Talks

The detections of gravitational waves (GWs) from merging binary black holes (BHs) have motivated many studies on the dynamical formation of such compact black hole binaries (BHBs). Recent works have suggested that tertiary-induced merger via Lidov–Kozai (LK) oscillations may play a significant role in producing the BHBs detected by the LIGO/VIRGO collaboration. I will talk about the dynamics of merging compact binaries near a rotating supermassive black hole (SMBH) in a hierarchical triple configuration, including various general relativistic (GR) effects. I will show that these GR effects significantly increase the merger fraction of BHBs and produce a wide range of spin orientations when the BHB enters LIGO band. I will also discuss the hierarchical BH mergers in multiple systems, focusing on the constraints on the formation of GW190412, GW190814 and GW190521-like events.

The problem of quantum gravity -- i.e. to determine the microscopic structure underlying quantum mechanical theories that reproduce general relativity at long distances -- is a major outstanding problem in modern physics.  Solving the quantum gravitational scattering problem is one sharp way to address this question.  While in principle effective field theory (EFT) provides a systematic framework for solving scattering problems, in quantum gravity the complete answer requires an infinite number of measurements and thereby fails to predict details of the microscopic structure.

I will present two developments that provide new insight into the gravitational scattering problem.   The first is a class of infinite-dimensional symmetries generically found to arise in gauge and gravitational scattering.  The infinite number of constraints implied by the symmetries are equivalent to quantum field theoretic soft theorems, which prescribe the pattern of soft radiation produced during a scattering event.  The second development is a reformulation of the gravitational scattering problem in which Lorentz symmetry is rendered manifest and realized as the action of the global conformal group in two dimensions.  This reformulation, which involves scattering particles of definite boost weight as opposed to energy, offers a new approach precisely because it does not admit the decoupling of low and high-energy physics that underpins the traditional EFT approach.  I will describe new perspectives ensuing from these developments on various properties of the gravitational scattering problem, including collinear limits, infrared divergences and universal behavior associated to black hole formation. 

Many physical states of interest, such as ground states of gapped quantum many-body systems, are expected to obey an area law of entanglement entropy. I will report on a series of recent results that suggest a deep connection between area law and two seemingly unrelated subjects: topological quantum field theory and quantum marginal problem. Recently, we deduced --- only using area law and quantum information-theoretic tools --- the existence of new topological charges and invariants associated with the domain walls between topologically ordered systems in two spatial dimensions. Moreover, the same set of tools were also used in finding a solution to the quantum marginal problem. This is the problem in which one asks whether a set of reduced density matrices on bounded subsystems are compatible with some globally well-defined many-body quantum state. Since this problem was first posed in 1959, a solution that goes beyond the mean-field ansatz has remained elusive until now. These results suggest that area law is not just a qualitative statement about entanglement; it is an important equation that lets us "solve" quantum many-body systems that appear in nature.

Based on arXiv:2008.11793 and arXiv:2010.07424