Talks

Strong gravitational lenses with measured time delays between the multiple images can be used to determine the Hubble-Lemaitre constant (H0) that sets the expansion rate of the Universe. An independent determination of H0 is important to ascertain the possible need of new physics beyond the standard cosmological model, given the tension in current H0 measurements. A program initiated to measure H0 to <3.5% in precision from strongly lensed quasars is in progress, and I will present the latest results and their implications. Search is underway to find new lenses in imaging surveys. An exciting discovery of the first strongly lensed supernova offered a rare opportunity to perform a true blind test of our modeling techniques. I will outline a new research program on lensed supernovae, showing their bright prospects as a competitive and unique probe of cosmology and stellar physics.

Magnetohydrodynamics (MHD) describes the low-energy physics of electromagnetically conducting plasmas. In the conventional formulation of MHD, one introduces dynamical electromagnetic fields on top of the usual hydrodynamic setup by hand. In this talk, we will explore an alternate effective view of MHD purely based on symmetries, as a "string fluid" of magnetic field lines, without any assumption about the underlying microscopic field content. We will argue that MHD is described by a novel theory of superfluidity with a partially broken one-form symmetry. We will also discuss the implications of this broken symmetry for constructing hydrostatic partition functions describing MHD. The talk is based on [arXiv:1808.01939, arXiv:1811.04913]. 

Principal bundles and their moduli have been important in various aspects of physics and geometry for many decades. It is perhaps not so well-known that a substantial portion of the original motivation for studying them came from number theory, namely the study of Diophantine equations. I will describe a bit of this history and some recent developments.

I discuss a geometric interpretation of the twisted indexes of 3d (softly broken) $\cN=4$ gauge theories on $S^1 \times \Sigma$ where $\Sigma$ is a closed genus $g$ Riemann surface, mainly focussing on quivers with unitary gauge groups. The path integral localises to a moduli space of solutions to generalised vortex equations on $\Sigma$, which can be understood algebraically as quasi-maps to the Higgs branch. I demonstrate that the twisted indexes computed in previous work reproduce the virtual Euler characteristic of the moduli spaces of twisted quasi-maps. I investigate 3d $\cN=4$ mirror symmetry in this context, which implies an equality of enumerative invariants associated to mirror pairs of Higgs branches under the exchange of equivariant and degree counting parameters. I will conclude with some remarks about how holomorphic Morse theory can be used to access the spaces of supersymmetric ground states in limits where $\cN=4$ supersymmetry is fully restored. These spaces of ground states may be related to the spaces of conformal blocks for the VOAs introduced by Costello and Gaiotto.