This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
In this talk I will outline the process of institutional change begun at the University of Michigan in 2001 and continuing today.
Symmetry protected topological (SPT) states are bulk gapped states with gapless edge excitations. The SPT phases in free fermion systems, like topological insulators, can be classified by K-theory. However, it is not yet known what SPT phases exist in general interacting systems. In this talk, I will first present a systematic way to construct SPT phases in interacting bosonic systems, which allows us to identify many new SPT phases.
Everything around us, everything each of us has ever experienced, and virtually everything underpinning our technological society and economy is governed by quantum mechanics. Yet this most fundamental physical theory of nature often feels as if it is a set of somewhat eerie and counterintuitive ideas of no direct relevance to our lives. Why is this? One reason is that we cannot perceive the strangeness (and astonishing beauty) of the quantum mechanical phenomena all around us by using our own senses.
Renormalization is a principled coarse-graining of space-time. It shows us how the small-scale details of a system may become irrelevant when looking at larger scales and lower energies. Coarse-graining is also crucial, however, for biological and cultural systems that lack a natural spatial arrangement. I introduce the notion of coarse-graining and equivalence classes, and give a brief history of attempts to tame the problem of simplifying and "averaging" things as various as algorithms and languages.
In (relatively) recent years some philosophers of physics have developed and advocated a new view about how to understand spatiotemporal structures posited in theories such as classical mechanics, relativistic theories and GR; it is called the 'dynamical approach' to spacetime (H. Brown 2005, Physical Relativity). The dynamical approach (DA) holds that spacetime structure should not be thought of as conceptually prior to the laws of nature, or as constraining the forms that the laws may have.
Quantum many-body systems ranging from a many-electron atom to a solid material are described by effective Hamiltonians which are obtained from more accurate Hamiltonians by neglecting or treating weak interactions perturbatively. Quantum complexity theory asks about the quantum computational power of such quantum many-body models for both practical as well as fundamental purposes.
Gravity in 1+1 dimension is classically trivial but, as shown by A. Polyakov in 1981, it is a non-trivial quantum theory, in fact a conformal field theory (the Liouville theory), and also a string theory. In the last decades many important results and connexions with various areas of mathematics and theoretical physics have been established, but some important issues remain to be understood.
The supermassive black hole in the centre of the Milky Way, Sgr A*, is an ideal target for testing the properties of black holes. A number of experiments are being prepared or conducted, such as the monitoring of stellar orbits, the search for radio pulsars or the recording of an image of the shadow of a event horizon. The talk puts these efforts in context with other tests of general relativity and its alternatives.
Quantum information theory has taught us that quantum theory is just one possible probabilistic theory among many others. In the talk, I will argue that this "bird's-eye" perspective does not only allow us to derive the quantum formalism from simple physical principles, but also reveals surprising connections between the structures of spacetime and probability which can be phrased as mathematical theorems about information-theoretic scenarios.