Talks

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.