Other

While it’s undeniably sexy to work with infinite-dimensional categories “model-independently,” we contend there is a categorical imperative to familiarize oneself with at least one concrete model in order to check that proposed model-independent constructions interpret correctly. With this aim in mind, we recount the n-complicial sets model of (∞,n)-categories for 0 ≤ n ≤ ∞, the combinatorics of which are quite similar to its low-dimensional special cases: quasi-categories (n=1) and Kan complexes (n=0). We conclude by reporting on an encounter with 2-complicial sets in the wild, where a suitably-defined fibration of 2-complicial sets enables the comprehension construction introduced in joint work with Verity. Special cases of the comprehension construction can be used to “straighten” a co/cartesian fibration of (∞,1)-categories into a homotopy coherent functor, exhibit a quasi-categorical version of the “unstraightening” construction, and define an internal model of the Yoneda embedding for (∞,1)-categories.

A century ago, Emmy Noether published an article, "Invariante Variationsprobleme", which contained 2 theorems on symmetries and conservation laws in the Gottingen Nachrichten. How original, how modern, how influential were her results? Did they shed light on the question of energy conservation that had arisen in the general theory of relativity? I shall comment on the curious transmission of her theorems and the later recognition of their wide applicability in very numerous fields of physics.

Most machine learning algorithms involve optimizing a single set of parameters to decrease a single cost function. In adversarial machine learning, two or more "players" each adapt their own parameters to decrease their own cost, in competition with the other players. In some adversarial machine learning algorithms, the algorithm designer contrives this competition between two machine learning models in order to produce a beneficial side effect. For example, the generative adversarial networks framework involves a contrived conflict between a generator network and a discriminator network that results in the generator learning to produce realistic data samples. In other contexts, adversarial machine learning models a real conflict, for example, between spam detectors and spammers. In general, moving machine learning from optimization and a single cost to game theory and multiple costs has led to new insights in many application areas.

The strong interaction of quarks and gluons is described theoretically within the framework of Quantum Chromodynamics (QCD). The most promising way to evaluate QCD for all energy ranges is to formulate the theory on a 4-dimensional Euclidean space-time grid, which allows for numerical simulations on state of the art supercomputers. We will review the status of lattice QCD calculations providing examples such as the hadron spectrum and the inner structure of nucleons. We will then point to problems that cannot be solved by conventional Monte Carlo simulation techniques, i.e. non-zero baryon density, the matter-antimatter asymmetry and real time simulations. It will be demonstrated at the example of the 1+1 dimensional Schwinger model that tensor network techniques are able to overcome these problems showing that with this approach --and eventual quantum simulations-- a path for solving QCD is opening up.

Energy and momentum are conserved in Newton's laws of gravitation.
Numerical integration of the equations of motion should comply to
these requirements in order to guarantee the correctness of a
solution, but this turns out to be insufficient.  The steady growth of
numerical errors and the exponential divergence, renders numerical
solutions over more than a dynamical time-scale meaningless.  Even
time reversibility is not a guarantee for finding the definitive
solution to the numerical few-body problem.  As a consequence,
numerical N-body simulations produce questionable results.  Using
brute force integrations to arbitrary numerical precision I will
demonstrate empirically that the statistics of an ensemble of resonant
3-body interactions is independent of the precision of the numerical
integration, and conclude that, although individual solutions using
common integration methods are unreliable, an ensemble of approximate
3-body solutions accurately represent the ensemble of true solutions.

I give an overview of trapped ion quantum information experiments and discuss prospects for implementing multi-valued quantum logic using trapped ions. Qudits (the multi-state generalization of qubits) are attractive for quantum computing because they enable a much larger Hilbert space for the same number of trapped ions, which may allow us to improve the information capacity of a quantum processor. I describe possible advantages and disadvantages of using qudits in place of qubits, and lay out some of the protocols that my lab will test for implementing measurements, single-qudit operations, and two-qudit operations in a trapped ion system.

