Mathematics seminars

Binary-coupling sparse SYK model: Spectral statistics and chaotic dynamics

2 May 2023

Speaker: Onur Oktay (University of Surrey).

Abstract: The Sachdev-Ye-Kitaev (SYK) model has garnered significant attention in the past few years due to its maximally chaotic behavior at low temperatures and holographic correspondence. The sparse version of the SYK model, which reduces the number of disorder parameters while keeping the essential properties of the original model intact, has been proposed as an improvement. Recently, we further simplified the sparse SYK model by setting nonzero couplings to ±1, rather than sampling from a continuous distribution such as Gaussian.

In this talk, we will focus on the binary-coupling sparse SYK model, which exhibits strong correlations in the energy spectrum and is better suited for quantum simulations of quantum chaotic behavior and holographic metals. We will present our recent findings on the spectral form factor this model, comparing it with other variants of SYK. Additionally, we discuss the out-of-time-order correlators (OTOC) of the binary-coupling model and its comparison with the sparse SYK model.

The R-mAtrIx Net

25 April 2023

Speaker: Suvajit Majumder (City University London).

Abstract: This talk will be based on arxiv: 2304.07247. We provide a novel Neural Network architecture that can:

1. Output the R-matrix for a given quantum integrable spin chain
2. Search for an integrable Hamiltonian and the corresponding R-matrix under assumptions of certain symmetries or other restrictions
3. Explore the space of Hamiltonians around already learned models and reconstruct the family of integrable spin chains to which they belong.

The neural network training is done by minimising loss functions encoding the Yang-Baxter equation, regularity and other model-specific restrictions such as hermiticity. Holomorphy is implemented via the choice of activation functions. We demonstrate the work of our Neural Network on the two-dimensional spin chains of difference form. In particular, we reconstruct the R-matrices for all 14 classes.

We also demonstrate its utility as an Explorer, scanning a certain subspace of Hamiltonians and identifying integrable classes after clusterisation. The last strategy can be used in future to carve out the map of integrable spin chains in higher dimensions and in more general settings where no analytical methods are available.

Strings and Spins in Deformed AdS/CFT

14 March 2023

Speaker: Leander Wyss (University of Surrey).

Abstract: We will first delve into the massless integrable scattering problem within AdS3/CFT2 set within a 1+1-dimensional short representation. We study Hopf algebraic structures within the context of a modified Poincaré algebra and construct suitable R-matrices both for the undeformed and q-deformed case. We find peculiar connections between the boost operator J and the R-matrices, and study the non-coassociative structure that arises in one particular instance in more detail. We then extend the analysis of the boost operator and its coproduct to the representation-independent case and classify admissible boost (Hopf) algebraic structures. We conclude by analysing in more depth the cases relevant to AdS3 string theory.

Moving on from Hopf algebraic considerations, we consider a particular 3-parameter deformed AdS3 background in the Landau-Lifshitz limit. Constructing an effective field theory from the associated Polyakov action, we obtain an effective Lagrangian up to next-to-leading order in the energy parameter κ. Parametrising the dynamical coordinates by means of a single complex field that we later quantise, we proceed with standard QFT tools, analyse propagator and ground state properties and compute the 2-body S-matrix elements at leading and subleading order in the string tension λ.

In the last part of the talk, we dedicate ourselves to a study in linear algebra and spin chain Hamiltonians. First, we construct an algorithmic framework to find the generalised eigensystem of a defective matrix by perturbing it in such a way that it becomes diagonalisable before analysing its eigensystem, only to then later turn off the perturbation again in a particular way. In doing so, we find that the case of non-singular geometric multiplicity requires particular caution. Having established a rigorous methodology, we apply our machinery to the eclectic spin chain while making use of the Nested Coordinate Bethe Ansatz.

Mathematical model of sexual response

7 March 2023

Speaker: Dr Konstantin Blyuss, University of Sussex, UK.

