Participants
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) 

Nezhla Aghaei  Combinatorial Quantisation of Super Chern Simons theory GL(11) ChernSimons theories with gauge supergroups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. In this talk we explain the combinatorial quantisation of ChernSimons theories and also the GL(11) generalisation of it, for punctured Riemann surfaces of arbitrary genus. We construct the algebra of observables, and study their representations and applications to the construction of 3manifold invariants. This work has also an application to Topological Phases of Matter. 
John Baez (virtual)  The Tenfold Way The importance of the tenfold way in physics was only recognized in this century. Simply put, it implies that there are ten fundamentally different kinds of matter. But it goes back to 1964, when the topologist C. T. C. Wall classified the associative real super division algebras and found ten of them. The three “purely even” examples were already familiar: the real numbers, complex numbers and quaternions. The rest become important when we classify representations of groups or supergroups on Z/2graded vector spaces. We explain this classification, its connection to Clifford algebras, and some of its implications. 
Rinat Kashaev  The quantum dilogarithm and its applications. The quantum dilogarithm is a special function of two variables that finds various applications in quantum theory. Although a special case of that function 
JeongHyuck Park  Double Field Theory as Closed String Gravity What is the gravity that string theory predicts? While the conventional answer is General Relativity, this talk will introduce Double Field Theory as an alternative. The theory gravitises the whole closed string massless sector, possesses its own Einstein equation, and describes not only Riemannian geometry but also various nonRiemannian ones where some known (Riemannian) curvature singularities are to be identified as regular nonRiemannian backgrounds.

Milena Radnovic  Poncelet porism, integrable billiards, and extremal functions We present classical and new results inspired by XIX century works of JeanVictor Poncelet. Different streams of his work have been recently connected in the study of resonance of ellipsoidal billiards. 
Remy Adderton  Generalised TemperleyLieb Algebras I will discuss a coupled TemperleyLieb algebra featuring N ‘coupled’ copies of the standard TemperleyLieb algebra. The generalised cubic relations and the diagrammatic interpretation will be introduced as well as the relation to the chiral Potts and staggered XX quantum spin chains. 
Alhanouf Almutairi  
Michael Assis  Statistical mechanics and folliculogenesis – a review of the current state of modelling In this talk we will review the current state of modelling of folliculogenesis from the perspective of statistical mechanics. Women are born with between 0.52 million eggs encased in follicles, which decrease exponentially throughout life, leading to menopause when the number reaches around 1000 [1]. While this decrease is exponential, it is quite striking that the ovulation number is a constant, one egg a month. It is even more striking when one considers that there are two ovaries. Only a total of around 500 eggs are ovulated in a lifetime; the vast majority of eggs atrophy and die in a process called atresia. The initial pool of follicles is in a primordial, dormant state. Once they proceed to a growing state, they grow from primary, to secondary, and then antral follicle states, a process called folliculogenesis. Many eggs die at each stage, leading to fewer at each step. Nevertheless, this large pool of eggs contributes to a group dynamic before they die, marked by the appearance of order: the ovulation of one and only one egg each month. This group dynamic affects growing eggs in both ovaries simultaneously, since serum levels of hormones are shared between them. Midmenstrual cycle, follicle stimulating hormone (FSH) is released by the pituitary, which protects follicles, helping them to keep growing. As they grow, the follicles develop receptors to luteinizing hormone (LH), which helps them express the hormone estradiol. As the follicles continue to grow, the levels of estradiol rise, which has the effect of decreasing the FSH levels, which in turn hinders further growth. In other words, follicle growth is dependent on a feedback system, several in fact. To first order, one could consider the growth of ovarian follicles as a manybody problem with spatially independent interactions. There have been several mathematical models developed based on hormone levels which show the emergence of order from straightforward assumptions (e.g. [2]). Recently multiscale models have been developed that consider the growth of individual cells and their receptivity to hormones or their expression of hormones (see e.g. [3]). One motivation for studying these models is to understand disorders that possibly arise from a dysfunctional feedback system, for example polycystic ovarian syndrome (PCOS). Nevertheless, current models leave out much new research on the roles of various proteins in folliculogenesis, some having their own feedback systems. The roles of these proteins could be elucidated through exploration within more accurate models. It is the goal of this talk to summarize and review the current state of the understanding of folliculogenesis and its modelling from the perspective of statistical mechanics in the hope of involving more of the mathematical community, including students, into this fascinating endeavour. 1. Wallace, W. Hamish B., and Thomas W. Kelsey. “Human ovarian reserve from conception to the menopause.” PloS one 5.1 (2010): e8772. 2. Michael Lacker, H., and Allon Percus. “How do ovarian follicles interact? A manybody problem with unusual symmetry and symmetrybreaking properties.” Journal of statistical physics 63.5 (1991): 11331161. 3. Clément, Frédérique, and Danielle Monniaux. “Mathematical modeling of ovarian follicle development: A population dynamics viewpoint.” Current Opinion in Endocrine and Metabolic Research 18 (2021): 5461. 
