Talks

This study presents the modeling of the gravitational wave (GW) bias parameter by bridging a connection between simulated GW sources and galaxies in low redshift galaxy surveys 2MPZ and WISExSCOS (WISC). We study this connection by creating a mock GW catalog, populating galaxy surveys with binary black holes (BBHs) for different scenarios of the GW host-galaxy probability as a function of the galaxy stellar mass. We probe the observable consequences of this connection by exploring the spatial clustering of the GW sources in terms of the GW bias parameter. We consider a phenomenological broken power law model for the host-galaxy probability function, with a potential turnover M_K at high stellar mass (10^{11} solar mass in the fiducial model) where the star formation efficiency begins to drop. We vary the parameters of the GW host-galaxy probability function and find that generically the GW bias increases as M_K increases (and gets suppressed as M_K decreases). The change in the GW bias parameter shows a maximum change of about 30% for different scenarios explored in this work in comparison to the galaxy bias. Future measurements of the GW bias can help constrain M_K and the slopes of the host-galaxy probability function and thus offer insights into the underlying astrophysical processes.

Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily forbids useful knowledge about the other. Two quantum measurements that do not commute form an example of complementary measurements, and this phenomenon can also be defined for ensembles of states. Although a key quantum feature, it is unclear whether complementarity can be understood more operationally, as a necessary resource in some quantum information task. Here we show this is the case, and relates to a task which we term unambiguous exclusion. As well as giving complementarity a clear operational definition, this also uncovers the foundational underpinning of unambiguous exclusion tasks for the first time.

In this talk, I will present the construction of the Yangian of a cotangent Lie algebra from the geometry of the equivariant affine Grassmannian. Furthermore, I will discuss how this quantum group can be dynamically twisted to a quantum groupoid over a neighborhood in the moduli space of G-bundles over a compact Riemann surface. These constructions are motivated by relations between a certain holomorphic-topological 4d gauge field theory and the geometric Langlands correspondence. Representations of the Yangian are pertubative line operators of said theory, while the dynamical twist of the Yangian controls the action of these operators via Hecke modifications in this setting. This talk is based on the two joint works arXiv:2405.19906 and arXiv:2411.05068 with Wenjun Niu.

In this talk, we develop a comprehensive framework for realizing anyon condensation of topological orders within the string-net model by constructing a Hamiltonian that bridges the parent string-net model before and the child string-net model after anyon condensation. Our approach classifies all possible types of bosonic anyon condensation in any parent string-net model and identifies the basic degrees of freedom in the corresponding child models. Compared with the traditional UMTC perspective of topological orders, our method offers a finer categorical description of anyon condensation at the microscopic level. We also explicitly represent relevant UMTC categorical entities characterizing anyon condensation through our model-based physical quantities, providing practical algorithms for calculating these categorical data.

Various models of physics beyond the Standard Model predict the existence of ultralight bosons. These particles can be produced through superradiant instabilities, which create boson clouds around rotating black holes, forming so-called "gravitational atoms". In this talk, I review a series of papers that study the interaction between a gravitational atom and a binary companion. The companion can induce transitions between bound states of the cloud (resonances), as well as transitions from bound to unbound states (ionization). These processes back-react on the binary’s dynamics and leave characteristic imprints on the emitted gravitational waves (GWs), providing direct information about the mass of the boson and the state of the cloud. However, some of the resonances may destroy the cloud before the binary enters the frequency band of future gravitational wave detectors. This destruction leaves a mark on the binary’s eccentricity and inclination, which can be identified through a statistical analysis of a population of binary black holes.

Quasi-Einstein equations are generalizations of the Einstein equation. They arise from warped product Einstein metrics (Kaluza-Klein reductions), Ricci solitons, cosmology, near-horizon geometries, and smooth measured Lorentzian length spaces. Despite their apparent generality, they often have a surprising rigidity. I will review some recent developments in the area, focusing on near-horizon geometries, including Dunajski and Lucietti's near-horizon version of the Hawking rigidity theorem. I will discuss an application to 5-dimensional extreme (Myers-Perry type) black holes whose horizons admit the structure of the group SU(2).