Abstract: In this talk I will discuss a mathematical model of Masters-Johnson human sexual response cycle. As a starting point, I will review cusp catastrophe and will show why earlier studies that interpreted sexual response cycle using this catastrophe were incorrect. I will then present a derivation of a phenomenological psycho-physiological model of human sexual response cycle. Bifurcation analysis is performed to identify stability properties of the model’s steady state, and numerical simulations are performed to illustrated different types of dynamics associated with the cycle. We will then look at the stochastic version of the model, where I will discuss properties of the spectrum and variance of stochastic oscillations around deterministically stable steady state, as well as the computation of confidence regions. To make a better understanding of stochastic dynamics, I will show how large deviation theory can be used to compute optimal escape paths from the neighbourhood of the steady state, and will discuss clinical implications of results.

Monge-Ampere Geometry and Geophysical Fluid Dynamics

27 February 2023

Speaker: Roberto D'Onofrio (University of Surrey).

Non-abelian T-duality in superspace

21 February 2023

Speaker: Daniele Bielli (University of Surrey).

Abstract: Super non-abelian T-duality of principal chiral and coset models on general Lie supergroups is analysed. We start from principal chiral models, studying the OSp(1|2) case as a prime example and arguing that while the initial model is a proper three-dimensional supergravity background, its T-dual falls outside of this class. We then proceed by studying two families of coset models, namely symmetric and semi-symmetric spaces.

In all these three classes of integrable models, dualisation along non-commuting bosonic and fermionic directions leads to the exchange of Maurer-Cartan equations with the equations of motion, so that integrability is preserved and the construction of T-dual Lax connections allowed. Potential impediments arise in the dualisation procedure of coset models when integrating out the gauge fields in favour of the dual variables. This process cannot be performed in general and we isolate the obstruction, briefly discussing two examples in which a solution can be found.

2d integrable field theories from 4d Chern-Simons theory

14 February 2023

Speaker: Benoit Vicedo (University of York).

Abstract: In recent years various unifying frameworks for constructing and understanding 2d integrable field theories have emerged. I will review the framework of Costello and Yamazaki which is based on 4d Chern-Simons gauge theory. In particular, I will explain how it can be used to construct a very broad class of 2d integrable field theories known as integrable E-models.

If time permits, I will explain the connection to an alternative framework based on Gaudin models associated with affine Kac-Moody algebras. The talk is based on joint works arXiv:1908.07511, arXiv:1909.13824, arXiv:2008.01829, arXiv:2011.13809 and arXiv:2301.09583.

A talk of two halves: “Practical catastrophe theory”, and “Hidden dynamics of maps and sleep cycles”

7 February 2023

Speaker: Dr Mike Jeffrey, University of Bristol.

Abstract: During covid I did the unusual thing of discovering something that might actually be useful. Actually two things, so I’d like to present them both briefly. One concerns how to handle discontinuities in maps, and one concerns how we locate bifurcations in (also unusually for me) smooth dynamical systems. I’ll give examples taken from reaction-diffusion PDEs in part 1 (Practical catastrophe theory for the modern age), and from sleep-wake cycle maps in part 2 (Hidden dynamics of maps and sleep cycles, and when “period 1+2 implies chaos”).

Monge-Ampere Geometry and the Navier-Stokes Equation

6 February 2023

Speaker: Lewis Napper (University of Surrey).

Abstract: For partial differential equations of Monge-Ampère type, it has been shown that solutions correspond to Lagrangian submanifolds of the associated phase space. Building from the observation that the Poisson equation for the pressure of an incompressible, two-dimensional, Navier-Stokes flow is a Monge-Ampère equation, this talk introduces a framework for studying fluid dynamics using properties of the aforementioned submanifolds. In particular, it is noted that such a submanifold may be equipped with a metric whose signature acts as a diagnostic for the dominance of vorticity and strain. We provide an illustrative example in two dimensions and probe the motivational question: ‘What is a vortex?’ We conclude with comments on extensions to fluid flows in higher dimensions and some open questions.

Modelling dryland vegetation patterns: the impact of non-local seed dispersal and mechanisms of species coexistence

27 January 2023

Speaker: Dr Lukas Eigentler, University of Bielefeld, Germany.

