Non-shearing congruences of null geodesics on four-dimensional Lorentzian manifolds are fundamental objects of mathematical relativity. Their prominence in exact solutions to the Einstein field equations is supported by major results such as the Robinson, Goldberg-Sachs and Kerr theorems. Conceptually, they lie at the crossroad between Lorentzian conformal geometry and Cauchy-Riemann geometry, and are one of the original ingredients of twistor theory. Identified as involutive totally null complex distributions of maximal rank, such congruences generalise to any even dimensions, under the name of Robinson structures. Nurowski and Trautman aptly described them as Lorentzian analogues of Hermitian structures. In this talk, I will give a survey of old and new results in the field. Email m.godazgar@qmul.ac.uk for zoom link

Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system. Email m.godazgar@qmul.ac.uk for zoom link.

Part of the London TQFT Journal Club; it will be possible to follow this talk online (please register at https://london-tqft.vercel.app)

On a background Minkowski spacetime, the relativistic Euler equations are known, for a relatively general equation of state, to admit unstable homogeneous solutions with finite-time shock formation. By contrast, such shock formation can be suppressed on background cosmological spacetimes whose spatial slices expand at an accelerated rate. The critical case of linear, ie zero-accelerated, spatial expansion, is not as well understood. In this talk, I will present two recent works concerning the relativistic Euler and the Einstein-Dust equations for geometries expanding at a linear rate. This is based on joint works with David Fajman, Todd Oliynyk and Max Ofner. Email m.godazgar@qmul.ac.uk for zoom link

Ensembles of quantum chaotic systems are expected to exhibit random matrix universality in their energy spectrum. The presence of this universality can be diagnosed by looking for a linear in time 'ramp' in the spectral form factor, but for realistic systems this feature is typically only visible after a sufficiently long time. Given the wide prevalence of this random matrix behavior, it is natural to ask for an effective field theory which predicts the ramp and computes corrections to it arising from physical constraints. I will present such an effective theory based on fluctuating hydrodynamics. The theory can also be adapted to describe the effects of spontaneous symmetry breaking on spectral correlations. [for zoom link please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

TBA; part of the London TQFT Journal Club; it will be possible to follow this talk online (please register at https://london-tqft.vercel.app)

Relative theories are non-topological theories living at the boundaries of TQFTs in one higher dimension. An interesting and well-studied class of relative theories are 6d N=(2,0) theories. I will introduce the notion of relative defects in relative theories, which are non-topological defects of the relative theory living at the boundary of a topological defect of the above-mentioned TQFT in one higher dimension. I will argue that codimension two defects of 6d N=(2,0) theories are relative defects. Relative defects carry ''trapped'' higher-form symmetries localized on their world-volume which are independent from the higher-form symmetries of the bulk theory. When the bulk theory is compactified with the insertion of relative defects, the trapped higher-form symmetries provide extra contributions to the higher-form symmetries of the lower-dimensional theory resulting from the compactification. For example, when 6d N=(2,0) theories are compactified on a Riemann surfaces with punctures (which are relative codimension-two defects) then the 1-form symmetry of the resulting 4d N=2 Class S theory obtains contributions from the 1-form symmetries trapped at the punctures, along with the well-known contribution coming from the 2-form symmetry of the 6d N=(2,0) theory; part of London TQFT Journal Club; it will be possible to follow this talk on Zoom (please register at https://london-tqft.vercel.app)

I will discuss the paper https://arxiv.org/abs/2103.09283, where 3D non-unitary TQFTs are obtained from 3D N=4 rank 0 SCFTs; It will be possible to follow this talk on Zoom (please visit https://london-tqft.vercel.app to register).

Discussion of https://arxiv.org/pdf/2111.01139.pdf and https://arxiv.org/pdf/2111.01141.pdf. Part of new "London TQFT Journal Club" series at QMUL, please visit https://london-tqft.vercel.app to register for this and future events; some of these future meetings will be more like standard talks with speakers discussing their own work, while some will be--like this meeting--a more traditional journal club event. (Now on Zoom instead!)