Murray Batchelor  The imaginary world of free parafermions TBA 
Rodney Baxter  
Nicholas Beaton  A solvable model of weighted SAWs in a box We consider a solvable model of selfavoiding walks (SAWs) which cross an $L \times L$ box, namely partially directed walks (PDWs). For SAWs, the number is conjectured to be asymptotic to $\Lambda^{L^2+bL+c}\cdot L^g$, for constants $\Lambda, b, c, g$. Moreover, when a Boltzmann weight $t$ is associated with the length of the walks, a phase transition occurs at $t=\mu^{1}$, where $\mu$ is the connective constant for the lattice. For $t<\mu^{1}$ the average walk is of length $O(L)$, while for $t>\mu^{1}$ it is of length $O(L^2)$. Here we solve the PDW version of this model and compute the asymptotic behaviour for all $t$. The phase transition occurs at $t=1$, and we use quite different methodology for $t$ below, above and at the critical point. 
Lachlan Bennett  Integrable Multiwell Bosonic Tunnelling Models For this presentation, I’ll introduce a family of quantum integrable models. These models, characterised by a Hamiltonian, describe boson tunnelling in multiwell systems. After discussing the properties of these models, I will demonstrate how a Bethe Ansatz technique can be applied to find exact solutions. These solutions allow us to analyse the quantum dynamics and measurement outcomes at specified times. If physically realised, this family of Hamiltonians can be beneficial in studying entanglement. 
JeanEmile Bourgine  Algebraic engineering and integrable hierarchies The algebraic engineering consists in constructing observables of supersymmetric gauge theories within the representation theory of a quantum group. It is based on the branes system realization in string theory, this system being mapped to a network of modules on which act intertwining operators. The algebraic construction brings new perspectives on many important properties of gauge theories (e.g. AGTcorrespondence, dualities, integrability,…). In this talk, I will briefly review the recent advances on this topic, and then use the underlying algebra to revisit the relation between topological strings and the KP integrable hierarchy. This talk will be based on the preprint arXiv:2101.09925. 
Peter Bouwknegt  Tduality for toroidal orbifolds through group cohomology In this talk I will show how Tduality for circle bundles over tori with background Hflux can be reformulated in terms group cohomology. This will then be generalised to Tduality for circle bundles over toroidal orbifolds with background flux. The geometric counterpart of this Tduality will be discussed in a talk by my PhD student Jaklyn Crilly. 
Tony Bracken  
Eve Cheng  Topological Data Analysis of the extended SSH models The Hermitian twoband SSH model proposed by Su, Schrieffer and Heeger is the simplest topological insulator model. It describes the single spinless noninteracting fermion Hamiltonian on a onedimensional finite lattice with staggered hopping amplitudes. The topological properties of this system have been thoroughly researched, including bulkboundary correspondence, the existence of edge states (also zeroenergy states), and topological invariants calculated using Berry curvature. There have been numerous Hermitian and nonHermitian extensions of the SSH model. The Hermitian extensions include longrange hoppings, extended unit cells and the inclusion of onsite potentials and spinorbit interaction. The nonHermitian SSH models can be roughly divided into two main classes: the ones with asymmetrical hopping (either longrange or shortrange) and the ones with complex onsite potentials. There are also other higher dimensional SSH models proposed in the area of superconductivity. In this talk, I explore the possibility of using topological data analysis to detect the topological phases in Hermitian and nonHermitian SSH models. I will review the current literature and introduce my inhouse program. I will also sketch out some directions for future analysis with more complicated models using this method. 
Nathan Clisby  
Catherine Colbert  
Jaklyn Crilly  Tduality on Orbifolds In this talk, I will focus on global aspects of Tduality applied to geometric backgrounds and explore how Tduality affects a group action on such background. This will naturally lead to exploring how Tduality applies to orbifolds, and backgrounds in the presence of a discrete torsion factor. 
