Talks

Motivated by the frame independence of the Bekenstein-Hawking black hole entropy, and the possibility of it being fundamentally entanglement entropy, I will present a spacetime definition for the entanglement entropy of free quantum fields. This definition is a spectral formulation, conducive to frame independent regularization. I will then go on to show an example calculation in Rindler spacetime, and comment on more general applications.

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.

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.

In this talk, we develop a systematic framework for understanding symmetries in topological phases in \(2+1\) dimensions using the string-net model, encompassing both gauge symmetries that preserve anyon types and global symmetries permuting anyon types, including both invertible symmetries describable by groups and noninvertible symmetries described by categories. As an archetypal example, we reveal the first noninvertible categorical gauge symmetry of topological orders in \(2+1\) dimensions: the Fibonacci gauge symmetry of the doubled Fibonacci topological order, described by the Fibonacci fusion \(2\)-category. Our approach involves two steps: first, establishing duality between different string-net models with Morita equivalent input UFCs that describe the same topological order; and second, constructing symmetry transformations within the same string-net model when the dual models have isomorphic input UFCs, achieved by composing duality maps with isomorphisms of degrees of freedom between the dual models.

We present a tensorization algorithm for constructing tensor train representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the tensor train representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing tensor trains in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.