Talks

Entanglement spectrum (ES) contains more information than the entanglement entropy, a single number. For highly excited states, this can be quantified by the ES statistics, i.e. the distribution of the ratio of adjacent gaps in the ES. I will first present examples in both random unitary circuits and Hamiltonian systems, where the ES signals whether a time-evolved state (even if maximally entangled) can be efficiently disentangled without precise knowledge of the time evolution operator. This allows us to define a notion of entanglement complexity that is not revealed by the entanglement entropy.

In the second part, I will discuss how quantum states are scrambled via braiding in systems of non-Abelian anyons through the lens of ES statistics. We define a distance between the entanglement level spacing distribution of a state evolved under random braids and that of a Haar-random state, using the Kullback-Leibler divergence $D_{\mathrm{KL}}$. We study $D_{\mathrm{KL}}$ numerically for random braids of Majorana fermions (supplemented with random local four-body interactions) and Fibonacci anyons. Our results reveal a hierarchy of scrambling among various models --- even for the same amount of entanglement entropy --- at intermediate times, whereas all models exhibit the same late-time behavior. In particular, we find that braiding of Fibonacci anyons scrambles more efficiently than the universal H+T+CNOT set. Our results promote $D_{\mathrm{KL}}$ as a quantifiable metric for scrambling and quantum chaos, which applies to generic quantum systems.

Most current dark matter detection strategies, including both direct and indirect efforts, are based on the assumption that the galactic dark matter number density is quite high, allowing for the detection of rare scattering events. Such a paradigm arises naturally if the dark matter self-interactions are weak. However, strong interactions within the dark sector can give rise to large composite objects, whose detection requires a different experimental paradigm. We call these object Dark Blobs. In such theories, the energy transfer due to a single collision with a Standard Model particle tends to be small, below the energy threshold of many nuclear recoil experiments. Fortunately, due to their exponentially large composite nature, the interactions between these objects and a terrestrial detector can be coherently enhanced. Therefore, while the effect on a single probe is small, the large collective effect can be quite dramatic and, importantly, above experimental thresholds. In this talk, I will briefly motivate the early Universe formation of certain types of Dark Blobs and then focus on multiple detection avenues for these objects.

This talk will explore the applications of the computing power of numerical relativity to gravitational theories beyond general relativity. Specifically, I will consider dynamical Chern-Simons gravity, which has roots in string theory and loop quantum gravity. I will discuss our  formalism and efforts to simulate binary black holes in this theory to generate waveforms LIGO and LISA. Additionally, I will discuss the generation of numerical black hole solutions in this theory, and applications to probing black hole shadows with the Event Horizon Telescope. 

Stars orbiting in the halo of our galaxy, the Milky Way, are a window into the distribution of dark matter. In particular, tidally disrupted star clusters, which produce thin stellar streams, are optimal tracers of matter. Based on a Fisher-information calculation, we expect that the current data on the known Milky Way streams should constrain the radial profile and the shape of the inner halo to a precision of a few percent. In addition, stellar streams retain a detailed record of the matter field on small scales. Typically, streams are very thin -- approximately 100 times longer than they are wide, so even small gravitational perturbations introduce observable variations in the density of stars along the stream. Recently, significant gaps were detected in the GD-1 stellar stream, as well as stream stars displaced from the main stream. The observed structure is naturally reproduced in simulations where a stream like GD-1 encounters a massive perturber. None of the known Milky Way satellites has recently crossed paths with GD-1. If confirmed, the encounter scenario indicates the presence of an unknown, massive (~10^7 Msun) and compact (~<10 pc) object in the Milky Way -- the first evidence of dark substructure in a galactic halo.

Work of Bezrukavnikov on local geometric Langlands correspondence and works of Gorsky, Neguţ, Rasmussen and Oblomkov, Rozansky on knot homology and matrix factorizations suggest that there should be a categorical version of a certain natural homomorphism from the affine Hecke algebra to the finite Hecke algebra in type A, sending basis lattice elements on the affine side to Jucys-Murphy elements on the finite side. I will try to explain some of the structures involved and will talk about recent progress towards a construction of such a categorification in the setting of Hecke categories.

I will sketch why self-dual versions of the moduli of G-Higgs bundles are expected to arise physically from the study of 4d theories of class S. I will then describe an extension of the Langlands duality results of Hausel-Thaddeus (G=SL(n)) and Donagi-Pantev (arbitrary reductive G) that yields self-dual moduli spaces as a corollary.

The Alday-Gaiotto-Tachikawa correspondence connects gauge theory on a fourfold with conformal field theory. We are interested in a certain algebro-geometric incarnation of this framework, where the fourfold is an algebraic surface and instantons/differential geometry are replaced with sheaves/algebraic geometry. In this talk, we will present a certain approach to AGT that yields partial results for quite general surfaces, and ask questions about what still needs to be done to state and prove the full correspondence in the language of algebraic geometry.