Jan de Gier  
Chris Djelovic  
Norman Do  The topological vertex and its symmetries The topological vertex is a beautiful theory that was inspired by topological strings and allows one to explicitly compute GromovWitten invariants of toric CalabiYau threefolds. In this talk, we briefly describe some of the rich algebraic, combinatorial, and geometric structures underlying the theory. Finally, we state a recent result obtained with Brett Parker, which presents symmetries for the topological vertex that are captured by a quantum torus Lie algebra. 
Allan Ernest  Gravitational quantum theory and dark matter The accepted paradigm for understanding the nature of dark matter is based on the existence of an intrinsically weakly interacting, “as yet unknown”, particle beyond the standard model. Calculations from gravitational quantum theory, however, show quite conclusively that ordinary protons and electrons can similarly exhibit reduced interaction cross sections in the weak gravity regions of large gravitational wells like galaxy halos, by virtue of their gravitational eigenspectral composition [1,2]. A galaxy halo consisting entirely of baryonic gas would appear largely invisible, its fraction of “dark matter” depending on the proximity to equilibrium, the halo particles’ position and uncertainty in phase space, and the size and depth of the gravitational well they are in. This environmentally induced darkness is in some ways analogous to an electronic wavefunction in mixtures of dark atomic eigenstates. 
Justine Fasquel  
Zachary Fehily  Free field realisations and Walgebras Walgebras are an important class of vertex operator algebras that appear frequently in both mathematics and physics. Understanding their structure and representation theory is therefore a fruitful endeavour. In this talk, I will discuss how free field realisations and screening operators can help. 
Ethan Fursman  
Alexandr Garbali  Shuffle algebras and lattice models I will talk about some recent developments related to connections between integrable lattice models and shuffle algebras associated to quantum algebras. 
Tim Garoni  
Gregory Gold  The GaussBonnet Invariant in 5D, N=1 Gauged Supergravity To probe detailed phenomena predicted by the AdS/CFT correspondence, quantum corrections (i.e., higherderivative corrections) to gauged supergravity must be constructed, the classification of which remains an open problem. For instance, only two curvature squared invariants are currently known in the presence of a cosmological constant (gauged supergravity) in five dimensions which is dual to fourdimensional quantum field theories. In 2014, a third invariant was constructed in superspace, but its component field structure has only now been constructed. Importantly, this third invariant is key to obtain the extension of the GaussBonnet term which is expected to describe the first quantum correction of compactified string theory in five dimensions. In this talk, I review aspects of our new analysis of the 5D N=1 GaussBonnet term and its applications. For example, recent studies of supersymmetric blackhole entropy by quantum corrected 5D gauged supergravity were performed using only two curvaturesquared invariants. The offshell supersymmetric extension of the GaussBonnet term in gauged supergravity allows one to extend these results which has relevance in studying the entropy of asymptotically AdS5 black holes. 
Pinhas Grossman  New examples of modular data Modular tensor categories arise as representation categories of rational conformal field theories, and in recent years have also attracted interest for their role in topological quantum computation. Given a modular tensor category, there is associated a pair of matrices $S$ and $T$ called the modular data. The $S$ and $T$ matrices generate a projective unitary representation of $SL(2,\mathbb{Z})$, and the fusion rules of the category can be recovered from the $S$ matrix via the Verlinde formula. In this talk we will discuss recent discoveries of large classes of modular data defined in terms of pairs of involutive metric groups. This is joint work with Masaki Izumi, generalizing work of Evans and Gannon. 
Tony Guttmann  
Lucas Hackl  Volumelaw entanglement entropy of typical pure quantum states In this talk, I will discuss the statistical properties of the entanglement entropy, which serves as a natural measure of quantum correlations between a subsystem and its complement. Entanglement is a defining feature of quantum theory and understanding its statistical properties has applications in many areas of physics. First, I will introduce the class of physical models and explain its relevance for practical applications. Second, I will explain how the statistical ensemble of quantum states can naturally be described through the methods of random matrix theory. Third and finally, I will discuss a number of new results describing the typical properties (e.g., average, variance) of the entanglement entropy for various ensembles of quantum states (general vs. Gaussian, arbitrary vs. fixed particle number). See PRX Quantum 3, 030201 for further details. 
Bolin Han  Coupled free fermions and qidentities It has been demonstrated in the literature that combining techniques from number theory and mathematical physics can produce useful and interesting, or even unexpected results for both areas. During our study of Gepner’s coupled free fermions from the coset construction and coupled free fermions constructed from scaled root lattices, we observe some qidentities, including some of RogersRamanujan type, from their charaters and universal chiral partition functions, which are then rigorously proved using various techniques of qseries. These identities further motivate us to investigate more general qidentities and help reveal a connection between these two constructions. 
