Week 04.04.2022 – 10.04.2022

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.

Email m.godazgar@qmul.ac.uk for zoom link. Abstract: I will present the derivation of the antipodal matching relations used to demonstrate the equivalence between soft graviton theorems and BMS charge conservation across spatial infinity. To this end I will provide a precise map between Bondi data at null infinity and Beig-Schmidt data at spatial infinity in a context appropriate to the gravitational scattering problem and celestial holography. I will also demonstrate that, among various proposals of BMS charges at null infinity found in the literature, only a subset match the conserved charges at spatial infinity and are therefore preferred from that perspective.

Gravitational-wave (GW) cosmology provides a new way to measure the expansion history of the Universe and test General Relativity (GR) at cosmological scales in the tensor sector, based on the fact that GWs are direct distance tracers. Obtaining the redshift (whose knowledge is essential to test cosmology) is instead the challenge of GW cosmology. In absence of a direct electromagnetic counterpart to the GW event, the source goes under the name of ``dark siren'' and statistical techniques are used. This talk aims at giving an overview of the state-of-the-art for these techniques as well as discussing perspectives for the future. After introducing GW cosmology and statistical methods, I will present the latest measurements of the Hubble parameter and of the phenomenon of ``modified GW propagation'' (that takes place whenever GR is modified at cosmological scales), obtained from the latest Gravitational Wave Transient Catalog 3 with new, independent, open-source codes. In particular, the two techniques applied to real data so far consist in using the statistical correlation with galaxy catalogues and information from the mass distribution of Binary Black Holes. I will discuss methodological aspects, relevant sources of systematics, the interplay with population studies, current challenges and possible ways forward. I will finally present some not-yet-applied ideas for statistical dark siren techniques, in particular for third generation (3G) ground-based GW detectors.

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.

In this talk I will review the basic ingredients which allows one to formulate 10D super-Yang-Mills on pure spinor superspace. The respective pure spinor master action in the gauge b_{0}V = QΞ, will then be used to show that tree-level scattering amplitudes calculated via perturbiner methods, match those obtained from pure spinor CFT techniques. I will also discuss how to compute pure spinor kinematic numerators through the use of standard Feynman rules, and show these are described by compact expressions involving the b-ghost operator. Remarkably, it will be shown how color-kinematics duality immediately emerges in this pure spinor framework after imposing the Siegel gauge condition b_{0}V = 0. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]