-Yau compactifications of string theory. We show that the proposed formula holds for Calabi-Yaus that have a description in terms of Landau-Ginzburg orbifolds. Furthermore we show that the result is consistent with the hemisphere partition function of the associated gauged linear sigma model. |

Sergii Koval | |

Jonathan Kress | Second order superintegrable systems in arbitrary dimensions Second order maximally superintegrable systems are Hamiltonian systems possessing 2n-1 integrals quadratic in the momenta and include well known examples such as the harmonic oscillator and Kelper-Coulomb system. Superintegrable systems have been extensively studied in recent years because of their intimate connection with special functions. Recent work with Konrad Sc”obel and Andreas Vollmer provides a framework for extending to higher dimensions important classification results already achieved in 2 and 3 dimensions. A simple set of algebraic defining an algebraic variety parameterising non-degenerate second order superintegrable systems will be presented. |

Charlotte Kristjansen | Twisted Yangians and spin chain overlaps Using representation theory of twisted Yangians we derive exact expressions for overlaps between spin chain Bethe eigenstates and matrix product states. These overlaps are of relevance for the calculation of one-point functions in the gauge-gravity duality as well as for the study of quantum quenches in statistical mechanics. |

Sergei Kuzenko | Manifestly duality-invariant interactions in diverse dimensions TBA |

Zimin Li | Level statistics of the anisotropic quantum Rabi model The quantum Rabi model is a fundamental model for light-matter interaction. The anisotropic version of the quantum Rabi model has two coupling parameters: the rotating term coupling $g_1$ and the counter-rotating term coupling $g_2$, with the quantum Rabi model recovered when $g_1 = g_2$. In this talk I will report results for the level statistics of the anisotropic quantum Rabi model. Particularly, the distribution of the ratio of consecutive level spacings $r_n$ is calculated with different coupling strengths $g_1$ and $g_2$. In addition, a new quantity $d$ is introduced to describe the deviation from Poisson distribution. The numerical results indicate that there is no chaotic property in the spectrum of the anisotropic quantum Rabi model, specifically, in the narrow coupling regime where $g_1 sim g_2$, the spectrum behaves like the harmonic oscillator while in most other areas the distribution $P(r)$ is Poissonian. Moreover, regarding the spectral statistics, there is no significant difference between the two couplings. |

Jon Links | |

Ian Marquette | Quadratic Racah algebras and superintegrable systems on curve spaces I will discuss how finitely generated polynomial algebras are related with superintegrable systems. Their representations are connected with various aspects of special functions and orthogonal polynomials. I will present recent results on higher dimensional quadratically superintegrable systems and their higher rank quadratic algebras. I will point out how these constructions allow to provide algebraic derivation of their spectrum. I will present some recent ideas on Racah algebra, generalizations and superintegrable models on curved spaces that can also be described via intertwining operators. |

Andrei Marshakov | On supersymmetric gauge theories and isomonodromic deformations TBA |

Ian McCulloch | Tensor network approach to the Bethe Ansatz TBA |

Jock McOrist | |

Aby Nasrawi | The length of self-avoiding walks on the complete graph We are interested in certain properties of the self-avoiding walk process on the complete graph. In particular, we will be looking for how quickly the walk length moments grows with the system size, around a pseudocritical point. In Yadin’s 2014 paper, they find the moments at the critical point. In this paper, we will study the behaviour of the walk length moments on the complete graph in a critical window, where the rate and direction of convergence is controlled by parameters we have introduced. |

Jeremy Nugent | Semidegenerate superintegrable systems in 3d Superintegrable systems are physical systems with the maximum amount of symmetry. The most well studied case is the nondegenerate systems, where a potential function satisfies a particular set of PDE’s. If some of these conditions are relaxed, we find the next ‘highest’ level of symmetry allowed leads to a semi degenerate system, of which there has been no classification. This talk will discuss efforts to classify these in 3 dimensions using recent techniques. |

Judy-anne Osborn | |

Paul Pearce | |

Xavier Poncini | |

Michael Ponds | Conformal higher-spin gauge theories in curved backgrounds The problem of a consistent coupling of conformal higher-spin (CHS) gauge fields to conformal gravity in diverse dimensions has been a subject of investigation in theoretical physics for decades. In four dimensions, gauge-invariant actions for free CHS fields propagating in Minkowski space were proposed over thirty years ago. Since then, many attempts have been made to promote these models to curved backgrounds but the appearance of curvature dependent terms, which break the higher-spin gauge-symmetry, present a huge obstacle. In this talk I will show how techniques from conformal (super)gravity can be used to smoothly navigate these hurdles in any conformally flat background. This prescription also works for so-called generalised conformal gauge fields, whose defining features are higher-derivative gauge transformations. For the generalised spin-3 field, I will demonstrate how to extend the gauge symmetry to the most general type of conformal gravity background – that of a Bach-flat spacetime. The corresponding model exhibits novel features and is the first higher-spin example of its kind. |