Daniel Hutchings  Superprojectors in fourdimensional N=2 antide Sitter space (Super)spin projection operators have found numerous applications within the landscape of high energy physics. In particular, recent studies of these projectors in antide Sitter (AdS) space have revealed an innate connection to partially massless fields. This observation yields a novel method to derive the characteristics of these exotic fields. In this talk, we will explore this relationship in the context of fourdimensional N=2 AdS superspace. 
Jessica Hutomo  Threepoint functions of conserved higherspin supercurrents in 4D N=1 superconformal field theory In (super)conformal field theory, two and threepoint correlation functions of conserved (super)currents are important physical observables. This talk will review the recent results of arXiv:2106.14498 and 2208.07057. I will first describe a formalism aimed at deriving all constraints imposed by N=1 superconformal symmetry and conservation laws on the threepoint function of higherspin supercurrents. This formalism is then applied to constrain several new mixed threepoint functions involving higherspin supercurrents and the flavour current multiplet. 
Phillip Isaac  
Vladimir Jakovljevic  Confocal Families of Quadrics on Hyperboloids in PseudoEuclidean Spaces We study the geometry of confocal families on hyperboloids in pseudoEuclidean spaces of dimension four in all signatures. The aim is to completely classify and describe them, and to prove Chasles’ theorem in this ambient. The methodology we use includes concepts of pseudoEuclidean and Euclidean geometry, and linear algebra as well. We also give a clue about the natural characteristics confocal families possess to be applied in a billiard theory. This research is done as a part of a Ph.D. project at the University of Sydney. 
Peter Jarvis  Indecomposable representations of type I Lie superalgebras We study the class of indecomposable representations of superalgebras in which a given finite dimensional representation is repeated with arbitrary multiplicity. Such “replicant” or “matryoschka” modules have dimension rD, with r composition factors equivalent to the fixed Ddimensional module. For the case of the classical Lie superalgebras sl(m/n) and osp(2/2n) and r=2, we prove by a cohomology argument that for each Kac module there is a 1parameter family of indecomposable doubles. For general r, we provide an explicit construction of the replicant Kac modules. In conclusion, we give some illustrative examples from physics, including a possible application to family generation structure in the standard model. 
Mitchell Jones  On the gl(21) Gaudin Algebra An examination on the interesting properties of the Gaudin Algebra derived from the gl(21) Lie Superalgebra. 
Andrew Kels  $\mathbb{C}^8\times Q(E^8)$ extension of the elliptic Painlevé equation The elliptic Painlevé is the top level equation that arises from Sakai’s classification. Recently, Noumi has given the construction of hypergeometric taufunctions for the elliptic Painlevé equation by solving the appropriate forms of the Hirota bilinear equations. Such taufunctions are defined on an infinite sequence of hyperplanes parallel to the highest root in $E_8$ and their restriction to each individual hyperplane is invariant under the action of the Weyl group of type $E_7$. In this talk, I will present an extended version of such Hirota bilinear equations, and their solutions, which involve an additional 8 independent discrete parameters taking values from the $E_8$ root lattice. Based on A.P. Kels, M. Yamazaki, Int. Math. Res. Not. 1, 110151 2021 
Mario Kieburg  Winding Number Statistics for Chiral Random Matrices Topological invariance is an extremely important concept in physics. On the one hand, it leads to a classification of systems that will share similar behaviour in some regimes. On the other hand, topological properties are especially robust against perturbations. In a system, where the Hamiltonian is chiral and shows a spectral gap about the origin, one particular quantity is the winding number of the determinant of the offdiagonal block matrix. The spectrum of this offdiagonal block is complex ad shows interesting and universal behaviour. We investigated the local statistic of this winding number with the help of a Gaussian random matrix field on a one dimensional Brillouin zone. I will report on these developments in my presentation. 
Johanna Knapp  
Nowar Koning  Supertwistor realisation of NExtended AdS superspace The most natural and efficient setting for analysing the properties of superconformal field theories is conformally compactified Minkowski superspace. Amongst the most powerful formulations of the latter are those utilising supertwistor techniques. These supertwistor methods have recently been extended to three and four dimensional AdS superspaces. In this talk I will discuss a supertwistor realisation of four dimensional Nextended AdS superspace, as well as the procedure to develop field theory on such a space using a variant of Cartan’s coset construction. 
Jonathan Kress  Algebra conditions for conformally superintegrable systems The Stäckel transform of natural Hamiltonian systems gives rise to a conformally invariant notion of second order superintegrability. Nondegenerate second order superintegrable systems have been classified on threedimensional conformally flat spaces, but extending methods used were not easily extended to higher dimensions. In this talk, simple algebraic conditions describing these systems in arbitrary dimensions will be given. It is hoped that this formulation will lead to a similar classification of nondegenerate second order superintegrable systems in all dimensions. 