Geometric singular perturbation analysis of the multiple-timescale Hodgkin-Huxley equations

17 January 2023

Speaker: Dr Panos Kaklamoanos,  Maxwell Institute for Mathematical Sciences, University of Edinburgh.

Accommodating data structure in clinical trials and other applied studies

6 December 2022

Speaker: Professor Simon Skene, Professor of Medical Statistics and Director of Surrey Clinical Trials Unit.

Twisted covariant form hierarchies and hidden symmetries

6 December 2022

Speaker: Edgar Perez Bolanos (King's College London).

Abstract: Recently, it was shown that the conditions imposed on the Killing spinors bilinears by the gravitino Killing spinor equation in any supergravity theory can be arranged in a geometric structure callled Twisted Covariant Form Hierarchy (TCFH), which in turn implies that they satisfy a Generalised Conformal Killing-Yano equation.

It has been known for a while that Killing-Yano tensors generate symmetries in spinning particle actions and they are related to hidden symmetries. This raises the question on whether supersymmetry is closely related to integrability. In this talk we explore the hidden symmetries and TCFH’s of 4D, 5D and 11D supergravities, giving some partial answers to this question.

Uniqueness of supersymmetric AdS₅ black holes

29 November 2022

Speaker: Sergei Ovchinnikov (University of Edinburgh).

Abstract: The classification of anti de Sitter black holes is an open problem of central importance in holography. In this talk, I will present new advances in classification of supersymmetric solutions to five-dimensional minimal gauged supergravity. In particular, we prove a black hole uniqueness theorem within a ‘Calabi-type’ subclass of solutions with biaxial symmetry. This subclass includes all currently known black hole solutions within this theory.

Synthesis of Dip-Ramp-Plateau, black holes and a semi-classical analysis

22 November 2022

Speaker: Arnab Kundu (Saha Institute of Nuclear Physics).

Abstract: We consider a probe scalar field in a black hole geometry with a stretched horizon. This horizon provides a cut-off and allows us to compute the normal modes of the probe scalar field.

We will demonstrate how the corresponding scalar spectrum, despite exhibiting no evidence of conventional level-repulsion in the spectrum, shows a clear indication of a robust Dip-Ramp-Plateau structure in the corresponding Spectral Form Factor. This behaviour is expected from a full quantum description of a black hole, which we currently lack. We will further discuss several related intriguing features in this set up and comment on possible future directions.

Modelling in early discovery for large molecules

15 November 2022

Speaker: Dr Adam Nasim, GSK.

Integrable deformations of Z2 and Z4 permutation cosets

15 November 2022

Speaker: Ben Hoare (Durham University).

Abstract: Strings on certain AdS3 space-times are described by integrable 2d sigma models on Z2 and Z4 permutation cosets with G x G symmetry group. The product structure of the symmetry group leads to a richer space of integrable deformations.

In this talk I will outline recent progress in mapping out this space, before discussing a special class of deformations of AdS3 x S3 x T4 that preserve half the supersymmetry. Interestingly, these deformations can either be found via Yang-Baxter deformations, proving their integrability, or by U-duality transformations.

Spectral Duality in 2d CFT: Yangian W Algebras and Dual-AGT Correspondence

8 November 2022

Speaker: Fabrizio Nieri (Trinity College Dublin).

Abstract: Inspired by Seiberg-Witten integrable systems featuring in 4d N=2 quiver gauge theories and the AGT correspondence linking the latter to 2d CFT with higher spin symmetry, a Yangian or ε-deformation of W algebras is proposed. These are argued to be (bi-)spectral dual to ordinary conformal W algebras, in particular, the ε-deformed conformal blocks manifestly reproduce instanton partition functions (in the combinatorial form) or give dual Mellin-Barnes-like integral representations of 2d CFT correlators.

The role of the new algebras in Calogero-Moser-Sutherland and Ruijsenaars-Schneider many-body integrable systems is also explored. This Dual-AGT perspective points towards an alternative approach to 2d CFT when other methods fail, akin to massless factorized scattering and form factor theory.

