The pioneering work of Bekenstein and Hawking in the 1970s showed that black holes have thermodynamic properties like temperature and entropy in the quantum theory, just like the air in this room. This leads to the question: can we account for the thermodynamic entropy of a black hole as a statistical entropy of an ensemble of microscopic states? One of the big successes of string theory is to answer this question in the affirmative for a large class of black holes.

The pioneering work of Bekenstein and Hawking in the 1970s showed that black holes have thermodynamic properties like temperature and entropy in the quantum theory, just like the air in this room. This leads to the question: can we account for the thermodynamic entropy of a black hole as a statistical entropy of an ensemble of microscopic states? One of the big successes of string theory is to answer this question in the affirmative for a large class of black holes.

We will describe the duality between two integrable systems: the 2D Sine-Gordon model and the 2D Thirring model. We will spend some time describing the classical and quantum Sine-Gordon model, in particular its spectrum, S-matrices and underlying quantum-group symmetry. We will then present the duality with the Thirring model as originally stated by Coleman and refined in subsequent literature. All the basic elements will be provided without relying on too many pre-requisites beyond standard graduate-level quantum field theory. The notes comprise a series of exercises.

https://lims.ac.uk/event/skyrme-theory-at-60/ Prof. Nick Manton, FRS, will give a colloquium on Skyrmions, followed by book launch and reception, celebrating his latest book on the subject, in the historic Faraday Suites of the London Institute for Mathematical Sciences (LIMS). Schedule 2 - 3 Colloquium 3 - 3:30 Introduction by Prof. Yang-Hui He, Fellow of LIMS 3:30 - 5 Book launch + Reception: Prof. Manton Address: LIMS, Royal Institution, 21 Albemarle St., Mayfair.

We will describe the duality between two integrable systems: the 2D Sine-Gordon model and the 2D Thirring model. We will spend some time describing the classical and quantum Sine-Gordon model, in particular its spectrum, S-matrices and underlying quantum-group symmetry. We will then present the duality with the Thirring model as originally stated by Coleman and refined in subsequent literature. All the basic elements will be provided without relying on too many pre-requisites beyond standard graduate-level quantum field theory. The notes comprise a series of exercises.

We will describe the duality between two integrable systems: the 2D Sine-Gordon model and the 2D Thirring model. We will spend some time describing the classical and quantum Sine-Gordon model, in particular its spectrum, S-matrices and underlying quantum-group symmetry. We will then present the duality with the Thirring model as originally stated by Coleman and refined in subsequent literature. All the basic elements will be provided without relying on too many pre-requisites beyond standard graduate-level quantum field theory. The notes comprise a series of exercises.

Recent works in quantum gravity, motivated by the factorization problem and baby universes, have considered sums over bordisms with fixed boundaries in topological quantum field theory. I will discuss this construction, its scope and its limitations, and describe the total amplitude in this class of theories in terms of a curious splitting formula; Part of the London TQFT Journal Club; it will be possible to follow this talk online (please register at https://london-tqft.co.uk)

We study Chern-Simons theories at large N with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite 't Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation together with the spectrum of boundary operators are sufficient to uniquely determine the expectation values of these operators. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators. ----- Part of the London Integrability Journal Club. If you are a new participant please register at integrability-london.weebly.com. Link emailed on Tuesday.

The quantum Church-Turing thesis would imply that there is a unique model of quantum computing. It follows that quantum computers could simulate quantum field theories efficiently.After a review on the simulation of topological quantum field theories, we will focus on a lattice approach to conformal field theories from anyonic chains.; it will be possible to follow this talk online (please register at https://london-tqft.co.uk)

With a view towards constructing Calabi Yau manifolds, we present some rudiments of the intersection between algebraic, differential and arithmetic geometry. Throughout we will take the opposite of the Bourbaki approach and work through explicit examples, rather than to emphasise on the theory.

TTbar and JTbar - deformed CFTs provide an interesting example of non-local, yet UV-complete two-dimensional QFTs that are entirely solvable. I will start by showing that both classes of theories possess Virasoro x Virasoro or Virasoro- Kac- Moody x Virasoro - Kac- Moody symmetry. For the case of JTbar, I will discuss the classical realization of these symmetries in terms of field-dependent coordinate transformations and show how the associated generators can be used to define an analogue of "primary" operators in this non-local theory, whose correlation functions are entirely fixed in terms of those of the undeformed CFT. In particular, two and three-point functions are simply given by the corresponding momentum-space correlator in the undeformed CFT, with all dimensions replaced by particular momentum-dependent conformal dimensions. Interestingly, scattering amplitudes off the near-horizon of extremal black holes are known to take a strikingly similar form. -------- Part of the London Integrability Journal Club. If you are a new participant please register at integrability-london.weebly.com. Link emailed on Tuesday.