Sergei Kuzenko  
Jon Links  Integrabilitybased NOON state protocol The study of integrable quantum systems has recently made inroads into the field of quantum technology. Examples include general results towards a deeper understanding of quantum circuits, and specific investigations such as simulation of the groundstate for the 1d Heisenberg model on a quantum computer. NOON states are “all and nothing” examples of Schroedingercat states. They have been wellstudied over the last 20 years, for both fundamental tests of quantum theory and potential applications in quantum metrology. In this presentation I will describe a simple protocol, designed around Hamiltonian time evolution of an integrable system and local measurement, to produce highfidelity NOON states. 
Xilin Lu  
Vladimir Mangazeev  CTM approach to the LeeYang singularity in the 2D Ising model We study the 2D Ising model in a complex magnetic field in the vicinity of the LeeYang edge singularity. Using Baxter’s CTM method combined with analytic techniques, we obtain the scaling function together with an accurate estimate of the location of the LeeYang singularity. Our results are in excellent agreement with the Ising field theory calculations by Fonseca, Zamolodchikov (2001) and Zamolodchikov, Xu (2022). 
Ian Marquette  Algebraic constructions of superintegrable systems from commutant It was discovered how polynomial algebras appear naturally as symmetry algebra of quantum superintegrable quantum systems. They provide insight into their degenerate spectrum, in particular for models involving Painlevé transcendents for which usual approaches of solving ODEs and PDEs cannot be applied. Those algebraic structures extend the scope of usual symmetries in context of quantum systems, but they also been connected to different areas of mathematics such as orthogonal polynomials. Among them, the wellknown Racah algebra which also admit various generalisations. I will take a different perspective on those algebraic structures which is based on Lie algebras, their related enveloping algebras, partial Casimir and commutant. I will discuss how such approach differs from using differential operator realizations and why this framework offers advantages for their classification. I will point out as well how different methods from the study of Casimir invariant of non semisimple algebras which involves solving systems of PDEs can be applied in this context and greatly facilitate making calculations. The talk will present various explicit examples, and in particular the symmetry algebra of the generic superintegrable systems on the 2sphere which can be understood in a purely algebraic manner using an underlying Lie algebra. The talk is based on following works: R CampoamorStursberg, I Marquette, Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems, Annals of Physics 424 168378 (2021), arXiv 2020.168378 F Correa, MA del Olmo, I Marquette, J Negro, Polynomial algebras from su(3) and a quadratically superintegrable model on the two sphere, J.PhysA. Math. and Theor 54 015205 (2021) arXiv:2007.11163 R CampoamorStursberg, Ian Marquette, Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrodinger algebras, Annals of Physics. 437 168694 (2022) arXiv 2021.168694 D Latini, I Marquette, YZ Zhang, Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras, J.PhysA Math. and Theor. (2022) arXiv:2204.06840 Rutwig CampoamorStursberg, Danilo Latini, Ian Marquette, YaoZhong Zhang, Algebraic (super)integrability from commutants of subalgebras in universal enveloping algebras, arXiv:2211.04664 
Daniel Mathews  The geometry of spinors in Minkowski space Work of Penrose and Rindler in the 1908s developed a formalism for spinors in relativity theory. In their work they gave geometric interpretations of 2component spinors in terms of Minkowski space. We present some extensions of this work, involving 3dimensional hyperbolic geometry. 
William Mead  Exclusion Process Dualities from Integrable Vertex Models We demonstrate a method for obtaining expectation values of duality observables in the asymmetric simple exclusion process. This approach is then mimicked using an integrable vertex model which allows for some generalisations of the duality observables for higherrank exclusion processes. 
Paul Norbury  Volumes of moduli spaces of super hyperbolic surfaces Mirzakhani produced recursion relations between polynomials that give WeilPetersson volumes of moduli spaces of hyperbolic surfaces. Stanford and Witten described an analogous construction for moduli spaces of super hyperbolic surfaces producing Mirzakhanilike recursion relations between polynomials that give super volumes. This was achieved in the socalled NeveuSchwarz case. Both of these stories have an algebrogeometric description, and in particular this led Mirzakhani to a new proof of Witten’s conjecture on intersection numbers over the moduli space of stable curves. In this lecture, via the algebrogeometric description, I will describe what occurs in the Ramond case of the super construction. It produces deformations of the NeveuSchwarz polynomials again satisfying Mirzakhanilike recursion relations. 