Heterotic de-Sitter solutions

1 November 2022

Speaker: Daniele Farotti (University of Surrey).

Abstract: We classify all warped product de-Sitter backgrounds in heterotic supergravity, up to two loops. We find that warped dS_n​ backgrounds, with n≥3, are R^1,n×M_9−n​, where M_9−n​ is a (9−n)-dimensional Riemannian manifold. Moreover, we establish that warped dS₂​ backgrounds are AdS₃​×M_7​, where M₇​ is a 7-dimensional Riemannian manifold.

Open quantum dynamics for plant motions

25 October 2022

Speaker: Professor Dorje Brody, School of Mathematics and Physics, Surrey.

Bosonic strings on AdS3×S3 with Neveu-Schwarz-Neveu-Schwarz flux

21 June 2022

Speaker: Roberto Ruíz (Complutense University of Madrid).

Abstract: The  AdS3/CFT2 correspondence is the holographic duality between gravity on AdS₃ and the low-energy limit of the two-dimensional quantum field theory on the boundary of  AdS₃. In this talk, we shall present the analysis of the system by bosonic strings on AdS₃×S³ with  Neveu-Schwarz-Neveu-Schwarz flux at the semi-classical level. Our results should help to specify type IIB superstring theory on AdS₃×S³×T⁴ with general mixed Ramon-Ramond and Neveu-Schwarz-Neveu-Schwarz fluxes and its connection with the AdS3/CFT2 correspondence.

Matrix Entanglement

7 June 2022

Speaker: Vaibhav Gautam (University of Surrey).

Abstract: In gauge/gravity duality, matrix degrees of freedom on the gauge theory side play important roles for the emergent geometry. In this paper, we discuss how the entanglement on the gravity side can be described as the entanglement between matrix degrees of freedom. We consider several classes of quantum states to which our approach can play important roles.

When applied to fuzzy sphere, matrix entanglement can be used to define the usual spatial entanglement in two-brane or five-brane world-volume theory nonperturbatively in a regularized setup. Another application is to a small black hole in AdS5×S5 that can evaporate without being attached to a heat bath, for which our approach suggests a gauge theory origin of the Page curve. The confined degrees of freedom in the partially-deconfined states play the important roles.

Jordan blocks and the Bethe ansatz: the eclectic spin chain as a limit

24 May 2022

Speaker: Juan Miguel Nieto Garcia (University of Surrey).

Abstract: In this talk, I will present a procedure to extract the generalised eigenvectors of a non-diagonalisable matrix by considering a diagonalisable perturbation of it and computing the non-diagonalisable limit of its eigenvectors. As an example, I will show how to compute a subset of the spectrum of the eclectic spin chain by computing the appropriate limit of the Bethe states of a twisted su(3) spin chain.

De Sitter horizons and holography

10 May 2022

Speaker: Damián Galante (King's College London).

Abstract: Asymptotically AdS spacetimes have shown to be a powerful tool to probe black hole event horizons in the context of holography. Observers in de Sitter are surrounded by cosmological event horizons. In order to use the tools from holography to describe the cosmological horizon, we need to embed (a patch of) de Sitter into an asymptotically AdS spacetime.

I will show how to build these geometries in the context of two-dimensional dilaton-gravity theories. Then I will focus on one particular observable: the length of spacelike geodesics anchored at the boundaries of double-sided geometries. I will show important differences between the black hole and the cosmological horizon case and comment on possible interpretations of this result in terms of the microscopic dual theories.

Supersymmetric de Sitter solutions in D=11 supergravity

26 April 2022

Speaker: Daniele Farotti (University of Surrey).

Abstract: We determine the necessary and sufficient conditions for warped product dSⁿ solutions, n ≥ 5 to preserve supersymmetry in D = 11 supergravity. We prove that for n ≥ 7, all such solutions are flat, with vanishing 4-form. We also show that the only warped product dS⁶ solutions are either the maximally supersymmetric AdS₇ × S⁴ solution, or R_^1,6 × N₄ where N₄ is hyperKähler, with vanishing 4-form. We also fully classify all supersymmetric warped product dS⁵ solutions. The 6-dimensional internal space is shown to be a warped product S¹ ×_w S¹ ×_w M₄, where M₄ is conformal to a hyperKähler manifold. Furthermore, we prove that if the 4-form is parallel, then M₄ admits a hyperKähler potential.

