Talks

The Petrov classification of the Weyl tensor is an important tool in the study of exact solutions of the Einstein equation in 4d. For example, the Kerr solution was discovered in a study of spacetimes with algebraically special Weyl tensors. Algebraic classification of the Weyl tensor has been extended to higher dimensions. I shall review this classification and describe known families of algebraically special solutions. Recent progress towards obtaining a higher dimensional generalization of the Goldberg-Sachs theorem will be described.

I will discuss recent joint work with A. Ionescu and S. Klainerman on the black hole uniqueness problem. A classical result of Hawking (building on earlier work of Carter and Robinson) asserts that any vacuum, stationary black hole exterior region must be isometric to the Kerr exterior, under the restrictive assumption that the space-time metric shouldbe analytic in the entire exterior region. We prove that Hawking's theorem remains valid without the assumption of analyticity, for black hole exteriors which are apriori assumed to be ''close'' to the Kerr exterior solution in a very precise sense. Our method of proof relies on certain geometric Carleman-type estimates for the wave operator. Time permitting, some more recent developments will also be surveyed.

Einstein's theory of General Relativity has taught us that empty space (or, more precisely, spacetime) is in itself a dynamical and wonderfully rich entity for both theoretical physicists and science fiction authors alike. Although it may stretch our imagination, astrophysical observations leave little doubt that spacetime can bend, move and vibrate. If we want to explain these phenomena from an underlying microscopic and more fundamental structure, we need to bring in quantum theory, leading to even more exotic possibilities such as spacetime foam and wormholes. Do they really exist? How would we know? Are they in conflict with known physics? At least some of these questions may already be within the reach of our fundamental physical theories, not just qualitatively, but also quantitatively. In this talk, Professor Loll will share her insights into how much we know and how much we can still hope to learn about quantum gravity - the elusive quantum theory of space and time.

I will describe a very special (infinite-parameter) family of gravity theories that all describe, exactly like General Relativity, just two propagating degrees of freedom. The theories are obtained by generalizing Plebanski's self-dual (chiral) formulation of GR. I will argue that this class of gravity theories provides a potentially powerful new framework for testing the asymptotic safety conjecture in quantum gravity.

Non-relativistic quantum mechanics is derived as an example of entropic inference. The basic assumption is that the position of a particle is subject to an irreducible uncertainty of unspecified origin. The corresponding probability distributions constitute a curved statistical manifold. The probability for infinitesimally small changes is obtained from the method of maximum entropy and the concept of time is introduced as a book-keeping device to keep track of how they accumulate. This requires introducing appropriate notions of instant and of duration. A welcome feature is that this entropic notion of time incorporates a natural distinction between past and future. The Schroedinger equation is recovered when the statistical manifold participates in the dynamics in such a way that there is a conserved energy: its curved geometry guides the motion of the particles while they, in their turn, react back and determine its evolving geometry. The phase of the wave function—not just its magnitude—is explained as a feature of purely statistical origin. Finally, the model is extended to include external electromagnetic fields and gauge transformations.

The seminar is devoted to the solution of the AdS/CFT spectral problem, both for infinite and finite volume cases, using integrability. The basic constructions will be explained using an analogy with the relativistic O(4) sigma model. We devote a special attention to the study of the so called dressing factor. This is a scalar factor of the scattering matrix fixed using discrete crossing symmetry. We will show how to explicitly solve the equations dictated by the crossing symmetry, discuss essential properties of the dressing factor and give a shorthand and suggestive notation for the Bethe Ansatz of AdS/CFT. Then we will sketch a shorthand way to pass from the Bethe Ansatz to the Y-system.

Dark matter, constituting a fifth of the mass-energy in the Universe today, is one of the major "known unknowns" in physics. A number of different experimental and observational techniques exist to try to identify dark matter. However, these techniques are not only sensitive to the "physics" of dark matter (mass, cross sections, and the theory in which the dark matter particles live) but to the "astrophysics" of dark matter as well, namely the phase-space density of dark matter throughout the Milky Way and other galaxies and its evolution through cosmic time. In order to accurately map signals in experiments or observations to the particle-physics properties of dark matter, we need to understand the astrophysics of dark matter. In this talk, I will demonstrate how to get robust constraints on the particle-physics properties of dark matter either by careful modeling the astrophysics properties of dark matter or by elevating the astrophysics properties of dark matter as something to be extracted from future data sets alongside particle-physics parameters, and which approach (modeling vs. empirical) is more useful for given problems. As an example, I will show which aspects of the local dark-matter phase-space density can be understood through modeling and which aspects may be possible to infer empirically, and what the implications are for determining the particle-physics of dark matter from direct and indirect detection.