Physics

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
periodicity emerge from the computations.

Elliptic cohomology is a fancy version of K-theory which can be
thought of as the K-theory of the loop space. A useful slogan is that
K-theory is to quantum mechanics, what elliptic cohomology is to
string theory. This cohomology theory satisfies a version of Bott
periodicity, with period 576. I will explain where that number 576
comes from, and what physical significance this might have.

I conjecture that the above 576-fold periodicity reflects itself in
the classification of 3d TQFTs. Here, the relevant TQFTs are the ones
associated to the chiral Majorana fermion (a type of abelian
Chern-Simons theory of central charge c=1/2). The claim is that the
theory becomes trivial once the central charge reaches 576·1/2 = 288.
The classification of abelian Chern-Simons theories has been
considered by Belov-Moore (2005), who claimed that the periodicity was
reached at c = 24 and later by Kapustin-Saulina (2010), who claimed
that the periodicity was never reached. Our proposal lies strictly in
between those of Belov-Moore and Kapustin-Saulina.

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.

In this talk I will look broadly at data science in physics, and how and why it
has taken an increasingly central role. I'll highlight specifically my current
area of research, radio cosmology: discussing why it is one of the most
challenging areas for data science, and describing my work developing optimal
and efficient statistical methods for turning terabytes of timestreams into
cosmology.

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
astrophysics that will be acquiring increasingly large and rich
datasets in the coming years.  I will highlight a few examples of
particular interest to fundamental physics, including gravitational
wave observations, fast radio bursts, and cosmological surveys.

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 the foreseeable future, the gravitational wave astronomy will be exponentially growing, with more detectors targeting gravitational waves at different frequencies and more events detected every week. This will provide us great opportunities but also impose challenges as well. In the first part of my talk, I will discuss the physics of gravitational wave detectors, emphasizing its basic principles and dominant noise sources, as well as ongoing efforts to improve detector sensitivity to fulfill the growing need. In the second half of my talk, I will discuss the astrophysics of gravitational-wave sources - especially compact sources such as black holes and neutron stars. I shall explain the spacetime dynamics, gravitational-wave emission during compact binary mergers and possible electromagnetic radiation from these compact objects. In the next few years with new gravitational-wave observations and possible electromagnetic counterpart measurements, we may dramatically improve our understandings on the astrophysics of these sources.

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.