This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
Bott periodicity (1956) is a classical and old result in mathematics.
Its easiest incarnation of which concerns Clifford algebras. It says
that, up to Morita equivalence, the real Clifford algebras Cl_1(R),
Cl_2(R), Cl_3(R), etc. repeat with period 8. A similar result holds
for complex Clifford algebras, where the period is now 2. The modern
way of phrasing Bott periodicity in is terms of K-theory: I will
explain how one computes K-theory, and we will see the 8-fold Bott
Almost fifteen years after LIGO started listening to the cosmos, and 100 years after Einstein discovered general relativity, gravitational waves have been detected by ground-based interferometers, opening a new window on the universe. In this talk I will address some of the most exciting areas of research advanced LIGO will allow us to explore in the coming years. Detection and characterization of gravitational wave transients will be discussed, as well as their impact on astrophysics.
In recent decades probing for the subtle indications of new physics in
experimental data has become increasingly difficult. The datasets have gotten
much bigger, the experiments more complex, and the signals ever smaller. Success
stories, like LIGO and Kepler, require a sophisticated combination of statistics
and computation, coupled with an appreciation of both the experimental realities
and the theoretical framework governing the data.
I will begin by giving an overview of the current state of exoplanet
science, a field that has advanced tremendously in just the last few
years. While specialized instrumentation and observational facilities
have provided the data driving this advance, the development and
application of statistical techniques to interpret this data have been
of critical importance. These same tools are also at the core of all
data-driven science, and are thus applicable to many other fields of
Gravitational waves, as predicted by Einstein one hundred years ago, have been detected by the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) in September last year. This finding marks the beginning of gravitational-wave astronomy. From now on, we are able to probe our universe using both long-range forces in nature.
In any quantum field theory, the energy flux at a point of spacetime can be negative. This would produce a repulsive gravitational field causing nearby light rays to defocus. This in turn threatens to produce a variety of exotic phenomena including traversable wormholes, warp drives, time machines, and evasion of singularity theorems. I will describe a new "quantum focusing conjecture" that prevents such pathologies. In the flat spacetime limit it reduces to a novel lower bound on the energy density, which can be proven for several classes of field theories.
Precision atom interferometry is poised to become a powerful tool for discovery in fundamental physics. Towards this end, I will describe recent, record-breaking atom interferometry experiments performed in a 10-meter drop tower that demonstrate long-lived quantum superposition states with macroscopic spatial separations.
Radio pulsars are Nature's most perfect clock and hence are useful for precision work on a wide variety of physical and astrophysical topics, ranging from sensitive tests of relativistic gravity to constraining the equation of state of ultradense matter. I will describe current ongoing surveys for radio pulsars using the two largest radio telescopes in the world, and how these surveys are also valuable for searching for Fast Radio Bursts, a newly recognized astrophysical phenomenon of unknown origin.
In the summer of 2015, the speaker led a team at Microsoft Research, comprised primarily of research interns from seven universities, to demonstrate a social, ambulatory, Mixed Reality system for the first time. Each intern developed a preliminary, domain-specific exploration of how such a system could be used. One of the interns, Andrzej Banburski of the Perimeter Institute, demonstrated an interface to Mathematica.