With a view towards constructing Calabi Yau manifolds, we present some rudiments of the intersection between algebraic, differential and arithmetic geometry. Throughout we will take the opposite of the Bourbaki approach and work through explicit examples, rather than to emphasise on the theory.

We numerically study an anyon chain based on the Haagerup fusion category, and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is ~2; it will be possible to follow this talk online (please register at https://london-tqft.co.uk)

ABS: TBC NB: The colloquium will follow naturally on from the LonTI lecture and there will be refreshments. BIO: Professor Peter Cochrane, DSc, OBE, is Professor of Sentient Systems at the University of Suffolk, and visiting Professor to The University of Hertfordshire, Salford, and Nottingham Trent University has received numerous awards including the IEEE Millennium Medal, Martlesham Medal, Prince Philip Medal, Queens Award for Export and Technology and an OBE by The Queen in 1999. He retired from BT as CTO in 2000 to form his own consultancy company. This saw the founding of eBookers, Shazam Entertainment, and a raft of smaller start ups. Peter has also seen assignments with UK, Singapore and Qatar government departments; HP, Motorola, 3M, Dupont, Ford, Sun, Apple, Cisco, Rolls Royce, BMW, Jersey Tel, Chorus, FaceBook, et al.

With a view towards constructing Calabi Yau manifolds, we present some rudiments of the intersection between algebraic, differential and arithmetic geometry. Throughout we will take the opposite of the Bourbaki approach and work through explicit examples, rather than to emphasise on the theory.

The Liouville equation has many applications: it describes surfaces of constant negative curvature and plays an important role in non-critical string theory. In this talk we discuss how to put the Liouville equation on the lattice in a completely integrable way; it will be possible to follow this talk online (please register at https://london-tqft.vercel.app)

With a view towards constructing Calabi Yau manifolds, we present some rudiments of the intersection between algebraic, differential and arithmetic geometry. Throughout we will take the opposite of the Bourbaki approach and work through explicit examples, rather than to emphasise on the theory. Address: 21 Albemarle St, London W1S 4BS Floor 2: London Institute of Mathematical Sciences (LIMS)

Topological twists of 3d N=4 gauge theories naturally give rise to non-semisimple 3d TQFT's. In mathematics, prototypical examples of the latter were constructed in the 90's (by Lyubashenko and others) from representation categories of small quantum groups at roots of unity; they were recently generalized in work of Costantino-Geer-Patureau Mirand and collaborators. I will introduce a family of physical 3d quantum field theories that (conjecturally) reproduce these classic non-semisimple TQFT's. The physical theories combine Chern-Simons-like and 3d N=4-like sectors. They are also related to Feigin-Tipunin vertex algebras, much the same way that Chern-Simons theory is related to WZW vertex algebras. (Based on work with T. Creutzig, N. Garner, and N. Geer.); part of the London TQFT Journal Club; it will be possible to follow this talk online (please register at https://london-tqft.vercel.app)

In these lectures, we will present to seemingly different theories. The first one is a theory of gravity in two dimensions, called Jackiw-Teitelboim (JT) gravity, that is relevant in the context of higher-dimensional, near-extremal black holes. The second one is a quantum mechanical theory of fermions, with no gravity, called the Sachdev, Ye and Kitaev (SYK) model. We will explore precisely how JT gravity emerges from the SYK model by studying their actions, correlation functions and thermodynamic properties. This constitutes the simplest toy model of what theoretical physicists now call the holographic principle. Address: 21 Albemarle St, London W1S 4BS Floor 2: London Institute of Mathematical Sciences (LIMS)

We study the N = 4 SYM stress tensor multiplet 4-point function for any value of the complexified coupling tau, and in principle any gauge group (we focus on SU(2) and SU(3) for simplicity). By combining non-perturbative constraints from the numerical bootstrap with two exact constraints from supersymmetric localization, we are able to compute upper bounds on low-lying CFT data (e.g. the Konishi) for any value of tau. These upper bounds are very close to the 4-loop weak coupling predictions in the appropriate regime. We also give preliminary evidence that these upper bounds become small islands under reasonable assumptions, in which case our method would provide a numerical solution to N = 4 SYM for any gauge group and tau. -------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant.