These lectures aim to provide a self-contained introduction to the modern conformal bootstrap method. The study of conformal field theory (CFT) will first be motivated and the “old” way of studying CFTs as endpoints of RG flows will be explained. The set of ideas necessary to understand the conformal bootstrap method will then be introduced, and both analytic and numerical implementations of the conformal bootstrap method will be discussed.

G-Research are a leading quantitative research and technology company based in London. Day to day we use a variety of quantitative techniques to predict financial markets from large data sets worldwide. Mathematics, statistics, machine learning, natural language processing and deep learning is what our business is built on. Our culture is academic and highly intellectual. In this seminar I will explain our background, current AI research applications to finance and our ongoing outreach and grants programme. The seminar will be aimed at PhD and Masters students who are curious about quant finance or interested in internship opportunities. The presentation will be of a duration of 45 minutes with 15 minutes for Q&A. We will cover the following topics: Introducing G-Research What happens in the black box? What does a Quant look like? Our recruitment and internship processes Q&A Bio: Dr Charles Martinez is the Academic Relations Manager at G-Research. Charles started his studies as a physicist at University Portsmouth Physics department's MPhys programme, and later completed a PhD in Phonon interactions in Gallium Nitride nanostructures at the University of Nottingham. Charles then worked on indexing and abstract databases at the Institution for Engineering and Technology (IET) before moving into sales in 2010. Charles' previous role was as Elsevier's Key Account Manager, managing sales and renewals for the UK Russell Group institutions, Government and Funding body accounts, including being one of the negotiators in the recent UK ScienceDirect Read and Publish agreement. Since leaving Elsevier Charles is dedicated to forming beneficial partnerships between G-Research and Europe's top institutions, and is living in Cambridge, UK. ​​

A new approach to strong turbulence based on ideas of dynamical geometry and topological conservation laws is developed. In terms of the quantum field theory, this is another example of the duality between a fluctuating vector field and fluctuating geometry. Some new exact solutions of Navier-Stokes and Euler equations are found. The loop equation suggested in the early 90-ties is investigated in detail. The loop equation plays the same role in our theory as the Boltzmann kinetic equation in statistical physics. It has the form of the Schrödinger equation with a complex Hamiltonian in loop space. The viscosity plays the role of Planck's constant. Strong turbulence corresponds to the WKB limit of the loop equation. In this limit, we find a fixed point of the loop equation we call Kelvinon. Kelvinon has a conserved circulation for a fixed loop in space, generalizing Kelvin's theorem. Clebsch field of this solution has nontrivial topology with two winding numbers. These topological conservation laws allow us to compute the PDF of circulation in a WKB limit (large circulation in the viscosity units). This PDF perfectly matches the results of numerical simulations of the conventional forced Navier-Stokes equation.

A new approach to strong turbulence based on ideas of dynamical geometry and topological conservation laws is developed. In terms of the quantum field theory, this is another example of the duality between a fluctuating vector field and fluctuating geometry. Some new exact solutions of Navier-Stokes and Euler equations are found. The loop equation suggested in the early 90-ties is investigated in detail. The loop equation plays the same role in our theory as the Boltzmann kinetic equation in statistical physics. It has the form of the Schrödinger equation with a complex Hamiltonian in loop space. The viscosity plays the role of Planck's constant. Strong turbulence corresponds to the WKB limit of the loop equation. In this limit, we find a fixed point of the loop equation we call Kelvinon. Kelvinon has a conserved circulation for a fixed loop in space, generalizing Kelvin's theorem. Clebsch field of this solution has nontrivial topology with two winding numbers. These topological conservation laws allow us to compute the PDF of circulation in a WKB limit (large circulation in the viscosity units). This PDF perfectly matches the results of numerical simulations of the conventional forced Navier-Stokes equation.

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.

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.

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.

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)

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)

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.

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)

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.