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.

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)

Liouville conformal field theory (LCFT) was introduced by Polyakov in 1981 as an essential ingredient in his path integral construction of string theory. Since then Liouville theory has appeared in a wide variety of contexts ranging from random conformal geometry to 4d Yang-Mills theory with supersymmetry. Recently, a probabilistic construction of LCFT on general Riemann surfaces was provided using the 2d Gaussian Free Field. This construction can be seen as a rigorous construction of the 2d path integral introduced in Polyakov's 1981 work. In contrast to this construction, modern conformal field theory is based on representation theory and the so-called bootstrap procedure (based on recursive techniques) introduced in 1984 by Belavin-Polyakov-Zamolodchikov. In particular, a bootstrap construction for LCFT has been proposed in the mid 90's by Dorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ) on the sphere. The aim of this talk is to review a recent series of work which shows the equivalence between the probabilistic construction and the bootstrap construction of LCFT on general Riemann surfaces. In particular, the equivalence is based on showing that LCFT satisfies a set of natural geometric axioms known as Segal's axioms; part of the London TQFT Journal Club; it will be possible to follow this talk online (please register at https://london-tqft.vercel.app)

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.

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)

I will review recent progress in the study of a class of integrable deformations of sigma models known as "homogeneous Yang-Baxter". These deformations can be understood as generalisations of the well known TsT transformations. In fact, rather than deformations, the homogeneous Yang-Baxter procedure too can be reinterpreted as imposing twisted worldsheet boundary conditions in the undeformed sigma model. I will explain how to construct the twist in the generic case, which generalises the twist of TsT from abelian to non-abelian. I will also use the expression for the twist to discuss the construction of the classical spectral curve in some examples. To conclude, I will mention some open questions related to the quantum integrability of these models. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

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 show that every conformal net has an associated vertex algebra, thus identifying the class of conformal nets with a sub-class of the class of unitary vertex algebras. We also characterise those unitary vertex algebras that arise from a conformal net. (We conjecture that every unitary vertex algebras arises in this way, and hence that there is a bijective correspondence between conformal nets and unitary vertex algebras.) To construct the correspondence between conformal nets and unitary vertex algebras, we introduce a new notion of "field localised in a segment embedded in a Riemann surface", which could be of independent interest. This is joint work with James Tener; 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 this talk, I will describe crosscap states in integrable field theories and spin chains in 1+1 dimensions. I will derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. I will then compute the crosscap entropy, i.e. the overlap for the ground state, in some examples. In the examples analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. I will discuss crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. I will comment on the realization of crosscap states in holography. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

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)

I will review a recent progress in computing four-point correlation functions of infinitely heavy half-BPS operators in planar N = 4 SYM. Taking advantage of integrability of the theory, these correlation functions can be constructed in terms of fundamental building blocks - the octagon form factors. We show that the octagon form factor can be expressed as a Fredholm determinant of an integrable Bessel operator and demonstrate that this representation is very efficient in finding its dependence on the ’t Hooft coupling and two cross ratios. At weak coupling, this yields a known series representation of the octagon in terms of ladder integrals. At strong coupling, we apply strong Szego limit theorem to develop a systematic expansion of the octagon in the inverse powers of the coupling constant and calculate accompanying expansion coefficients analytically. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

The application of random matrix techniques in QCD and non-Abelian gauge theories in general has a long history e.g. in counting Feynman diagrams, going back to 't Hooft and others. In this talk I will focus on a different aspect that relates the two in the low energy spectrum of the QCD Dirac operator, as initiated by Shuryak and Verbaarschot. First, I will explain what is the approximation studied here where spectral statistics of random matrices apply, and where for example the technique of orthogonal polynomials can be useful in comparing to QCD lattice data. It is given by a particular finite volume low energy limit, the epsilon regime of chiral perturbation theory of Gasser and Leutwyler. I will mention how QCD parameters like quark masses, zero-modes, finite lattice spacing or chemical potential can be incorporated into the random matrix ensemble. In the last part I will discuss some recent work with my former student Tim Wurfel on the inclusion of finite temperature, that leads out of the standard classes of random matrices, but still remains analytically tractable. This talk is mainly based on the review arXiv:1603.06011 and the paper with Tim arXiv:2110.03617; 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 this talk, I will discuss how to compute the spectral curve of "segmented strings" in AdS_3. The motion of a string in this target space is integrable and the worldsheet theory can be discretized while preserving integrability. The corresponding embeddings are segmented strings, which generalize piecewise linear strings in flat space. I will present several examples. Next, I will introduce "brane tilings", which are doubly-periodic planar bipartite graphs. I will show that the motion of a closed segmented string can be embedded into the mutation dynamics of a certain brane tiling. This will enable us to compute the spectral curve by taking the determinant of the dressed adjacency matrix of the tiling. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

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. -------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. Link emailed on Tuesday.

The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in $\mathcal{N}$=4 SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameter $\zeta$ has a non-trivial beta function and may be viewed as a running coupling constant in a 1d defect QFT. We continue the study of this operator, generalizing previous results for the beta function and Wilson loop expectation value to the case of an arbitrary representation of the gauge group and away from the planar limit. Focusing on the scalar ladder limit where the generalized Wilson loop reduces to a purely scalar line operator in a free adjoint theory, and specializing to the case of the rank $k$ symmetric representation of $SU(N)$, we also study a certain "semiclassical" limit where $k$ is taken to infinity with $k \zeta^2$ fixed. This limit can be conveniently studied using a 1d defect QFT representation in terms of path integral over $N$ commuting 1d bosons. Using this representation, we compute the beta function and circular loop expectation value in the large $k$ limit, and use it to derive constraints on the structure of the beta function for general representation. We discuss the corresponding 1d RG flow and comment on the consistency of the results with the 1d defect version of the F-theorem. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

Since time immemorial, mankind has responded to stories. Recently, anthropologists and scientists—from Joseph Campbell to Randy Olsen—have tasked themselves with exploring the fundamental structures of stories, uncovering story types and patterns that repeat across the centuries. Film-makers and novelists have used these to tremendous effect, harnessing the power of the hero's journey to create unforgettable narratives. Yet scientists, by contrast, have been slow on the uptake. In this event, Prof. Alison Woollard talks about the science of storytelling and storytelling in science. A Royal Institution Trustee who gave the iconic Christmas Lectures, she touches on the neuroscience of learning, the role of story in primitive cultures and the structure of story. Moreover, she argues that story is a crucial ingredient in communicating scientific discovery, which we hold as a core belief at the London Institute. The event is in our 2nd-floor seminar room in the Royal Institution. After introductory drinks at 5:00, the talk starts at 5.30, followed by drinks and discussion afterwards. RSVP at smc@lims.ac.uk.

It is well understood how the 2d free scalar CFT emerges from 3d Chern-Simons theory with chiral boundary conditions. Adapting a recent proposal of Costello and Stefanski, I will show how bosonic string theory can be obtained from this description by coupling to a dynamical Beltrami differential in the 3d theory. In particular, I will show how this Beltrami differential restores worldsheet diffeomorphism and Weyl invariance in the 2d theory, and recover the Polyakov action explicitly. By rewriting the theory in the BV formalism, I will show how the bc ghost system arises from the 3d perspective. Finally, if there is sufficient time, I will provide the 3d realization of vertex operators. This talk is based on work in progress with Kevin Costello and Bogdan Stefanski. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.