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Recently powerful techniques have emerged for performing multi-loop computations of scattering amplitudes in quantum gravity and  supergravity.  These techniques include generalized unitarity and the double-copy property, related to color-kinematics duality in gauge theory.  Using these  techniques, the ultraviolet divergence structure of N=8 supergravity, and more recently pure N=4 supergravity, have been assessed, not only in four space-time dimensions but also in higher dimensions.  The results can be compared to expectations based on potential counterterms that can be constructed using (conjectured) superspace formalisms or nonlinear symmetry constraints.  Interestingly, the critical ultraviolet dimension in which N=8 supergravity first diverges is equal to that for N=4 super-Yang-Mills theory through four loops.  If this statement were to hold to all loop orders, then N=8 supergravity would represent a perturbatively finite, point-like theory of quantum gravity in four dimensions.  In this talk, I will review all of this recent progress.

I describe recent work with with Stefan Hollands that establishes a new criterion for the dynamical stability of black holes in $D \geq 4$ spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamic stability is equivalent to the positivity of the canonical energy, $\mathcal E$, on a subspace of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon.  We further show that $\mathcal E$ is related to the second order variations of mass, angular momentum, and horizon area by $\mathcal E = \delta^2 M - \sum_i \Omega_i \delta^2 J_i - (\kappa/8\pi) \delta^2 A$, thereby establishing a close connection between dynamic stability and thermodynamic stability.

Thermodynamic instability of a family of black holes need not imply dynamic instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that all black branes corresponding to
thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of $\mathcal E$ is equivalent to the satisfaction of a ``local Penrose inequality,'' thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability.

The direct detection of gravitational waves promises to open up a new spectrum that is otherwise mostly closed to electromagnetically based astronomical observations. Detecting gravitational waves from binary black holes and neutron stars, as well as estimating their parameters, requires a sufficiently accurate prediction for the expected waveform signal. Unfortunately, the state of the art for the pillars of gravitational wave theory -- numerical relativity, the post-Newtonian approximation, and linear black hole perturbation theory -- have yet to cover accurately the entire parameter space even when taken together. In this talk, I present a new direction for systematically describing compact binaries that is valid over a potentially very large portion of the parameter space.

The approach uses high-order black hole perturbation theory in the mass ratio together with ideas and techniques borrowed from effective field theory for incorporating the physics of extended masses like spin and tidal effects. I discuss recent advances, future prospects, and potential impacts in this direction.

Spins play a major role in the strong-field dynamics of
black-hole binaries and their gravitational-wave emission. By detecting spin
effects in the waveforms, existing and future gravitational-wave detectors
therefore provide a natural way to test gravity in strong-field, highly
dynamical regimes.

In the first part of my talk, I will show that the
inclusion of the spins in the gravitational templates for future space-based
detectors will permit testing scenarios for the formation and cosmological
evolution of supermassive black holes, and possibly shed light on models of
galaxy formation. In the second part, I will show that the effective-one-body
(EOB) model provides an efficient way to account for spin effects in both the
dynamics and waveforms, by combining information from post-Newtonian theory,
the self-force formalism, and numerical-relativity simulations.

The ground-based gravitational-wave telescopes LIGO and Virgo approach the era of first detections.  Gravitational-wave observations will provide a unique probe for exploring strong-field general relativity and compact-binary astrophysics.  In this talk, I describe recent predictions regarding the distributions of black-hole and neutron-star binary mergers, and progress on solving the inverse problem of turning gravitational-wave observations into astrophysical information. I highlight some exciting recent investigations into the use of gravitational waves as tests of general relativity.

Causal dynamical triangulations (CDT) define a nonperturbative path integral for quantum gravity as a sum over triangulations. Causality is enforced on the kinematical level by means of a preferred
foliation.

In this talk I present a new model of dynamical triangulations based on Lorentzian building blocks, where the triangulations in general do not have such a preferred foliation. The essential ingredients of the new model are a local causality constraint and a consistency condition on the global flow of time. After a compact review on CDT I discuss the theoretical aspects of the new model in 1+1 and 2+1 dimensions, followed by a presentation of numerical results in 2+1 dimensions. These results show that the new model and CDT have similar long-distance properties in 2+1 dimensions.

By way of presenting some classic and many new results, my talk will indulge shamelessly in
advertising "Causal Dynamical Triangulations (CDT)" as a hands-on approach to nonperturbative quantum gravity that reaches where other approaches currently don't. After summarizing the rationale and basic ingredients of CDT quantum gravity and some of its key findings (like the emergence of a classical de Sitter space), I will focus on some very recent results: how we uncovered the presence of a second-order phase transition (so far unique in 4D quantum
gravity), news on the controversy between doing things the Lorentzian or the Euclidean way, and new results on the role of the preferred time slicing in CDT - all hopefully worth your while!

We discuss well-posed initial-boundary value formulations
in general relativity. These formulations allow us to construct solutions of
Einstein's field equations inside a cylindrical region, given suitable initial
and boundary data. We analyze the restrictions on the boundary data that result
from the requirement of constraint propagation and the minimization of spurious
reflections, and choosing harmonic coordinates we show how to cast the problem
into well-posed form. Then, we consider the particular case where the boundary
represents null infinity of an asymptotically flat spacetime. Here, the rôle of
the boundary conditions is to provide adequate regularity and gauge conditions
at infinity.

As an application of our setup we mention ongoing work on
the computation of quasi-stationary scalar field configurations on a
non-rotating supermassive black hole background.

Causal set quantum gravity is based on the marriage between the concept of causality as an organising principle more basic even than space or time and fundamental atomicity. Causal sets suggest novel possibilities for "dynamical laws" in which spacetime grows by the accumulation of new spacetime atoms, potentially realising within physics C.D. Broad's concept of a growing block universe
in which the past is real and the future is not. To do justice to relativity and general covariance, the atoms must accumulate in a partial order, exactly the order that the atoms have physically amongst themselves. That this is possible is demonstrated by the Rideout-Sorkin Classical Stochastic Growth models. This proof of concept -- of the compatibility of relativity and ``becoming'' -- is, however, classical and is challenged by the global character of the physical world within a path integral framework for quantum theory. Out of the struggle to reconcile the global and local natures of the physical world may arise a quantal dynamics for causal sets.