Towards the quantum entropy of BPS AdS5 black holes

29 March 2022

Speaker: Davide Cassani (University of Padua).

Abstract: The talk will illustrate some recent progress in enumerating the microstates of 1/16 BPS black holes in AdS₅. Through holography, a generating function for this counting problem is the supersymmetric index of the dual SCFT. Imposing non-trivial boundary conditions for the SCFT fields around a circle in the geometry and taking the circumference to be small allows to set up a supersymmetric 3d effective field theory which captures the black hole microstates.

I will describe how, up to exponentially small corrections, the index is then completely characterized by a universal, finite series made of 3d local terms, the supersymmetric Casimir energy and a simple logarithmic term. Taking the large-N limit of this series reproduces the Bekenstein-Hawking black hole entropy. The subleading terms in the large-N expansion are expected to match higher-derivative and quantum corrections to the entropy. The last part of the talk will discuss current efforts towards computing such corrections directly on the gravity side.

Large N matrix models using Monte Carlo and Bootstrap

22 February 2022

Speaker: Raghav Govind Jha (Perimeter Institute).

Abstract: We will present results from our ongoing investigations of the multi-matrix (BMN) model, which is a massive deformation of the BFSS model (describing D0 branes) in the large N limit using Monte Carlo (MC) methods.

We then discuss a simple (unsolved) Hermitian two-matrix model and compare the results obtained using MC and the recently developed bootstrap method. We will comment on how combining these methods can help us in other interesting problems in the future.

Separation of variables and correlation functions in high-rank integrable systems

8 February 2022

Speaker: Paul Ryan (King's College, London).

Abstract: The spectral problem for N=4 Super Yang-Mills can be formulated as a set of quantisation conditions on a handful of functions called Q-functions. Recent analysis suggests that the Q-functions can be used as simple building blocks for 3-point correlation functions which closely resembles the situation in quantum integrable spin chains.

In this talk I will describe the recently developed Functional Separation of Variables (FSoV) technique which is based on the famous Baxter TQ equation. This is a new tool for computing correlation functions in integrable models, and is applicable to both spin chains and 4D QFTs at finite coupling alike and naturally expresses observables as simple expressions in Q-functions. I will discuss new results obtained using this approach, in particular the computation of a complete family of correlation functions in high-rank non-compact SL(N) spin chains. Based on 2011.08229 and soon-to-appear work with N. Gromov and N. Primi. 

Super non-abelian T-duality of principal chiral and coset models

11 January 2022

Speaker: Daniele Bielli (University of Surrey).

Abstract: Super non-abelian T-duality of principal chiral and coset models on general Lie supergroups is analysed. We start from general principal chiral models, studying the OSp(1|2) case as a prime example and arguing that while the initial model is a proper three-dimensional supergravity background, its T-dual falls outside of this class.

We then proceed by studying two families of coset models, namely symmetric and semi-symmetric spaces, highlighting where potential issues with T-duality may arise. In all these three classes of integrable models, dualisation along non-commuting bosonic and fermionic directions leads to the exchange of Maurer-Cartan equations with the equations of motion, so that integrability is preserved and the construction of T-dual Lax connections allowed.

Weyl anomalies for conformal defects

7 December 2021

Speaker: Brandon Robinson (KU Leuven).

Abstract: In this talk, I will cover recent progress made toward characterizing and classifying extended objects (defects) in conformal field theories through anomalies. In particular, I will discuss the Weyl anomaly for two- and four-dimensional conformal defects, and I will show how defect Weyl anomaly coefficients can be computed using correlation functions and holographically. I will demonstrate the utility of these methods in computing some of the 29 defect Weyl anomaly coefficients for monodromy defects in six-dimensional free field theories and for AdS₅ probe branes in AdS_d+1.

