Talks

The coalescence of black hole-black hole (BHBH), black hole-neutron star (BHNS) and neutron star-neutron star (NSNS) systems are among the most promising sources of gravitational waves (GWs) detectable by Advanced LIGO/Virgo and NANOGrav. In addition, distinct observable electromagnetic radiation may accompany these GWs. Such "multi-messenger" sources can be powerful probes of fundamental physics such as the state of matter under extreme conditions, cosmology, as well as our theories of gravity. However, the identification, detection and interpretation of multimessenger signals from such sources requires careful theoretical modeling through the last stages of the compact binary inspiral, during which all approximations to general relativity break down. The only avenue to theoretically understanding these highly non-linear systems is solving the Einstein equations with the aid of supercomputers. This task is far from trivial: ill-posed formulations of the Einstein equations, gauge issues, the presence of singularities, shocks, and large range of length and time scales inherent to these systems pose strong theoretical and computational challenges. In this talk I will review these challenges, describe state-of-the-art numerical relativity techniques that overcome them, and present results from recent supercomputer simulations of binary NSNSs, and BHBHs around magnetized disks. I will conclude by discussing future directions and applications of numerical relativity.

Light sterile neutrinos are predicted in many theories beyond the Standard Model and may be hinted at in short-baseline data. However cosmological data seems to rule out these neutrinos. Intriguingly, this tension is ameliorated when these new neutrinos are self-interacting. I will explore the impact of this self-interaction on their evolution in the early universe and on the spectrum and flavor of IceCube's ultrahigh energy neutrinos.

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.