The basic geometry of the Solar System - the shapes, spacings, and

orientations of the planetary orbits - has long been a subject of

fascination as well as inspiration for planet-formation theories. For

exoplanetary systems, those same properties have only recently come

into focus. I will review our current knowledge of the occurrence of

planets around other stars, their orbital distances and

eccentricities, the orbital spacings and mutual inclinations in

multiplanet systems, the orientation of the host star's rotation axis,

and the properties of planets in binary-star systems. I will also

discuss opportunities to improve our understanding, with data from the

recently launched Transiting Exoplanet Survey Satellite.

I will discuss the status and future of numerical lattice Quantum Chromodynamics (QCD) calculations for nuclear physics. With advances in supercomputing, we are beginning to quantitatively understand nuclear structure and interactions directly from the fundamental quark and gluon degrees of freedom of the Standard Model. Recent studies provide insight into the neutrino-nucleus interactions relevant to long-baseline neutrino experiments, double beta decay, and nuclear sigma terms needed for theory predictions of dark matter cross-sections at underground detectors. I will also address new work constraining `exotic glue’ in nuclei, which will be measurable for the first time at a future electron-ion collider, and explain how machine learning tools are providing new possibilities in this field.

In this first of two lectures, intended to be a pedagogical introduction, I will review the quantum field theory origin of anomalies starting with the more familiar example of the axial anomaly in QED, emphasizing the infrared effects and the appearance of a two-particle massless state, similar to a Cooper pairing in superconductor, associated with both the axial and conformal anomalies in two and four dimensions. In both cases the effective action of the anomaly is non-local, but may be expressed in a local form by the introduction of a bosonic field, which one can verify becomes a bona fide propagating quantum field in its own right. At finite chiral chemical potential this boson is a chiral density wave, a gapless pseudo-scalar collective excitation of the Fermi surface of a dissipationless chiral superfluid, analogous to the Goldstone-Nambu boson of spontaneous symmetry breaking. In the limit of vanishing chiral background the boson is a chiral collective mode of the Dirac vacuum itself, which therefore supports an axion-like boson excitation with a two-photon coupling, arising directly from the axial anomaly.

 

While the term “wide-field telescope” might sound like an oxymoron, a strong argument can be made that wide-field instruments lie behind much of the success of Canadian astronomy. Furthermore, despite the large size of the optical-IR community in Canada, this success has been made possible by considering multiple wavelength windows, from gamma to radio, and access to a suite of facilities. Over the past two decades, through a pair of 10-year Long Range Plans, Canadian astronomy has carefully structured its facility access, to ensure, as best as can be reasonably hoped, that the community maintains access to world-leading facilities. I’ll summarize the progression of the community vision on wide-field astronomy, highlighting successes and some missteps. As we head towards the creation of the 3rd Canadian Long Range Plan for astronomy, I’ll also present some personal views on what scientific leadership means and the challenges that it presents for a smaller country (at least in the G7 sense!) like Canada.

Classical chaotic systems exhibit exponential divergence of initially infinitesimally close trajectories, which is characterized by the Lyapunov exponent. This sensitivity to initial conditions is popularly known as the  "butterfly effect." Of great recent interest has been to understand how/if the butterfly effect and Lyapunov exponents generalize to quantum mechanics, where the notion of a trajectory does not exist. In this talk, I will introduce the measure of quantum chaoticity  – a so-called out-of-time-ordered four-point correlator (whose semiclassical limit reproduces classical Lyapunov growth), and use it to describe quantum chaotic dynamics and its eventual disappearance in the standard models of classical and quantum chaos – Bunimovich stadium billiard and standard map or kicked rotor [1]. I will describe our recent results on the quantum Lyapunov exponent in these single-particle models as well as results in interacting many-body systems, such as disordered metals [2]. The latter many-body model exhibits an interaction-induced transition from quantum chaotic to non-chaotic dynamics, which may manifest itself in a sharp change of the distribution of energy levels from Wigner-Dyson to Poisson statistics. I will conclude by formulating a many-body analogue of the Bohigas-Giannoni-Schmit conjecture.
References:
[1] "Lyapunov exponent and out-of-time-ordered correlator's growth rate in a chaotic system,"  E. Rozenbaum, S. Ganeshan, and V. Galitski, Physical Review Letters 118, 086801 (2017)
[2] "Non-linear sigma model approach to many-body quantum chaos," Y. Liao and and V. Galitski, arXiv:1807.09799