Jeremy Nugent  Semidegenerate superintegrable systems Superintegrable systems are physical systems with the maximal amount of symmetry. A large portion of the literature deals with nondegenerate systems, which are the ‘nicest’ superintegrable systems. In this talk we discuss previous and current research efforts into semidegenerate superintegrable systems, which can be considered as the ‘secondnicest’ class of superintegrable systems. 
Jordan Orchard  Scattering in rightangled polygonal billiard channels Polygonal billiard channels are examples of pseudochaotic dynamics, a combination of integrable evolution and sudden jumps due to conical singular points that arise from the corners of the polygon. Such pseudochaotic behaviour, often characterised by an algebraic separation of nearby trajectories, is believed to be linked to the wild dependence that particle transport has on the billiard geometry. We focus on a twoparameter family of rightangled parallel billiard channels having either finite or infinite horizon and consider a scattering problem defined on the periodic boundaries of an elementary cell. Through studying singular points of the billiard flow, we partition the phase space into eighteen subsets for the finite horizon and sixteen for the infinite horizon, where each subset is associated with a unique itinerary. The corresponding eighteen and sixteen branch scattering maps are presented in explicit form with natural extensions enabling the study of transport from the scattering dynamics. 
Aleks Owczarek  SAW in a square and a proof from a Monte Carlo algorithm Selfavoiding walks (SAW) confined in a square admit a different window on the behaviour of SAW than the usual length scaling considered. Previously the endpoints of the walks have been fixed to the corners of the square or perhaps the sides of the square. A proof that the endpoints drive only subdominant behaviour can be made using an expanded set of moves of the endpoint that arises in a Monte Carlo algorithm for Hamiltonian walks. A separate Monte Carlo method and advanced series analysis confirm and expand on this result.

Anthony Parr  Symmetry Algebras of Superintegrable Systems We consider polynomial Lie algebras with two generators obtained from the set of symmetries of an exactly soluble Hamiltonian by the ladder operator approach. We develop the method for explicit computations of the algebra, obtain its Casimir and its spectrum. We show their realisations as differential operators and deformed oscillator algebras. 
Michael Ponds  Conformal higherspin supergravity as an induced action Conformal higherspin (CHS) gravity is a rare example of a local Lagrangian theory involving bosonic fields of all spins interacting with one another. It arises as the logarithmically divergent part of the effective action associated with scalar matter coupled to background CHS fields, or, in other words, as an induced action. In this talk, I will give a brief overview of this theory, and discuss its N=1 supersymmetric generalisation which was proposed recently.

Robert Pryor  Dbranes in Btwisted (2,2) Hybrid models Btwisted (2,2) Hybrid models are a class of superconformal field theories with string theoretic relevance. They can be understood as LandauGinzburg models fibred over nonlinear sigma models with on a compact Kahler manifold. The bulk theory of these hybrid models is relatively well understood. In particular, the spectra and correlators for several examples of topologically Btwisted theories are known. On the other hand, the boundary theory and the associated Dbranes are still relatively unexplored. In this talk, I will introduce these hybrid models, as well as some of their key features. I will then discuss Dbranes in Btwisted (2,2) LandauGinzburg and nonlinear sigma models, as well as some results about Dbranes in Btwisted (2,2) Hybrid models. In particular, I will focus on how these Dbranes arise physically, as well as their categorical interpretation and relevance. 
Cheng Kevin Qu  Extended Criticality of Deep Neural Networks The recent and continuing success of deep learning in many realworld problems has motivated an intense effort to theoretically understand the dynamical principles of deep learning in the training and generalization of complex tasks. Although empirical data has suggested that the weights of deep neural networks acquire heavytailed statistics after training, most theoretical studies have based their analysis on random networks with coupling weights obeying Gaussian statistics. In this work, we investigate the phenomenon of heavytailed coupling weights in deep neural networks (DNNs) across fully connected, convolutional and residual architectures. After verifying the emergence of heavytailed coupling across many common pretrained neural networks, we analyse the propagation of signals through DNNs with random, heavytailed weights using meanfield and random matrix theory. Importantly, we introduce a criterion for criticality using the entire set of Jacobian eigenvalues of random, heavytailed DNNs which extends the classical, edgeofchaos notion in a consistent fashion while accounting for empirical observations on signal propagation. In this manner, we establish an extended heavytailed regime of criticality across those architectures which classically have a fixed critical point under Gaussian coupling. We show that this extended critical regime allows networks already initialised with random, heavytailed coupling to learn realworld tasks faster without finetuning the weight statistics. Surprisingly, our empirical simulations reveal that despite the fullyconnected meanfield analysis, the predictions of our theory are largely shared by residual networks which continue to benefit from heavytailed initialisation from a classically chaotic regime. 
