M-theory on spaces with codimension 11-d singularities gives rise to a rich class of d-dimensional field theories. I will discuss how (d+1)-dimensional topological field theories (TFTs) encode the higher symmetries and anomalies of these d-dimensional theories, and how these TFTs can be extracted from the geometry of the singular space. I will illustrate the discussion by analysing some simple examples explicitly. [for zoom link please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

(Email m.godazgar@qmul.ac.uk for zoom link) Abstract: The exterior dynamics of black holes has played a major role in holographic duality, describing the approach to thermal equilibrium of strongly coupled media. The interior dynamics of black holes in a holographic setting has, in contrast, been largely unexplored. I will describe recent work investigating the classical interior dynamics of various holographic black holes. I will discuss the nature of the singularity, the absence of Cauchy horizons and a new kind of chaotic behavior that emerges in the presence of charged scalar fields.

I will present a way to promote the anomalous axial U(1) in 4d QED to an exact symmetry, with the price of losing its invertibility. I will then discuss some applications of this non-invertible U(1) symmetry. In particular, I will show how to couple this non-invertible symmetry to a gauge field. By taking this gauge field to be dynamical, we get a new type of gauge theory with unconventional interactions and constraints. By taking this gauge field to be background, we can study 't-Hooft anomalies of the non-invertible symmetry.

We demonstrate that the dynamics of neural networks trained with gradient descent and the dynamics of scalar fields in a flat, vacuum energy dominated Universe are structurally profoundly related. This duality provides the framework for synergies between these systems, to understand and explain neural network dynamics and new ways of simulating and describing early Universe models. Working in the continuous-time limit of neural networks, we analytically match the dynamics of the mean background and the dynamics of small perturbations around the mean field, highlighting potential differences in separate limits. We perform empirical tests of this analytic description and quantitatively show the dependence of the effective field theory parameters on hyperparameters of the neural network. As a result of this duality, the cosmological constant is matched inversely to the learning rate in the gradient descent update. [for zoom link, please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

After a brief introduction to some of the impact which integrable methods and the Bethe ansatz have had on the study of the AdS/CFT correspondence in string theory, we will focus on the axiomatic approach to S-matrix theory in 1+1 dimensions. We will highlight the issues that arise when the particles are massless, and how this is in fact connected to Zamolodchikov's way of describing two-dimensional conformal field theories by means of integrability techniques. We will then mention how the axiomatic approach extends to form-factors, which are the gate to access the n-point functions of the theory. If time permits, we will briefly depict how this finds a contemporary application in the area of the AdS_3/CFT_2 correspondence; part of London TQFT Journal Club (please register at https://london-tqft.vercel.app);

Celestial conformal field theory (CCFT) is a conjectured theory living on the celestial sphere of the asymptotic boundary of Minkowski. In analogy to the usual AdS/CFT dictionary, CCFTs would be dual to gravitational theories in the bulk, with bulk scattering amplitudes being dual to correlation functions on the celestial sphere. OPE coefficients are basic building blocks of CFTs which should also have an analogue in CCFTs. It has been shown that CCFT OPEs can be extracted from amplitudes with appropriate wavefunctions for external states, but there's still no direct computation using the CCFT itself since we lack a first principles definition. I will talk about recent work I have done computing these OPEs directly by using twistor strings, circumventing the issue of the target space theory. I will show how the worldsheet CFT of the twistor string gives a realization of the algebra of operators of the CCFT, reproducing the known leading OPE terms, as well as how it can be used to compute further regular terms in the OPE, beyond what is currently known. As a bonus, the worldsheet OPE also organizes the spectrum naturally in terms of the infinite dimensional symmetry algebras of CCFTs. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]

The Standard Model extended with non-renormalisable operators is increasingly becoming THE theory of the elementary particles and their interactions. A large part of current and future research is devoted to test this theory to the best possible accuracy. To this aim, though, substantial knowledge on its quantum structure is needed, both for theoretical reasons (constraints on the basis of relativity+quantum mechanics) and experimental ones (combine data gathered at very different energies). In this talk I will discuss the progress made over the years in this respect, with particular emphasis on major obstacles.

I will describe the space of effective field theories consistent with local, unitary, and analytic UV completions, which was termed the EFThedron. Recently the EFThedron was generalized to a non-projective geometry, which can be used to implement new constraints on spectral functions. These include the unitarity bound, which leads to analytic bounds on single Wilson coefficients (instead of bounds only on ratios), or the low spin dominance condition, which drastically reduces the landscape of allowed theories. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]