Scientific Series

This talk will explore the applications of the computing power of numerical relativity to gravitational theories beyond general relativity. Specifically, I will consider dynamical Chern-Simons gravity, which has roots in string theory and loop quantum gravity. I will discuss our  formalism and efforts to simulate binary black holes in this theory to generate waveforms LIGO and LISA. Additionally, I will discuss the generation of numerical black hole solutions in this theory, and applications to probing black hole shadows with the Event Horizon Telescope. 

Stars orbiting in the halo of our galaxy, the Milky Way, are a window into the distribution of dark matter. In particular, tidally disrupted star clusters, which produce thin stellar streams, are optimal tracers of matter. Based on a Fisher-information calculation, we expect that the current data on the known Milky Way streams should constrain the radial profile and the shape of the inner halo to a precision of a few percent. In addition, stellar streams retain a detailed record of the matter field on small scales. Typically, streams are very thin -- approximately 100 times longer than they are wide, so even small gravitational perturbations introduce observable variations in the density of stars along the stream. Recently, significant gaps were detected in the GD-1 stellar stream, as well as stream stars displaced from the main stream. The observed structure is naturally reproduced in simulations where a stream like GD-1 encounters a massive perturber. None of the known Milky Way satellites has recently crossed paths with GD-1. If confirmed, the encounter scenario indicates the presence of an unknown, massive (~10^7 Msun) and compact (~<10 pc) object in the Milky Way -- the first evidence of dark substructure in a galactic halo.

Work of Bezrukavnikov on local geometric Langlands correspondence and works of Gorsky, Neguţ, Rasmussen and Oblomkov, Rozansky on knot homology and matrix factorizations suggest that there should be a categorical version of a certain natural homomorphism from the affine Hecke algebra to the finite Hecke algebra in type A, sending basis lattice elements on the affine side to Jucys-Murphy elements on the finite side. I will try to explain some of the structures involved and will talk about recent progress towards a construction of such a categorification in the setting of Hecke categories.

I will sketch why self-dual versions of the moduli of G-Higgs bundles are expected to arise physically from the study of 4d theories of class S. I will then describe an extension of the Langlands duality results of Hausel-Thaddeus (G=SL(n)) and Donagi-Pantev (arbitrary reductive G) that yields self-dual moduli spaces as a corollary.

The Alday-Gaiotto-Tachikawa correspondence connects gauge theory on a fourfold with conformal field theory. We are interested in a certain algebro-geometric incarnation of this framework, where the fourfold is an algebraic surface and instantons/differential geometry are replaced with sheaves/algebraic geometry. In this talk, we will present a certain approach to AGT that yields partial results for quite general surfaces, and ask questions about what still needs to be done to state and prove the full correspondence in the language of algebraic geometry.

I will discuss certain irrelevant operator deformations of holographic conformal field theories that define a one parameter family of quantum field theories which are thought to be dual to quantum gravity in finite regions. 
Some examples include the "$T\bar{T}$ deformation of two dimensional holographic CFTs, its generalisations and higher dimensional cousins.
I will emphasise the key role played by emergent radial diffeomorphism invariance in this scenario. In particular, I will present an additional criterion for a theory, in the appropriate regime, to possess a dual description in terms of general relativity coupled to matter in one higher dimension. I will also discuss entanglement properties of such theories, and in a particular example, I will show how the holographic entanglement entropy conjectures still hold in the finite radius setting. This is based on the following work: arXiv:1707.08118 [hep-th], arXiv:1712.07955 [hep-th], arXiv:1806.07444 [hep-th] and arXiv:1808.07760 [hep-th]."

Performing a quantum adiabatic optimization (AO) algorithm with the time-dependent Hamiltonian H(t) requires one to have some idea of the spectral gap γ(t) of H(t) at all times t. With only a promise on the size of the minimal gap γmin, a typical statement of the adiabatic theorem promises a runtime of either O(γmin-2) or worse. In this talk, I provide an explicit algorithm that, with access to an oracle that returns the spectral gap γ(t) to within some multiplicative constant, reliably performs QAO in time Õ(γmin-1) with at most O(log(γmin-1)) oracle queries. I then construct such an oracle using only computational basis measurements for the toy problem of a complete graph driving Hamiltonian on V vertices and arbitrary cost function. I explain why one cannot simply perform adiabatic Grover search and prove that one can still perform QAO in time Õ(V2/3)  without any a priori knowledge of γ(t). This work was done in collaboration with Brad Lackey, Aike Liu, and Kianna Wan.