[there will be a pre-seminar for students at 13:30. For zoom link please email s.nagy@qmul.ac.uk] Following a proposal by H. Sati, we have recently stated a hypothesis about the mathematical home of the quantum charges in M-theory. This “Hypothesis H” refines the traditional proposal for quantization of D-brane charge from K-theory to the non-abelian cohomology theory known as 4-Cohomotopy, whose classifying space is the 4-sphere. Besides its motivation from homotopy-theoretic re-analysis of 11d supergravity and of the old brane scan, Hypothesis H is currently justified by its rigorous implication of a list of long-conjectured M-theoretic consistency conditions on C-field flux and M-brane charges – such as shifted C-field flux quantization, dual Page charge quantization and M2/M5-brane tadpole cancellation. But if Hypothesis H is a correct assumption about the nature of M-theory, this suggests that quantum states of full M-theory should be reflected in the positive cohomology of the moduli space of Cohomotopy cocycles, much like quantum states of non-perturbative Chern-Simons theory are in the Dolbeault cohomology of moduli spaces of (flat) connections. In this talk I discuss how, in the topological sector of D6/D8-brane intersections, such quantum states according to Hypothesis H are identified with *weight systems* on *horizontal chord diagrams*, and how these do reflect a range of phenomena expected from the traditional approaches to understanding these brane intersections, such as non-abelian DBI-theory, the BMN matrix model, Rozansky-Witten theory and Hanany-Witten theory. Specifically, we have proven that the sl(2,C)-weight system satisfies the positivity condition that characterizes physical (i.e. non-ghost) quantum states. Under the above identification, this quantum state corresponds to an elementary fuzzy funnel configuration and/or to the elementary transverse M5-brane state in the BMN matrix model – both as expected for D6/D8-brane intersections. Besides possible implications for the elusive formulation of M-theory, this result may provide a unifying explanation for the plethora of unexpected appearances that chord diagrams are recently making in fundamental high energy physics, notably in discussion of holographic entanglement entropy. Slides and further pointers available at: https://ncatlab.org/schreiber/show/Some+Quantum+States+of+M-Branes+under+Hypothesis+H

It is well known that the most general renormalizable quantum field theory one can write down for a finite spectrum of spin-0, 1/2, and 1 particles is a gauge theory, with possible spontaneously broken symmetries. The existence of Lie group structures in such a theory is dictated by perturbative unitarity of the on-shell scattering amplitudes. Armed with new tools developed for scattering amplitudes, we demonstrate very explicitly how broken symmetries emerge from the constraints of tree unitarity. We review the on-shell spinor helicity formalism, using which we enumerate all possible 3-pt and 4-pt tree amplitudes of massive spin-0, 1/2 and 1 particles satisfying unitarity constraints. We show in these amplitudes how massive vectors and scalars need to be in the same representation of some Lie group, and how the longitudinal components of these massive vectors are equivalent to scalars in the high energy limit. We will also comment on an extended color-kinematics duality that can be hiding in such a general theory.

Recently in their celestial holography programme, Strominger and coworkers attempt to provide a holographic description of conventional 4d gravity. In their investigations, they uncovered a hidden w-infinity symmetry in their `celestial soft OPEs' for graviton scattering. This talk will explain the origin of this symmetry in terms of old ideas of Newman and Penrose based on light-cone cuts of null infinity and their description in terms of asymptotic twistors and certain sigma models in asymptotic twistor space. W_n symmetries were introduced by Zamolodchikov as higher spin symmetries in 2d conformal field theories. These were given a geometric interpretation for n=infinity as area-preserving diffeomorphisms of the plane. I will explain how the corresponding loop algebra becomes a hidden symmetry of self-dual gravity via Penrose's nonlinear graviton construction. The action of this symmetry on the tree-level S-matrix of full gravity beyond the self-dual sector will then be obtained from its action on a sigma model in the asymtotic twistor space of a general space-time. This talk is based on https://arxiv.org/abs/2110.06066 and https://arxiv.org/abs/2103.16984.

[there will be a pre-seminar for students at 1.30PM; for zoom link please email s.nagy@qmul.ac.uk] The characterization of measurements using the EFT framework is becoming prevalent, not just in its traditional realm of low-energy physics, but now also with LHC high-energy probes. At the LHC, the EFT approach is viewed as a way to transcend models, to exploit the huge range of LHC topologies, and even as a form of data preservation. In this talk we will review this state-of-affairs, point out challenges with this approach and also discuss some new opportunities that more data will bring.

