Conference

We use 3d defect TQFTs and state sum models with defects to give a gauge theoretical formulation of Kitaev's quantum double model (for a finite group) and (untwisted) Dijkgraaf-Witten TQFT with defects. This leads to a simple description in terms of embedding quivers, groupoids and their representations. Defect Dijkgraaf-Witten TQFTs is then formulated in terms of spans of groupoids and their representations. This is work in progress with João Faría-Martins, University of Leeds.

I will describe models with on-site symmetry that permutes anyons with non-trivial mutual statistics, and show that the action of this symmetry on the boundary can effectively be that of a non-invertible symmetry such as Kramers-Wannier duality. I will sketch some implications of this for anomalies in non-invertible symmetries. Finally, I will introduce a construction (based on idempotent completion) that allows us to realize all possible anyon permuting symmetries of a given topological order in an on-site way.

I discuss some analogies between the Haag-Kastler approach to QFT and quantum statistical mechanics of lattice systems. As an illustrative example, I consider the interpretation of the Hall conductance of gapped 2d lattice systems as an obstruction to gauging a global symmetry of a gapped state. I argue that in order to define a proper analog of the net of algebras of observables one needs to study a category of subsets of the lattice equipped with a natural Grothendieck topology.

Increasing evidence for a stochastic gravitational background is being collected at pulsar timing arrays. The most plausible origin of the signal is the cumulative strain from the mergers of supermassive black holes at the center of galaxies across the history of the universe. I will discuss how the impact of dark matter dynamical friction on the black hole binary evolution can address some of the questions that this discovery raises. This includes the solution of the “final parsec problem” by which mergers would otherwise stall before gravitational wave emission can drive the coalesce. I will argue that the observational data favor the existence of dark matter self interactions with a cross-section and velocity dependence consistent with the ones capable of solving the small-scale structure problems of collisionless cold dark matter.

The absence of dark matter signals in direct detection experiments and collider searches has prompted interest in models in which dark matter belongs to a hidden sector minimally coupled to the Standard Model. In these scenarios, a long-lived massive particle might come to dominate the energy density of the early universe temporarily, causing an early matter-dominated era (EMDE) prior to the onset of nucleosynthesis. During an EMDE, matter perturbations grow more rapidly than they would in a period of radiation domination, which leads to the formation of microhalos as early as a redshift of ~5000. These microhalos generate distinct observable signatures, but the constraints on these signatures are highly sensitive to the small-scale cut-off in the matter power spectrum. We discuss the effects of an EMDE on the matter power spectrum, focusing on cases where the particle that dominates the Universe during the EMDE was initially relativistic, and the small-scale cut-off in the power spectrum is set by its pressure support. In addition, we present N-body simulations of the formation and dissipation of microhalos due to an EMDE, which imposes a free-streaming cut-off on the power spectrum after the EMDE. We discuss the implications of this gravitational heating on the (re)formation of microhalos close to the epoch of matter-radiation equality. We constrain these EMDE cosmologies using the observations of the Isotropic Gamma Ray Background and the boosted annihilation rates from the early bound structures resulting from an EMDE. In addition, we discuss prospects for observing these microhalos through pulsar timing arrays and microlensing.

The fundamental nature of dark matter (DM) so far eludes direct detection experiments, but it has left its imprint in the cosmic web. The standard cold DM model is remarkably well tested by cosmic microwave background and low-redshift galaxy surveys, but well-motivated particle candidates like ultra-light axions will leave signatures on small cosmic scales. These signatures are stronger at earlier times. Future 21 cm observations will transform our view of the primordial Universe, but we are already observing some of the first visible tracers of cosmic structure in the high-redshift galaxy population through the Hubble and James Webb Space Telescopes. I will present calculations of the effects of DM candidates like ultra-light axions on the high-z galaxy UV luminosity function. I will then present Hubble and Webb constraints on the allowed fraction of ULAs, accounting for uncertainties in how early galaxies trace the halo population, and discuss the implications for DM solutions to discrepancies in the late-time clustering of matter (S_8 tension).