Thomas Quella  Quantum group invariant spin chains, discrete symmetries and symmetryprotected topological phases We study the fate of certain discrete symmetries of spin chains under quantum group deformation of their continuous symmetry and report on the implications on the classification of symmetryprotected topological phases. 
Reinout Quispel  Building superintegrable LotkaVolterra systems using Darboux polynomials In this talk we show how to construct large classes of LotkaVolterra ODEs in Rn with n1 first integrals. The building blocks we use will be linear Darboux Polynomials of the ODE. In the talk these concepts will be defined, and the procedure explained. 
Emmanouil Raptakis  Conformal (p,q) supergeometries in two dimensions Local superconformal symmetry has played a major role in string theory and supergravity in two dimensions (2D). In particular, the N=1 and N=2 spinning strings may be formulated as a 2D linear sigma model coupled to conformal supergravity. In this talk I will report on some recent results in constructing superspace formulations for 2D conformal (p,q) supergravity as the gauge theory of the superconformal group OSp_0(p2;R) x OSp_0(q2;R) and some applications of this formalism. 
Christopher Raymond  Unifying Galilean Walgebras Galilean algebras are infinitedimensional symmetry algebras for conformal field theories in two dimensions. One way of obtaining these algebras is through a parametric contraction of conformal symmetry algebras such as the Virasoro algebra or affine Lie algebras. However, it does not generally apply to algebras such as Walgebras, which are of great interest in the literature. We provide an introduction to the problems that arise and discuss how to give a uniform construction of Galilean Walgebras via quantum hamiltonian reduction. 
David Ridout  
Pieter Roffelsen  Cubic surfaces, Segre surfaces and Painlevé equations A fundamental result due to M. Jimbo (1982), relates Painlevé VI to a family of affine cubic surfaces via the RiemannHilbert correspondence. In recent work with Nalini Joshi, a qanalog of this result was obtained, relating qPainlevé VI to a family of affine Segre surfaces. I will explain this result and some of its consequences. 
Yang Shi  Translations in affine Weyl groups and their applications in discrete integrable systems Recently, we reviewed [1] some properties of the affine Weyl group in the context of their applications to discrete integrable systems such as the discrete Painleve equations [2]. In particular, a dual representation is used to discuss translational elements of the Weyl groups. They are found to give rise to the dynamics of various discrete integrable equations. 
Liam Smith  New deformations of quantum field theories Quantum field theory (QFT) is one of the most successful frameworks to describe a wide array of physical phenomena from particle physics to condensed matter systems. It is also the core description of models of (quantum) gravity. Despite its success, the understanding of strongly coupled, interacting QFTs remains an outstanding mathematical problem. One route to make progress is to study exactlysolvable models and deformations thereof, together with symmetries, to move within the set of QFTs. The TT deformation is an exciting tool which aids in this exploration. Defined as the determinant of the stressenergy tensor for a twodimensional QFT, it has proven to preserve integrability, (super)symmetries, and it has shed new light on various areas of research including: nonlocal QFT, string theory, and holographic (AdS/CFT) dualities. TTbarlike deformations have been proposed also in D>2 dimensions finding surprising relations with interesting effective actions, such as the BornInfeld theory of nonlinear Electrodynamics, that describe universal sectors of string theory at lowenergy. A sqrt{TT} type of deformation have recently also been proven to lead to the ModMAX theory of nonlinear Electrodynamics in D=4 that has attracted substantial attention in the last couple of years. This talk will summarise our results in finding theories in higher dimensions which obey a TT “like” flow equation, as well as pioneering work on understanding the new aforementioned sqrt{TT} deformation, which, in the D=2 case, has been shown to preserve classical integrability for a large class of theories. Supersymmetric extensions will also be presented. 
