This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
Noncommutative geometry is a more general formulation of geometry that does not require coordinates to commute. As such it unifies quantum theory and geometry and should appear in any effective theory of quantum gravity. In this general talk we present quantum groups as a microcosm of this unification in the same way that Lie groups are a microcosm of usual geometry, and give a flavour of some of the deeper insights they provide. One of them is the ability to interchange the roles of quantum theory and gravity by `arrow reversal'.
The causal set -- mathematically a finitary partial order -- is a candidate discrete substratum for spacetime. I will introduce this idea and describe some aspects of causal set kinematics, dynamics, and phenomenology, including, as time permits, a notion of fractal dimension, a (classical) dynamics of stochastic growth, and an idea for explaining some of the puzzling large numbers of cosmology. I will also mention some general insights that have emerged from the study of causal sets, the most recent one concerning the role of intermediate length-scales in discrete spacetime theories.
Superconducting circuits based on Josephson junctions are promising candidates for the implementation of solid-state qubits. In most of the recent experiments on these circuits, the qubits are controlled by a classical field containing a large number of photons. The possibility of coherently coupling these systems to a single photon has been recently suggested, opening the possibility to study analogs of quantum optics in condensed matter systems.
A key issue in the context of (compact) extra dimensions is the one of their stability. Any stabilization mechanism is effective only up to some given energy scale; if they can approach this energy, 4$d observers can excite the fluctuations of the internal space, and probe its existence. Stabilization mechanisms introduce fields in the internal space; perturbations of these fields are mixed with perturbations of the metric, so that their study requires a complete GR treatment. After presenting the general framework, I will then discuss some relevant applications.
Since the seminal discovery of the neutrino by Cowan and Reines in the late 1950's, intense experimental and theoretical effort has focused on the elucidation of neutrino properties and the role they play in elementary particle physics, astrophysics, and cosmology. Neutrinos are born in the fusion reactions powering our Sun and are thought to be the driving mechanism for supernova explosions. Neutrinos exist in copious amounts as the primordial afterglow of the Big Bang and, if massive, would play a role in the evolution and ultimate fate of the Universe.