Scientific Series

In this talk, I will discuss two important cryptographic tasks in a post-quantum world. I will discuss the impossibility of bit-commitment and the possibility of physically unforgeable money in the framework of Generalized Probabilistic Theories. Our proofs rely crucially on cone programming, a natural generalization of semidefinite programming. This is based on work with John Selby, arXiv:1803.10279 and arXiv:1711.02662.  

Recently, we have shown that deep neural networks can be used to solve the Schrödinger Equation (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.042113), classical spin models (https://doi.org/10.1103/PhysRevE.97.032119), and 2d-materials such as graphene and boron-nitride (https://doi.org/10.1016/j.commatsci.2018.03.005).

I will argue that these "deep models" can be used to simulate and understand matter in a way which was not previously possible. Specifically, I will show how our recently reported extensive deep neural networks (https://arxiv.org/abs/1708.06686) can be used to infer the properties of meso-scale materials based on training data generated from much smaller structural motifs (evaluated using electronic structure methods such as density functional theory). Extensive deep neural networks scale as O(N) and can be efficiently evaluated in parallel using petascale computational platforms.

The talk will focus on issues connected with the quantization of initial data for vacuum general relativity on null hypersurfaces. Complete and constraint free initial data for GR can be given on pairs of intersecting null hypersurfaces. These offer a route to a canonical quantization of GR which avoids having to deal with constraints. However the Poisson algebra of these data is rather intricate and it is not obvious how one might quantize it. This algebra is however almost the same in the cylindrically symmetric case as in the full theory, which suggests that the cylindrically symmetric theory ought to offer valuable insights. Here I present recent joint work with Javier Peraza and Miguel Paternain relating the Poisson algebra in the cylindrically symmetric case to well studied algebraic structures.

Two years ago the Laser Interferometer Gravitational-wave Observatory.

(LIGO) announced the first direct detection of gravitational waves; minute distortions in space-time caused by cataclysmic events far away in the universe.  Very recently, the merger of a binary neutron star system was detected by both of the Advanced LIGO detectors and the Advanced Virgo detector in Italy, triggering a massive follow-up campaign by ground and space-based telescopes.  A counterpart to the gravitational-wave source was located, and transient emission was detected from gamma rays to radio.  I will talk about the sources of the signals we detected, the physics behind the detectors, and prospects for the future of this emerging field.

When performing numerical simulation of many-body systems we work with the goal of computing some set of averaged observables.  This process has a weakness in that, when our simulation is complete, we have no ability to determine what was the key physics that gave our result.  In this talk, I'll give a simple example, a gap in a single-particle density of states, and explain how we can use two-particle quantities to recover key 'hidden' information.  I'll then back up these claims with numerical results for the 2D Hubbard model.  For the second half of my talk I'll hope to keep your attention by introducing a parallel but MUCH more whimsical idea, unparticle physics. I'll at least TRY to explain what an unparticle is and how it might impact strongly correlated condensed matter systems.

There seem to be no good examples of UV complete theories that have low-lying massive higher spin states isolated by a large gap, despite the relative ease of constructing effective field theories describing such states.  We discuss constraints from analytic dispersion relations and subluminality of eikonal scattering that may help to explain this and provide insight into the possible interactions of massive higher spins.

First I will introduce the concept of the shadow of a black hole and what it means for the shadows of two observers to be degenerate. I will then present
our results showing that no continuous
degenerations exist between the shadows of observers at any point in the exterior region of any Kerr-Newman black hole spacetime of unit mass. Therefore an observer can, by measuring the black holes shadow, in principle determine the angular momentum and the charge of the black hole under observation, as well as his radial distance from the black hole and his angle of elevation above the equatorial plane.

CHIME is a new interferometric telescope at radio frequencies 400-800 MHz.The mapping speed (or total statistical power) of CHIME is among the largestof any radio telescope in the world, and the technology powering CHIME could be used to build telescopes which are orders of magnitude more powerful.This breakthrough sensitivity has the power to revolutionize radio astronomy, but meeting the computational challenges will require breakthroughs on the algorithmic side.  I'll give a status update on CHIME, with an emphasis on new algorithms developed at Perimeter to search for fast radio bursts (FRB's) and pulsars.

I will introduce our recent proposal that the state of the universe does *not* spontaneously violate CPT. Instead, the universe before the Big Bang is the CPT reflection of the universe after the bang. Phrased another way, the universe before the bang and the universe after the bang may be re-interpreted as a universe/anti-universe pair, created from nothing. CPT selects a unique vacuum state for the QFT on such a spacetime, which leads to a new perspective on the cosmological baryon asymmetry, and a new explanation for the observed dark matter abundance. In particular, if we assume that the matter fields in the universe are described by the standard model of particle physics (including right-handed neutrinos), we predict that one of the heavy neutrinos is stable, and that its density automatically matches the observed dark matter density if its mass is 4.8 x 10^8 GeV. Among other predictions, we have: (i) that the three light neutrinos are majorana; (ii) that the lightest of these is exactly massless; and (iii) that there are no primordial long-wavelength gravitational waves. I will mention connections to the strong CP problem and the arrow of time. (Based on arXiv:1803.08928 and arXiv:1803.08930, with Kieran Finn and Neil Turok.)

In the first part of the seminar I will give a short review of the frame-independent formulation of Newtonian gravity, called Newton-Cartan Gravity, and explain why there is a renewed interest into non-relativistic gravity in general.  In the second part I will discuss, as a particular application,  a recent proposal for an Effective Field Theory describing a massive spin-2 mode (the so-called GMP mode) in the Fractional Quantum Hall Effect.

This project examines the structure of a certain category of representations of a Lie algebra called Whittaker modules. Whittaker modules generalize highest weight modules, and the structure of the category is similar to that of Bernstein-Gelfand-Gelfand’s category O. In particular, Whittaker modules have finite length composition series and all irreducible Whittaker modules appear as quotients of standard Whittaker modules, which are generalizations of Verma modules. Using the localization theory of Beilinson-Bernstein, one obtains a beautiful geometric description of Whittaker modules as twisted sheaves of D-modules on the associated flag variety. I use this geometric setting to develop an algorithm for computing the multiplicities of irreducible Whittaker modules in the composition series of standard Whittaker modules. This algorithm establishes that the multiplicities are determined by parabolic Kazhdan-Lusztig polynomials.

Starting from the well known Laplace-Runge-Lenz vector of the Kepler problem, I will introduce a notion of dynamical (hidden)
symmetries. These are genuine phase space symmetries that stand in contrast to the more familiar symmetries of the configuration space
discussed in truncated versions of Noether's theorem. Proceeding to a relativistic description, I will demonstrate that such symmetries -- encoded
in the so called Killing-Yano tensors -- play a crucial role in the study of rotating black holes described by the Kerr geometry. Even more remarkably, I will show that one such special symmetry is enough to guarantee complete integrability of particle and light motion in general rotating black hole spacetimes in an arbitrary
number of spacetime dimensions. Recent developments on the separability of test fields in these spacetimes will also be discussed.