Colloquium

In recent years, precise cosmological measurements have provided strong evidence for new physics beyond the Standard Model, occurring both in the very early universe and also today.  In the near future, large-scale galaxy surveys will open another window on many different areas of physics, including tests of gravity, probes of dark energy, and cosmic inflation.  However, interpreting galaxy surveys presents new challenges, because galaxies are sensitive to astrophysics that are unimportant for the cosmic microwave background.  I will discuss how galaxies may be used to study cosmology, and will argue that the messy astrophysics in galaxies actually offers entirely new probes of fundamental physics.  I will illustrate this with 3 examples, related to inflation, neutrino masses, and the properties of dark matter.

I will argue that the standard model contains a rather strong hint that -- instead of being simply an ordinary continuous 4D manifold -- spacetime is actually the product of a 4D manifold and a certain discrete/finite 6D space (i.e. there are 6D discrete/finite "extra dimensions").  I will introduce this idea and the evidence for it in simple way, and then discuss various outstanding puzzles and future directions.

Tensor networks offer an efficient representation of many-body wave-functions in an exponentially large Hilbert space by exploiting the area law of ground state quantum entanglement. I will start with a gentle introduction to the tensor network formalism. Then I will describe its application to realizing Wilson's renormalization group directly on quantum lattice models (e.g. quantum spin chains), with emphasis on the RG fixed points corresponding to conformal field theories. We will see how to define both global and local scale transformations on the lattice in such a way that, intriguingly, conformal invariance can be tested (and conformal data extracted) right at the UV cut-off scale.

Scale invariant transfer matrices and Hamiltonians Abstract We investigate the possibility of strictly scale invariant transfer matrices in quantum spin chains based on a certain planar algebra, both as operators and as quadratic forms.

Recent explorations of the space of quantum field theories have provided novel topological and geometric information about this space. This voyage has resulted in the solution of some long-standing questions:  the computation of sought-after topological invariants (Gromov-Witten invariants) by a new physics-based approach, the first instance of exact correlation functions in a four-dimensional QFT and the unearthing of the action of dualities on the basic observables of three dimensional gauge theories.

Experimentalists are getting better and better at building qubits, but no matter how hard they try, their qubits will never be perfect.  In order to build a large quantum computer, we will almost certainly need to encode the qubits using quantum error-correcting codes and encode the quantum circuits using fault-tolerant protocols.  This will eventually allow reliable quantum computation even when the individual components are imperfect.  I will review the current state of the art of quantum fault tolerance and discuss progress towards answering the most important questions that will enable large fault-tolerant quantum computers.

Should we revisit the concept of space solely based on quantum mechanics?

Do we need a radically new physical principle to address the problem of quantum gravity?

In this talk I will adress these questions. I will review what are the central challenges one faces when trying to understand the theory of quantum gravity from first principles and focus on the main one which is non-locality.

I will present a collection of results and ideas that have been developed in the recent years that provides a radical new perspective on these issues.

One of the central concept I'll present is the idea that locality has to be made relative, and how this idea goes back to one of the founder of quantum mechanics: Max Born. I'll also explain how these new ideas remarkably force us to revisit the concept of space itself and propose a natural generalization that incorporate quantum mechanics in its fabric called modular space. I'll also sketch how these foundational ideas quite unexpectedly links with the most recent developments on the geometry of string theory, and generalized geometry.

Dark energy, the driver of the accelerated expansion of the universe, remains a conundrum. New physics may well be needed to explain it; from Lorentz invariance, this new physics should contain scalar fields, which should be straightforward to detect — so where are they? Physicists have now realized that scalar fields can hide from detection by three distinct screening mechanisms, which respectively rely on nonlinear features in the scalar’s kinetic energy, potential energy, or coupling to normal matter. These fields go by names such as galileons, chameleons, f(R) gravity, or symmetrons and range from theoretically well-motivated and natural to speculative. We will present new techniques to detect these particles, relying on interferometry with cold atoms in vacuum. The low density of such atoms compared to bulk matter avoids triggering some screening mechanisms, while the high sensitivity of the interferometer overcomes other screening mechanisms by brute force. We will show limits ruling out substantial regions of parameter space for chameleons and symmetrons [Science 349, 849 (2015)] and argue that an interferometer with 10,000 fold improved sensitivity will be able to search the gamut of screened scalar fields. A positive identification would revolutionize particle physics and cosmology, but even a null result would have important implications for our understanding of the dark sector. 

Fault-tolerant quantum computers will compute by applying
a sequence of elementary unitary operations, or gates, to an
error-protected subspace.   While algorithms are typically expressed
over arbitrary local gates, there is unfortunately no known theory
that can correct errors for a continuous set of quantum gates.
However, theory does support the fault-tolerant construction of
various finite gate sets, which in some cases generate circuits that
can approximate arbitrary gates to any desired precision.   In this
talk, I will present a framework for approximating arbitrary qubit
unitaries over a very general but natural class of gate sets derived
from the theory of integral quaternions over number fields, where the
complexity of a unitary is algebraically encoded in the length of a
corresponding quaternion.  Then I will explore the role played by
higher-dimensional generalizations of the Pauli gates in various
physical and mathematical settings, from classifying bulk-boundary
correspondences of abelian fractional quantum Hall states to
generating optimal symmetric quantum measurements with surprising
connections to Hilbert's 12th problem on explicit class field theory
for real quadratic number fields.

100 years after the existence of gravitational waves was first postulated by Albert Einstein, the LIGO and Virgo Collaborations detected gravitational waves for the first time on September 14, 2015. The gravitational waves originated from a pair of black holes that merged over one billion years ago.  The merger was so powerful that it shook the very fabric of space and sent a ripple across the Universe that we observed here on Earth at present day. Although this event was but a blip in a sea of data taken by various experiments over the last several decades, it represents a paradigm shift in how we study our Universe.

In this colloquium, I will present some of the history of this great discovery and what it means for our future at the dawn of gravitational wave astronomy.

Recent developments in our understanding of black hole evaporation and the information paradox suggest that effects from quantum gravity are not necessarily hidden at the Planck scale. They might even one day be testable by gravitational wave measurements. To prepare ourselves, we must first understand what quantum gravity really means. Thankfully, we are pre-armed with a deep principle about gravity—that spacetime is really a hologram—and a powerful model for making this idea precise: gauge/gravity duality. The present challenge is to translate our questions about gravity into the natural language of the dual conformal field theory (CFT). I will describe the foundation for such a program that links the integral geometry of a gravitational spacetime to a CFT operator product expansion.