Modulo some vitally important ansätze, subtleties, provisos, and work in progress, all topological quantum field theories are gauge theories for higher finite groups. [for zoom link please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

[for zoom link please email s.nagy@qmul.ac.uk] Next-generation gravitational wave detectors demand highly precise predictions for waveforms. We present advances in binary inspiral dynamics by taking classical limits of scattering amplitudes in perturbative quantum gravity. The amplitudes are calculated efficiently using modern methods for scattering amplitudes and loop integration techniques developed for colliders. Classical physics can be extracted by several complementary approaches, including effective field theory, eikonal exponentiation, and extrapolation of quantum observables defined by the S-matrix. For both conservative and radiative dynamics, we obtain new terms in the post-Minksowskian expansion which represent first advances in decades.

TBA

[for zoom link please email s.nagy@qmul.ac.uk] Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This task will encompass both understanding the statistics of initialized deep networks and determining the training dynamics of such an ensemble when learning from data. In terms of their "microscopic" definition, deep neural networks are a flexible set of functions built out of many basic computational blocks called neurons, with many neurons in parallel organized into sequential layers. Borrowing from the effective theory framework, we will develop a perturbative 1/n expansion around the limit of an infinite number of neurons per layer and systematically integrate out the parameters of the network. We will explain how the network simplifies at large width and how the propagation of signals from layer to layer can be understood in terms of a Wilsonian renormalization group flow. This will make manifest that deep networks have a tuning problem, analogous to criticality, that needs to be solved in order to make them useful. Ultimately we will find a "macroscopic" description for wide and deep networks in terms of weakly-interacting statistical models, with the strength of the interactions between the neurons growing with depth-to-width aspect ratio of the network. Time permitting, we will explain how the interactions induce representation learning. This talk is based on a book, "The Principles of Deep Learning Theory," co-authored with Sho Yaida and based on research also in collaboration with Boris Hanin. It will be published next year by Cambridge University Press.

[foor zoom link please email s.nagy@qmul.ac.uk] Infinite towers of massive modes arise for every compactification of higher dimensional theories. Understanding the properties of these Kaluza-Klein towers on non-trivial solutions with an AdS factor has been a longstanding issue with clear holographic interest, as they describe the spectrum of single-trace operators of the dual CFTs at strong coupling and large N. In this talk, I will focus on two classes of solutions of such kind. The first class consists of AdS4 solutions of D=11 and Type II supergravity that can be obtained from maximal gauged supergravities in D=4. For the later part, I will describe new families of solutions in N=(1,1) supergravity in D=6 which uplift from half-maximal supergravity in D=3. In both cases, the spectra can be computed using recent techniques from Exceptional Field Theory, and the information thus obtained leads to several unexpected conclusions.

[for zoom details please email s.nagy@qmul.ac.uk] In this talk we discuss a new swampland conjecture stating that the limit of vanishing gravitino mass corresponds to the massless limit of an infinite tower of states and to the consequent breakdown of the effective field theory. The proposal can be tested in large classes of models coming from compactification of string theory to four dimensions, where we identify the Kaluza-Klein nature of the tower of states becoming light. We point out a general relation between the gravitino mass and an abelian gauge coupling, which allows us to connect our conjecture to the weak gravity conjecture or the absence of global symmetries in quantum gravity. We discuss phenomenological implications of our conjecture in (quasi-)de Sitter backgrounds and extract a lower bound for the gravitino mass in terms of the Hubble parameter.

In this talk, we'll discuss the current state-of-the-art for constructing multi-loop integrands in N=4 super-Yang-Mills. After briefly covering some of the key goals, background, and ideas behind the multiloop integrand program, we turn to the cutting edge: constructing the complete (planar and non-planar) integrand for the six-loop four-point amplitude in maximal $D\le10$ super-Yang-Mills. This construction employs new advances that combat the proliferation of loops and state-sums when evaluating multi-loop $D$-dimensional unitarity cuts. Concretely, it uses two graph-based approaches, applicable in a range of theories, to evaluating generalized unitarity cuts in $D$ dimensions: 1) recursively from lower-loop cuts, or 2) directly from known higher-loop planar cuts. Neither method relies on explicit state sums or any sewing of tree-level amplitudes. The first method meshes particularly well with the Method of Maximal Cuts to allow direct construction of the complete six-loop integrand.