In this talk I will review the results of recent work in collaboration with  Cecilia De Fazio, Benjamin Doyon and István M. Szécsényi. We studied the entanglement of excited states consisting of a finite number of particle excitations. More precisely, we studied the difference between the entanglement entropy of such states and that of the ground state in a simple bi-partition of a quantum system, where both the size of the system and of the bi-partition are infinite, but their ratio is finite. We originally studied this problem in massive 1+1 dimensional QFTs where analytic computations were possible. We have found the results to apply more widely, including to higher dimensional free theories. In all cases we find that the increment of entanglement is a simple function of the ratio between region's and system's size only. Such function, turns out to be exactly the entanglement of a qubit state where the coefficients of the state are simply associated with the probabilities of particles being localised in one or the other part of the bi-partition. In this talk I will describe the results in some detail and discuss their domain of applicability. I will also highlight the main QFT techniques that we have used in order to obtain them analytically and  present some numerical data. 

In galaxy redshift surveys, the line-of-sight velocity information is encoded in the observed redshift as a Doppler component that radially distorts the galaxy positions. The linear component of such `Redshift-Space Distortions' (RSD) is directly proportional to the growth rate of structure, f(z), and motivates the interest in RSD as a powerful way to constrain gravity. However, the non-linear evolution of the density and velocity fields requires the use of sophisticated theoretical models to extract reliable cosmological information from quasi-linear scales. Alternatively, one can use tracers of the LSS less sensitive to the non-linear motions at small scales. After an overview of VIPERS I will present a novel method that uses the clustering of luminous blue galaxies to obtain an accurate estimate of the growth rate while keeping the theoretical model relatively simple.

I give an overview of work with Aasen and Mong on topologically invariant defects in two-dimensional classical lattice models, quantum spin chains and tensor networks. We show how to find defects that satisfy commutation relations guaranteeing the partition function depends only on their topological properties. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. These lattice topological defects have a variety of useful applications. In the Ising model, the fusion of duality defects allows Kramers-Wannier duality to be enacted on the torus and higher genus surfaces easily, implementing modular invariance directly on the lattice. These results can be extended to a very wide class of models, giving generalised dualities previously unknown in the statistical-mechanical literature. A consequence is an explicit definition of twisted boundary conditions that yield the precise shift in momentum quantization and thus the spin of the associated conformal field. Other universal quantities we compute exactly on the lattice are the ratios of g-factors for conformal boundary conditions. 

Black-hole recoils are arguably the strong-gravity phenomena with the most striking astrophysical consequences. In the late inspiral and final coalescence of black-hole binaries, anisotropic emission of gravitational waves causes significant linear momentum loss. The remnant black hole, therefore, recoils in the opposite direction. These final kicks can reach magnitudes up to 5000 km/s (“superkicks”), larger than the escape speed of even the most massive galaxies, thus opening the possibility of black hole ejections. In this talk, I summarize recent advances in modeling black-hole recoils and their astrophysical environments. I will address the relevance of disk-assisted spin alignment, new approaches to model black-hole recoils with waveform approximants, and prospects to directly detect superkicks with gravitational-wave detectors.

Large deviation theory gives a general framework for studying nonequilibrium systems which in many ways parallels equilibrium thermodynamics. In transport, according to the large deviation principle, the distribution of rare fluctuations of the total transfer (of charge, energy, etc.) between two baths take a special form encoded by the large deviation function, which plays the role of a free energy. Its Legendre transform is the scaled cumulant generating function (SCGF). For instance, in mesoscopic physics, full counting statistics for charge transport through quantum impurities are SCGFs. In this talk I propose a formalism giving access to SCGFs for ballistic transport in homogeneous, stationary states. The formalism is conjectured to hold for classical and quantum systems alike, and give exact results in terms of the theory of linear fluctuating hydrodynamics. I will explain how it applies to nonequilibrium steady states of integrable models such as the classical hard rod gas, the quantum Lieb-Liniger model and the XXZ chain, using generalised hydrodynamics. This largely extends earlier results for free fermions (Levitov-Lesovik) and for 1+1-dimensional conformal field theory (Bernard-Doyon). The formalism also applies to transport in nonequilibrium critical systems of arbitrary dimension. It is, in a sense, the ballistic counterpart to macroscopic fluctuation theory.