Scientific Series

In this talk, we will provide an overview of recent developments in the quantization of Cylindrically symmetric spacetimes, which contain the Einstein-Rosen gravitational waves. This class of solutions leads to an integrable field theory, and its phase space can be expressed directly in terms of initial data living on a null generator. The corresponding Poisson algebra appears in the double null sheet formulation of full 3+1 gravity (Reisenberger, 2007), as essentially a Poisson subalgebra on each null generator. This suggests that the algebraic quantization introduced by Korotkin-Samtleben in the context of cylindrically symmetric gravity is relevant for the search for the full quantum theory. We will present some results concerning this quantum algebra, where two Wick-type algebraic structures emerge. Finally, we will discus the known quantization of the Einstein-Rosen waves with one polarization, due to Ashtekar-Pierri, as a subsector of the general two polarizations case.

Gravitational waves (GW) from compact binaries provide excellent opportunities for testing general relativity (GR) in the strong- and dynamical-field regime. So far, inspiral-based tests have mostly assumed smooth deviations from GR within a post-Newtonian description, thereby overlooking certain beyond-GR effects that can arise in well-motivated extensions including quantum gravity, dark energy, and dark matter. In this talk, I will present an example of such an overlooked effect arising from massive scalar fields nonminimally coupled to gravity, and discuss recent constraints on this scenario using GW observations. I will then introduce a recently developed AI-based approach that incorporates both smooth and nonsmooth deviations within a unified, theory-agnostic parametrization for inspiral tests of GR. 

Discs are among the simplest manifolds, but their groups of diffeomorphisms can be very complicated. I will describe the techniques from geometry, topology, and dynamics that were used to understand these groups in low dimensions, the relationship of these groups to stable homotopy theory and number theory in high dimensions, and recent breakthroughs in understanding their rational homotopy type. This talk will be aimed at a broader audience.

Non-local quantum computation studies the complexity of implementing quantum channels non-locally and has fascinating connections to cryptography, complexity theory and quantum gravity. In this talk, I will survey some of these connections, with an emphasis on circuit and communication complexity. Building on ideas, I will present new lower bounds on the magic cost of quantum gates, quantum speedups in communication, and approaches to position verification with privacy guarantees.

The Kawai–Lewellen–Tye (KLT) relations are a striking example of how string theory can reveal hidden structures and connect a web of, in principle, very different theories. Originally, they state that (tree-level) closed-string amplitudes can be expressed as quadratic combinations of open-string amplitudes. In the field theory limit, this gives rise to the celebrated double-copy between gluons and gravitons. In this talk, I will discuss how much of this elegant structure survives away from flat space, focusing on AdS. As a first step, I will propose the fundamental building blocks of tree-level string amplitudes in AdS and then show how they are related via an AdS version of the KLT relations, whose kernel can be computed exactly. This structure not only significantly simplifies explicit calculations but also points to deeper algebraic and geometric structures to be uncovered.

This talk will be a brief and interactive introduction to my current research and the cosmological concepts that go along with it. I will assume limited prior knowledge of GR and cosmology so that even students in unrelated fields can learn something interesting.

When dealing with QFTs or with quantum mechanical systems in the thermodynamic limit, one encounters uncountable Hilbert spaces. These are mathematically wilder and physically less realistic than their countable counterparts. In this talk, we will explore how vacua encode a choice to reduce the Hilbert Space in size. In spite of the mathematically sounding intro, we’ll see this has interesting physical implications.