This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
Gauge theories lie at the heart of our understanding of three of the four known forces in nature: the electromagnetic, weak and strong forces. Moreover, our best understood non-perturbative definition of a theory of quantum gravity is also given by a gauge theory. Yet, despite their absolutely central role in physics, gauge theories are still far from being tamed with our current theoretical tools.
Topologically ordered states, such as the fractional quantum Hall (FQH) states, are quantum states of matter with various exotic properties, including quasiparticles with fractional quantum numbers and fractional statistics, and robust topology-dependent ground state degeneracies. In this talk, I will describe a new aspect of topological states: their extrinsic defects. These include extrinsically imposed point-like or line-like defects that couple to the topological properties of the state in non-trivial ways.
Living things operate according to well-known physical laws, yet it is challenging to discern specific, non-trivial consequences of these constraints for how an organism that is a product of evolution must behave. Part of the difficulty here is that life lives very far from thermal equilibrium, where many of our traditional theoretical tools fail us. However, recent developments in nonequilibrium statistical mechanics may help light a way forward.
Recently a new and rather unexpected connection between condensed matter physics and algebraic topology has been noted. Namely, it appears that phases of matter with an energy gap, no long-range entanglement, and fixed symmetry can be classified using cobordism theory. I will exhibit several examples of this connection and describe a possible explanation.
One of the most basic but intriguing properties of quantum systems is their ability to `tunnel' between configurations which are classically disconnected. That is, processes which are classically impossible, are quantum allowed. In this talk I will outline a new, first-principles approach combining the semiclassical approximation with the concepts of post-selection and weak measurement.
Analogies have played a very important role in physics and mathematics, as they provide new ways of looking at problems that permit cross-fertilization of ideas among different branches of science. An analogue gravity model is a generic dynamical system (typically but not always based on condensed matter physics) where the propagation of excitations/perturbations can be described via hyperbolic equations of motion possibly characterized be one single metric element for all the perturbations.
Rideout and Sorkin proposed a classical dynamics for causal sets based upon a sequential growth model. Comparing it with models for sequential growth in other systems, and with the dual goals of generating manifold-like causal sets and finding a quantum dynamics for them, we propose some modifications to their model. The resulting, admittedly speculative, proposal is a type of quantum random walk. We explore its properties in some simple cases.
We identify a new non-linear neutrino wake effect, due to the streaming motions of neutrinos relative to dark matter, analogous to the Tseliakhovich-Hirata effect. We compute the effect in moving background perturbation theory, compare to direct n-body simulations, and forecast its observability in current and future surveys. Depending on neutrino mass, this effect could be observable in upcoming surveys through a cross correlation dipole in lensing and galaxies.
We provide additional evidence that supersymmetrical quantum mechanical systems can contain a remarkable amount of information about supersymmetrical field
theories in greater than one dimension.
Equality of two mathematical objects is a seemingly simple and well-understood concept. In this talk, I will do three things to explain why this is a misconception: I will survey different notions of equality, explain how revising the notion of equality has led to an emerging alternative foundation of mathematics called "homotopy type theory", and try to convince you that thinking about equality is relevant to your research in quantum field theory, quantum gravity or quantum foundations.