Yury Stepanyants  Frequency downshifting of decaying NLS solitons in an ocean covered by ice floes We study a frequency downshifting in wavetrains propagating in an ocean covered by ice floes. Using the empirical model which suggests that smallamplitude surface waves in such an environment decay exponentially with the decay rate depending on frequency as ki ~ 3 [1, 2], we derive the frequency downshifting of a wavetrain within the framework of the linear theory. We show that the apparent downshifting appears due to the faster decay of highfrequency components compared to the lowfrequency components with no energy flux along the spectrum. The alternative model is also considered within the framework of the nonlinear Schrödinger (NLS) equation [3] augment by the empirical dissipative terms. This model describes the propagation and decay of weakly nonlinear wavetrains and accounts for an energy flux along the spectrum down to lower frequencies. Assuming that the dissipation is relatively small compared to the nonlinear and dispersive terms in the NLS equation and using the asymptotic approach [4], we derive the frequency downshift for the decaying envelope soliton. The comparison of the downshifting obtained within the framework of linear and nonlinear models shows that in the latter case the frequency downshifting is much greater. In conclusion, estimates for the real oceanic conditions will be provided. References [1] Meylan M.H., Bennetts L.G., Mosig J.E.M., Rogers W.E., Doble M.J., Peter M.A. Dispersion relations, power laws, and energy loss for 845 waves in the marginal ice zone. Journal of Geophysical Research: Oceans, 2018, v. 123, 3322–3335. DOI: 10.1002/2018JC013776 
Martin Sticka  On Special and Universal Geometry A simplistic overview of the moduli space of the heterotic string. In a physically unrealistic subset of heterotic vacuum solutions, we have special geometry, which is essentially the space of Calabi Yau manifolds. In a more general case, we have universal geometry, a fibration, which makes understanding the general case somewhat tractable. 
Benjamin Stone  Correlation functions of conserved currents in 3D/4D conformal field theory It is a well known fact that the general structure of two and threepoint correlation functions of primary operators is fixed up to finitely many parameters by conformal symmetry. In particular, correlation functions of conserved currents, such as the energymomentum tensor, vector current and more generally, higherspin currents, are of fundamental importance as they possess properties associated with spacetime and internal symmetries. Deriving the explicit form of threepoint functions of conserved currents for arbitrary spin remains an open problem. In this talk we will discuss a general formalism for constructing threepoint functions of conserved currents for arbitrary spin in 3D and 4D (S)CFT. 
Gabriele TartaglinoMazzucchelli  
James Tener  
Kai Turner  Embedding Formalism of Threedimensional Antide Sitter Superspaces Antide Sitter (AdS) superspaces originate as maximally symmetric solutions of supergravity theories. In three dimensions, the isometry supergroup of Nextended AdS superspace is labeled by two positive integers (p,q) with N=p+q. When working with AdS supergroups, supertwistor techniques serve as an effective tool, and have recently been used to construct threedimensional (p,q) AdS superspace. In this talk, I will discuss this supertwistor formulation, and also present the supercoset construction of threedimensional (p,q) AdS superspace. It is shown that this formalism is ideal for extracting geometric information which is crucial for developing field theories on these superspaces. 
Willem van Tonder  Integrability of the spin1/2 XY central spin model Central spin models are closely related to RichardsonGaudin models and have many present and potential physical applications. Recently the XX central spin model was shown to be integrable for arbitrary spin and the eigenstates and eigenvalues found using a BetheAnsatz method of solution. We have shown that integrability carries over to XY models albeit restricting to spin1/2. The conserved charges were found and a quadratic relation in these charges have been used to obtain the BetheAnsatz equations. 
Luc Vinet  Entanglement of free fermions on graphs The entanglement of free Fermions on graphs of the Hamming and Johnson schemes will be discussed. A parallel with time and band limiting problems will be made. The role of the Terwilliger algebra in the identification of a Heun type operator commuting with the truncated correlation matrix and the access it gives to the entanglement entropy will be explained. 
Ben Wootton  
Junze Zhang  Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces Superintegrable systems in 2D Darboux spaces were classified and it was found that there exist 12 distinct classes of superintegrable systems with quadratic integrals of motion (and quadratic symmetry algebras generated by the integrals) in the Darboux spaces. In this talk, I will explore obtaining exact solutions via purely algebraic means for the energies of all the 12 existing classes of superintegrable systems in four different 2D Darboux spaces. This is achieved by constructing the deformed oscillator realization and finitedimensional irreducible representation of the underlying quadratic symmetry algebra generated by quadratic integrals respectively for each of the 12 superintegrable systems. 
Yaozhong Zhang  
Zongzheng Zhou  Geometric upper critical dimension of the Ising model The Ising model is one of the most fundamental models in statistical physics and condensed matter. It is wellknown that, from the renormalizationgroup theory, the upper critical dimension of the Ising model is 4, above which the critical behaviour follows meanfield theory. However, under the geometric FortuinKasteleyn randomcluster representation, we argue that the Ising model simultaneously exhibits two upper critical dimensions: 4 and 6. In this talk, we will show strong numerical evidence to support this argument. 