Colloquium

The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk, I outline a brief history of the theorems, explain a bit of the language, translate the first theorem into coordinate invariant language and give a few examples. I will mention briefly their historical importance in physics and integrable systems. In the second part of the talk, I describe why they are still relevant: why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of surfaces of Bill Thurston and the open problems in higher dimensions. I will finish by mentioning two recent papers, one in math and the other in physics, which greatly simplify the derivations of important identities by using the theorems.

Zoom Link: https://pitp.zoom.us/j/96748003059?pwd=aElYTlNXVlY4dEhtcmd0YUcvOHZIdz09

LIGO and Virgo have observed over 80 gravitational-wave sources to date, including mergers between black holes, neutron stars, and mixed neutron star- black holes. The origin of these merging neutron stars and black holes -- the most extreme objects in our Universe -- remains a mystery, with implications for stars, galaxies and cosmology. I will review the latest LIGO-Virgo discoveries and discuss some recent astrophysical lessons, including mass gaps, black hole evolution with cosmic time, and implications for cosmology. While the latest gravitational-wave observations have answered a number of longstanding questions, they have also unlocked new puzzles. I will conclude by discussing what we can expect to learn from future gravitational-wave and multi-messenger discoveries.

Zoom Link: https://pitp.zoom.us/j/94857758725?pwd=MW1PNXZRNkFGL25xUkpjVWlabmNJZz09

The black hole information paradox — whether information escapes an evaporating black hole or not —  remains one of the greatest unsolved mysteries of theoretical physics. The apparent conflict between validity of semiclassical gravity at low energies and unitarity of quantum mechanics has long been expected to find its resolution in the deep quantum gravity regime. Recent developments in the holographic dictionary and in particular its application to entanglement, however, have shown that a semiclassical analysis of gravitational physics has a hallmark feature of unitary evolution. I will describe this recent progress and discuss some potential new avenues for working towards a resolution of the information paradox.

What is the global symmetry of Nature? In the absence of gravity, the most obvious answer to this question is given by special relativity and is associated with the Poincare transformations. As was noted a long time ago, the free Maxwell equations have a wider symmetry group - the 15 parameters conformal invariance, containing in addition to ten Poincare generators, four special conformal transformations, and dilatations. Dilatations change the length of the rulers, while special conformal transformation can bend the lines but do not alter the angles between them. Could it be that the symmetry of all interactions is conformal? We will show that the answer to this question is "yes". The essential feature of the theory is the anomaly-free extension of the spontaneously broken conformal symmetry to curved space-time. We discuss how the effective Lagrangian respecting this special Weyl symmetry can be used for the description of particle phenomenology and cosmology.

We develop a general approach to "interpret" what a network has learned by introducing strong inductive biases. In particular, we focus on Graph Neural Networks. 

The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

In particular, we will show examples of recovery of newton's law and masses of solar system bodies with real ephemeris data and recovery of navier-stokes equations with turbulence dataset.  We will speculate what one can do with this new tool.
 

Sociologists have interesting things to say about the practice of natural science. I will discuss the sociological phenomenon of multiples in scientific discoveries, with examples drawn from how the ΛCDM cosmology grew, and examples of possible multiple discoveries to come from issues arising in our present well-tested but certainly incomplete cosmology.

I will review the history of anyons, particles that are neither bosons nor fermions, starting with their theoretical proposal all the way to their definitive experimental observation over 40 years later.  I will further discuss why the more general idea of non-abelian anyons is of intense interest for quantum computation.  If time permits I will give a status report on some of the current non-abelian anyon experiments.

Zoom Link: https://pitp.zoom.us/j/98698779123?pwd=SWIyak9OZ0dud2ZGcWdoazdkVURHQT09

When an interacting quantum many-body system is cooled down to its ground state, there can be discrete "topological invariants" that characterize the properties of such ground states. This leads to the concept of "topological phases of matter" distinguished by these topological invariants. Experimental manifestations of these topological phases of matter include the integer and fractional quantum Hall effect, as well as topological insulators.

In this talk, after a general overview of topological phases of matter, I will explain how to define topological invariants that are specific to the ground states of regular crystals, i.e. systems that are periodic in space. I will discuss the physical manifestations of the resulting "crystalline topological phases", including implications for the properties of crystalline defects such as dislocations and disclinations. Then, I will explain how these ideas can be generalized to quasicrystals, which are a different class of materials that have long-range spatial order without exact periodicity. These ideas ultimately lead to a general classification principle for crystalline and quasicrystalline topological phases of matter.

Understanding IP ownership and ensuring that commercialization of research provides broad societal and economic benefit both in Canada and abroad is extremely important.  Perimeter Institute is also acutely aware that entrepreneurial oriented faculty and graduate students want to engage in commercial enterprise (i.e., through contract research and licensing opportunities with industry or independently with their own research outcomes).  In this colloquium you will learn the basics about the different types of IP protection available and some of the most common pitfalls to avoid.  Hear how IP is used to commercialize technology through licensing or start-up creation. 

Zoom Link: https://pitp.zoom.us/j/99022008403?pwd=NmEzdFJkNlJiRzUvY0VDVERuY3FlUT09

Currently, no general theory exists that explains what life is. While many definitions for life do exist, these are primarily descriptive, not predictive, and they have so far proved insufficient to explain the origins of life, or to provide rigorous constraints on what properties we might expect all examples of life to share (e.g., in our search for life in alien environments). In this talk I discuss new approaches to understanding what universal principles might explain the nature of life and elucidate the mechanisms of its origins, focusing on recent work in our group elucidating regularities and law-like behavior of biochemical networks on Earth from the scale of individual organisms to the planetary scale.

Zoom Link: https://pitp.zoom.us/j/91944267625?pwd=QzBmTzRKK0k3YXhXWnQ3WjNBSDR2UT09

In an ordinary quantum field theory, the "split property" implies that the state of the system can be specified independently on a bounded subregion of a Cauchy slice and its complement. This property does not hold for theories of gravity, where observables near the boundary of the Cauchy slice uniquely fix the state on the entire slice. The original formulation of the information paradox explicitly assumed the split property and we follow this assumption to isolate the precise error in Hawking's argument. A similar assumption also underpins the monogamy paradox of Mathur and AMPS. Finally the same assumption is used to support the common idea that the entanglement entropy of the region outside a black hole should follow a Page curve. It is for this reason that computations of the Page curve have been performed only in nonstandard theories of gravity, which include a non-gravitational bath and massive gravitons. The fine-grained entropy at future null infinity does not obey a Page curve for an evaporating black hole in standard theories of gravity but we discuss possibilities for coarse graining that might lead to a Page curve in such cases.

When a generic isolated quantum many-body system is driven out of equilibrium, its local properties are eventually described by the thermal ensemble. This picture can be intuitively explained by saying that, in the thermodynamic limit, the system acts as a bath for its own local subsystems. Despite the undeniable success of this paradigm, for interacting systems most of the evidence in support of it comes from numerical computations in relatively small systems, and there are very few exact results. The situation changed recently, with the discovery of certain solvable classes of local quantum circuits, in which finite-time dynamics is accessible and the subsystem-thermalization picture can be verified. After introducing the general picture I will present a recent example (arXiv:2012.12256) of a simple interacting integrable circuit, for which the finite-time dynamics can be exactly described, and the model can be shown to exhibit generic thermalization properties.