Supersymmetry Enhancement of Heterotic Horizons

16 November 2021

Speaker: Daniele Farotti (University of Surrey).

Abstract: The supersymmetry of near-horizon geometries in heterotic supergravity is considered. A necessary and sufficient condition for a solution to preserve more than the minimal N = 2 supersymmetry is obtained. A supersymmetric near-horizon solution is constructed which is a U(1) fibration of AdS3 over a particular Aloff-Wallach space. It is proven that this solution preserves the conditions required for N = 2 supersymmetry, but does not satisfy the necessary condition required for further supersymmetry enhancement. Hence, there exist supersymmetric near-horizon heterotic solutions preserving exactly N = 2 supersymmetry.

Global symmetries and partial confinement

2 November 2021

Speaker: Jack Holden (University of Southampton).

Abstract: In many gauge theories, spontaneous breaking of the centre symmetry provides a precise definition of deconfinement. In large-N gauge theories, evidence has emerged recently that between confined and deconfined phases a partially-confined phase can appear, in which only a subset of colours deconfine. In the partially-confined phase, the centre symmetry is spontaneously broken, raising the question of whether an order parameter exists that can distinguish fully- and partially-confined phases.

We consider two gauge theories in which a global symmetry is spontaneously broken in the confined phase and preserved in the deconfined phase, and we show that this symmetry is spontaneously broken also in the partially-confined phase. As a result, in these theories the transition from full to partial confinement is accompanied by the spontaneous breaking of a global symmetry. The two examples are CP symmetry in N = 1 super-Yang-Mills with a massive gaugino and theta-angle θ = π, and chiral symmetry in a strongly-coupled lattice gauge theory. We conjecture that such global symmetries may provide order parameters to distinguish fully- and partially-confined phases more generally, including at finite N.

Bootstrability for 1d defect CFT

12 October 2021

Speaker: Julius Julius (King's College, London).

Abstract: In this talk I will describe the “bootstrability” program, which combines integrability techniques in 4d N = 4 SYM and the conformal bootstrap to study beyond-the-spectrum observables in a CFT.

I will start with a review of the quantum spectral curve (QSC), a powerful integrability based method to compute the non-perturbative planar spectrum of N = 4 SYM. Then I will show how it is modified to capture the spectrum of operator insertions on a 1/2-BPS Maldacena-Wilson line in the theory, thus solving the spectral problem of the associated defect CFT.

Finally, I will show how the boostrability approach allows us to access previously unreachable quantities such as correlation functions at finite coupling — we used this method to compute with good precision a non-supersymmetric structure constant for a wide range of the 't Hooft coupling in the defect CFT.

Quantization of Monodromy data for confluent Painlevé systems, Calabi-Yau 3-algebras and degenerated non-commutative del Pezzo surfaces

5 October 2021

Speaker: Vladimir Rubtsov (University of Angers).

Abstract: I shall review relations between the subjects of my title based on my recent work with L. Chekhov and M. Mazzocco (Adv. Math. vol. 376, 2021). I shall describe quantum algebra of functions on affine cubic surfaces naturally appeared as SL₂ «tame» and «wild» character varieties naturally associated with Painlevé confluence. Various quantization schemes and their comparisons will be discussed.

Integrability in lower-dimensional AdS/CFT

17 - 20 August 2021

Explore the conference.

Higher gauge theory, BV formalism and self-dual theories from twistor space

27 July 2021

Speaker: Lorenzo Raspollini (University of Surrey).

Abstract: I will discuss how higher algebraic structures arise in ordinary field theory via the Batalin-Vilkovisky formalism. I will briefly review L_∞-algebras and their homotopy Maurer-Cartan theory introducing higher gauge theory. Finally, I will show how these ideas can be combined to those of twistor theory to discuss self-dual field theory in six dimensions.

Homotopy algebras, gauge theories and gravity

20 July 2021

Speaker: Tommaso Macrelli (University of Surrey).