Emmanouil Raptakis | Higher symmetries of the supersymmetric Dirac equation The study of symmetries of differential operators results in vibrant mathematical structures. For instance, it was proven by Eastwood that the higher symmetries of the Laplacian are generated by conformal Killing tensors (that is, higher-rank generalisations of conformal Killing vectors) and form a higher-spin algebra. In this talk, I extend this construction by studying the Wess-Zumino operator, which is a supersymmetric extension of the Dirac equation. |

Christopher Raymond | Staggered modules for N=2 superconformal algebras Conformal field theories with logarithmic divergences provide an interesting family of non-unitary quantum field theories. These divergences can be seen from a representation theory perspective as coming from modules referred to as staggered modules. Recent work on the coset construction of the N=2 superconformal algebras has developed a powerful tool for constructing their staggered modules. This talk will introduce the coset construction, discuss how it relates to staggered modules along with some concrete examples, and end with a discussion on how to progress towards a classification. |

David Ridout | Fractional-level WZW models Fractional-level WZW models are CFTs with affine symmetries that were introduced by Kent in order to extend the GKO coset construction to the non-unitary Virasoro minimal models. Despite a somewhat infamous history, they are now quite rightly regarded as fundamental examples of logarithmic CFTs. Recently, they have appeared as examples of 2D invariants (Schur indices, Higgs branches) in the 4D/2D correspondence of Beem et al. There is therefore a lot of interest in these models. Here, we report on a recent result which algorithmically determines all the irreducible weight modules consistent with these CFTs, provided that one already knows the consistent highest-weight modules. We also construct some of the reducible but indecomposable modules. |

Yibing Shen | Ground-state energy of a Richardson-Gaudin integrable BCS model We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open $p+ip$ models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result. |

Gabriele Tartaglino Mazzucchelli | TTbar deformations and supersymmetry In the last few years, there has been considerable interest in quantum field theories in two dimensions deformed by the irrelevant “TTbar” operator (the determinant of the stress-energy tensor). In this talk, I will describe some recent development concerning the TTbar deformation of supersymmetric theories. |

Guo Chuan Thiang | Edge-following states of topological insulators are cobordism invariant Without a boundary, a topological insulator is simply a spectrally-gapped Hamiltonian operator inside a non-trivial abstractly defined homotopy class. Physicists can now realise such operators in many settings. In all cases, a boundary causes the spectral gap to be filled by perturbation-immune edge-following states which propagate around defects and corners without dissipation. I will sketch the first rigorous proof of this universal phenomenon, which can handle geometrically complicated boundaries. The key conceptual ingredient is a certain cobordism invariance of a higher index associated to the edge states. |

Ben Wootten | |

Konstantin Zarembo | Bethe overlaps and defect CFT N=4 superconformal gauge theory is a remarkable example of quantum field theory that has an exact string description and is at the same time integrable. Operators in this theory correspond to Bethe eigenstates of an integrable spin chain. Expectation values that they acquire in the presence of a defect map to overlaps of Bethe eigenstates with matrix product states or Neel-type states, which have been studied previously in the condensed-matter context and can be efficiently computed with the help of the Algebraic Bethe Ansatz. |

Yao-Zhong Zhang | New R-matrices with non-additive/multiplicative spectral parameters and models of strongly correlated electrons We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible representations of the quantum superalgebra upon which the R-matrix acts. Applying to the quantum superalgebra Uq(gl(2|1)), we obtain the explicit expression for the Uq(gl(2|1))-invariant R-matrix which is of non-difference form in spectral parameters. Using this R-matrix we derive a new two-parameter integrable model of strongly correlated electrons with pure imaginary pair hopping terms. |

Zongzheng Zhou | The coupling time of the Ising Glauber dynamics Consider an ergodic Markov chain with $n$ states. Run $n$ chains simultaneously with distinct initial states but using the same randomness. There exists a nonnegative random variable $T_n$ such that starting at $-T_n$ the $n$ chains will all have coalesced by time 0. It was proved by Propp and Wilson that sampling at time 0 is exactly stationary. This procedure is called “coupling from the past”, and $T_n$ is called the coupling time. In this talk, we will discuss a limit theorem for the distribution of the coupling time of a specific Markov chain: Glauber dynamics of the Ising model on d-dimensional tori. The infinite temperature case simply corresponds to the coupon collecting problem, for which Erd{H o}s and R{‘ e}nyi proved the standardised coupling time converges to a Gumbel distribution. In our work, we prove that a similar limit theorem holds down to a finite temperature. |