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The double copy relates scattering amplitudes in gauge theory and gravity. But interaction potentials (and spacetime metrics) can be extracted from amplitudes, and so the double copy leads to a relationship between classical solutions of gauge theory and gravity. In this talk I will describe this relationship, provide a perspective on the Schwarzschild metric as a “square” of the Coulomb charge, and take a look at the “square root” of the Kerr metric.

In the last few years there have been demonstrations of quantum advantage using noisy quantum circuits that are believed to go beyond the limits of the classical computers that exist today.  In this talk I will give an overview of a different type of quantum advantage that can be attained by shallow (short-depth) quantum circuits.  I will discuss recent results which establish unconditionally that constant-depth quantum circuits can solve certain linear algebra problems faster than their classical counterparts. We will see that the reason quantum computers solve these problems provably faster (as measured by circuit depth) than classical computers is due to a strong form of quantum nonlocality that is present in their input/output statistics. 

Zoom Link: https://pitp.zoom.us/j/96752851897?pwd=R29GWHovN0MwVXVYWklaNE1QZ1c5dz09

In 1930, the famous statistician and geneticist Ronald Fisher claimed to have proved a "fundamental theorem of natural selection". He compared this result to the second law of thermodynamics, and described it as holding "the supreme position among the biological sciences". But others found it obscure, and in its most obvious interpretation it is simply false. Luckily there is a true result closely resembling Fisher's claim: a general theorem connecting dynamical systems and information theory. I'll explain this, give the very simple proof, and draw a few conclusions.

Zoom Link: https://pitp.zoom.us/j/99898585189?pwd=NytLaWt2RjFPOTVJOEptMlBBd1BvZz09

In the last quarter century, Capra has grown from a mere handful of people to a fully international meeting, which now represents a large diversity of interests. In that time, much progress has been made: many aspects of the first order problem are now in hand, and a multitude of techniques has been formulated for eventually use in full EMRI waveform generation. Yet, much needs to be done, most notably at second order. In Capra meetings of the past, we have often recognized the need to reach out to the younger generation. I think efforts in that direction have clearly been effective. At some Capra meetings, specific problems have often taken focus, both in discussions at the meeting, and in the work that evolves over the coming year. From experience, we know this approach has also clearly paid off. From the discussions that have taken place here, we need to go forward with specific goals for the year ahead, drawing wherever possible on the diversity we now have before us. Great things can be achieved if great problems are tackled. What have we formulated to work on as a community together before we can meet again in 2022?

The open question of whether a black hole can become tidally deformed by an external gravitational field has profound implications for fundamental physics, astrophysics and gravitational-wave astronomy. Love tensors characterize the tidal deformability of compact objects such as astrophysical (Kerr) black holes under an external static tidal field. We prove that all Love tensors vanish identically for a Kerr black hole in the nonspinning limit or for an axisymmetric tidal perturbation. In contrast to this result, we show that Love tensors are generically nonzero for a spinning black hole. Specifically, to linear order in the Kerr black hole spin and the weak perturbing tidal field, we compute in closed form the Love tensors that couple the mass-type and current-type quadrupole moments to the electric-type and magnetic-type quadrupolar tidal fields. For a dimensionless spin ~ 0.1, the nonvanishing quadrupolar Love tensors are ~ 0.002, thus showing that black holes are particularly "rigid" compact objects. We also show that the induced quadrupole moments are closely related to the physical phenomenon of tidal torquing of a spinning body interacting with a tidal gravitational environment.

The prospect of gravitational wave astronomy with EMRIs has motivated increasingly accurate perturbative studies of binary black hole dynamics. Studying the apparent and event horizon of a perturbed Schwarzschild black hole, we find that the two horizons are identical at linear order regardless of the source of perturbation. This implies that the seemingly teleological behaviour of the linearly perturbed event horizon, previously observed in the literature, cannot be truly teleological in origin. The two horizons do generically differ at second order in some ways, but their Hawking masses remain identical. In the context of tidal distortion by a small companion, we also show how the perturbed event horizon in a small-mass-ratio binary is effectively localized in time, and we numerically visualize unexpected behaviour in the black hole’s motion around the binary’s center of mass.

We show that perturbations of massless fields in the Kerr black hole background enjoy a hidden infinite-dimensional ("Love") symmetry in the properly defined near zone approximation. Love symmetry mixes IR and UV modes. Still, this approximate symmetry allows us to derive exact results about static tidal responses (Love numbers) of static and spinning black holes. Generators of the Love symmetry are globally well defined and have a smooth Schwarzschild limit. The Love symmetry contains an SL(2,R)×U(1) subalgebra. Generic regular solutions of the near zone Teukolsky equation form infinite-dimensional SL(2,R) representations. In some special cases these are highest weight representations. This situation corresponds to vanishing Love numbers. In particular, static perturbations of four-dimensional Schwarzschild black holes belong to finite-dimensional representations. Other known facts about static Love numbers also acquire an elegant explanation in terms of the SL(2,R) representation theory.