Abstract: After a review of homotopy algebras, we discuss how these structures emerge in quantum field theory. We focus then on the application of these sophisticated mathematical tools to scattering amplitudes (both tree- and loop-level) and to the understanding of the dualities between gauge theories and gravity, highlighting generalizations of old results and presenting new ones.

Towards the Virasoro—Shapiro Amplitude in AdS₅ × S⁵

11 May 2021

Speaker: Paul Heslop (Durham University).

Abstract: We propose a systematic procedure for obtaining all single trace 1/2-BPS correlators in N=4 super Yang-Mills corresponding to the four-point tree-level amplitude for type IIB string theory in AdS₅xS⁵. The underlying idea is to compute generalised contact Witten diagrams coming from a 10d effective field theory on AdS₅xS⁵ whose coefficients are fixed by the flat space Virasoro-Shapiro amplitude up to ambiguities related to commutators of the 10d covariant derivatives which require additional information such as localisation. We illustrate this procedure by computing stringy corrections to the supergravity prediction for all single trace 1/2-BPS correlators up to O(α′⁷), and spell out a general algorithm for extending this to any order in α′.

Hints of gravitational ergodicity

20 April 2021

Speaker: Chethan Krishnan (Indian Institute of Science).

Abstract: Recent developments on black holes have shown that a unitarity-compatible Page curve can be obtained from an ensemble-averaged semi-classical approximation. In this talk, we emphasize (1) that this peculiar manifestation of unitarity is not specific to black holes, and (2) that it can emerge from a single realization of an underlying unitary theory. To make things explicit, we consider a hard sphere gas leaking slowly from a small box into a bigger box.

We reproduce the unitarity-compatible Page curve of this system, semi-classically. Berry's ensemble in which the eigenstates live, plays a crucial role. The computation has structural parallels to replica wormholes, relies crucially on ensemble averaging at each epoch, and reveals the interplay between the multiple time-scales in the problem.

Working with the ensemble averaged state rather than the entanglement entropy, we can also engineer an information "paradox". Our system provides a concrete example in which the ensemble underlying the semi-classical Page curve is an ergodic proxy for a time average, and not an explicit average over many theories. The questions we address here are logically independent of the existence of horizons, so we expect that semi-classical gravity should also be viewed in a similar light.

Neural quantum state in matrix quantum mechanics

16 March 2021

Speaker: Xizhi Han (Stanford University).

Abstract: Matrix quantum mechanics are a class of models with emergent spatial dimensions. As quantum mechanical theories, they provide a clean framework for understanding microscopic aspects of holography. However, as interacting many-body systems, exact solutions are often unavailable.

Starting with reviewing previously solved cases, we use variational quantum Monte Carlo with neural network ansatz for solving low-energy states in both bosonic and supersymmetric theories. The emergent locality is captured by an entanglement measure that we propose, and we comment on potential broader applications to holography.

Supersymmetry and quantum computation

26 January 2021

Speaker: Marcos Crichigno (Imperial College, London).

Abstract: I will discuss various aspects of the interplay between supersymmetry and the theory of classical and quantum computation. An introduction to basic aspects of the theory of computation will be provided.

Amplitudes, tropical geometry, and cluster algebras

17 November 2020

Speaker: James Drummond (University of Southampton).

Abstract: Recently there are hints that there should be an underlying geometrical framework for describing scattering amplitudes in N=4 super Yang-Mills theory. Cluster algebras encode many interesting physical statements about the nature of singularities of these amplitudes and their relation to each other. We find the notion of tropical geometry allows one to obtain finite sets of singularities even when the cluster algebras become infinite and moreover leads to a natural definition of algebraic singularities of exactly the type seen in recent explicit calculations.

Classical integrability in Lie algebra expanded coset sigma models

13 October 2020

Speaker: Andrea Fontanella (Humboldt University of Berlin).

Abstract: In this talk I will present my recent work in collaboration with L. Romano. I will recall the technique of Lie algebra expansion and I will show how to apply it to the global symmetry of a string coset sigma model in order to systematically generate new sigma models. The main result will be a set of criteria for the existence of a Lax pair for these new models, which proves classical integrability. In the last part of the talk I will discuss how this result connects to non-relativistic string theory.

Symmetries of gerbes and applications in geometry and physics

22 September 2020

Speaker: Severin Bunk (University of Hamburg).

Abstract: Gerbes are geometric objects describing the third integer cohomology of a manifold and the B-field in string theory. They are related to line bundles in many ways, but their structure is significantly richer. Infinitesimal symmetries of gerbes on a manifold M are associated with algebroid structures on M.

In this talk, we investigate finite symmetries of gerbes; we demonstrate how, in the presence of a Lie group action on M, gerbes on M lead to higher extensions of the acting Lie group. These extensions have several applications in geometry and physics: they explain non-associative magnetic translations, describe anomalies in QFTs in odd dimensions, and give rise to new models for the string group.

BV formalism, QFT, and gravity: a homotopy perspective

1 September 2020

Speaker: Tommaso Macrelli (University of Surrey).

Abstract: After a review of Batalin-Vilkovisky formalism and homotopy algebras, we discuss how these structures emerge in quantum field theory and gravity. We focus then on the application of these sophisticated mathematical tools to tree- and loop-level scattering amplitudes and to double-copy, highlighting both generalizations of old results and new ones.

Quantum Computations of Partial Differential Equations

30 January 2026

Speaker: Shi Jin, Shanghai Jiao Tong University

Abstract: Quantum computers are designed based on quantum mechanics principle, they are most suitable to solve the Schrodinger equation, and linear PDEs (and ODEs) evolved by unitary operators. It is important to to explore whether other problems in scientific computing, such as ODEs, PDEs, and linear algebra that arise in both classical and quantum systems which are not unitary evolution, can be handled by quantum computers. We will present a systematic way to develop quantum simulation algorithms for general differential equations. Our basic framework is dimension lifting, that transfers non-autonomous ODEs/PDEs systems to autonomous ones, nonlinear PDEs to linear ones, and linear ones to Schrodinger type PDEs—coined “Schrodingerization”— with unitary evolutions. Our formulation allows both qubit and qumode (continuous-variable) formulations, and their hybridizations, and provides the foundation for analog quantum computing which are easier to realize in the near term. We will also present dimension lifting techniques for quantum simulation of stochastic DEs and PDEs with fractional derivatives, and quantum machine learning. A quantum simulation software—“UnitaryLab”—will also be introduced.

Bio: Prof Jin received a Feng Kang Prize of Scientific Computing in 2001., a Morningside Silver Medal in 2007. He is an inaugural Fellow of the American Mathematical Society (AMS) (2012), a Fellow of Society of Industrial and Applied Mathematics (SIAM) (2013), an inaugural Fellow of the Chinese Society of Industrial and Applied Mathematics (CSIAM) (2020), and an Invited Speaker at the International Congress of Mathematicians in 2018. In 2021 he was elected a Foreign Member of Academia Europaea and a Fellow of European Academy of Sciences. In 2024 he was awarded a Shanghai Natural Science Prize (first class).

Using data to accurately and efficiently model turbulent flows: Data assimilation and parameter recovery

30 March 2022

Speaker: Elizabeth Carlson.

Abstract: One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete. Data assimilation circumvents this issue by continually incorporating the observed data into the model. An emerging approach to data assimilation known as the Azouani-Olson-Titi (AOT) algorithm introduced a feedback control term to the 2D incompressible Navier-Stokes equations (NSE) in order to incorporate sparse measurements. The solution to the AOT algorithm applied to the 2D NSE was proven to converge exponentially to the true solution of the 2D NSE with respect to the given initial data.

In this talk, we present our tests on the robustness, improvements, and implementation of the AOT algorithm, as well as generate new ideas based off these investigations. First, we discuss the application of the AOT algorithm to the 2D NSE with an incorrect parameter and prove it still converges to the correct solution up to an error determined by the error in the parameters. This led to the development of a simple parameter recovery algorithm, whose convergence we recently proved in the setting of the Lorenz equations. It has now been proven by a co-author for the full 2D NSE, presenting new insights into the equation itself. We may also discuss applications to climate models.