Colloquium

The Cosmic Web is the fundamental spatial organization of matter in the Universe on scales of a few up to a hundred Megaparsec, scales at which the Universe still resides in a state of moderate dynamical evolution. Galaxies, intergalactic gas and dark matter exist in a wispy weblike spatial arrangement consisting of dense compact clusters, elongated filaments, and sheetlike walls, amidst large near-empty void regions. The weblike pattern is marked by prominent anisotropic features, a distinct multiscale character, a complex spatial connectivity of its various morphological components and a clear asymmetry between voids and overdense regions.

This seminar will describe recent work on the structure and dynamics of the Cosmic Web. For the analysis of its complex and multiscale structural pattern, we invoke concepts from computational topology and computational geometry. We apply the explicit multi-scale -- parameter-free and scale-free -- Nexus/MMF Multiscale Morphology formalism to dissect the cosmic mass distribution into clusters, filaments, walls and voids. This results in a systematic study ofthe evolving size and volume distribution of these structural components. Subsequently, we assess the mass and halo distribution in the filaments and walls, and follow their evolution.

To study the dynamical evolution of the cosmic web, we describe our adhesion model of cosmic structure formation based on Voronoi and Delaunay tessellations. Subsequently, we will shortly describe how a full phase-space analysis allows us to understand the growth of structural complexity in terms of the emergence and spatial connectivity of singularities and caustics. Finally, we will discuss the migration flows of matter and galaxies along the cosmic web and prospects of using voids to constrain dark energy and dark matter.

With the groundbreaking gravitational wave detections from LIGO/VIRGO, we have entered the era where we can actually observe the action of strongly curved spacetime originally predicted by Einstein.  Going hand in hand with this, there has been a renaissance in the theoretical and computational tools we use to understand and interpret the dynamics of gravity and matter in this regime.  I will describe some of the rich behavior exhibited by sources of gravitational waves such as the mergers of black holes and neutron stars. I will also discuss some of the open questions, and what these events could teach us, not only about the extremes of gravity, but about the behavior of matter at nuclear densities, the solution of astrophysical mysteries, and even the existence of new particles.

I will give an overview of the causal set approach to quantum gravity, and what makes this "fork in the road" distinct from other approaches.  Motivated by deep theorems in Lorentzian geometry, causal set theory (CST) posits that the underlying fabric of spacetime is  atomistic and encoded in a locally finite partially ordered set. In  the continuum  approximation,  the partial order corresponds to the causal structure, and the cardinality to the conformal factor.  Together, these give the approximate continuum geometry.  Lorentz invariance emerges as a consequence, but brings with it a certain  "non-locality”, which distinguishes CST  from other approaches in an essential way. It also makes the  reconstruction of spacetime geometry from the causal set particularly challenging.  I will describe some of the progress we have made in this geometric reconstruction program. I will then describe a particular formulation of CST dynamics inspired by the continuum path integral and discuss what we have learnt so far and where it is taking us. 

There is a long tradition of formulating Quantum Theory in an operational manner.  In one version of this a circuit is formed by wiring together operations. Each operation has knob settings and outcomes (lights flashing, detectors clicking, ..).  The question raised and answered in this colloquium is whether we can do the same for General Relativity.  There are hurdles that have to be overcome to do this - in particular, we need to define a diffeomorphism invariant notion of operations, identify what the knob settings and outcomes are, and what the wiring corresponds to.   In this colloquium I will provide an outline of how to formulate General Relativity like this providing a possibilistic calculus (we can calculate whether operationally described situations are possible or not).  This provides the beginnings of an operational approach to the problem of Quantum Gravity.  This talk is based on arxiv:1608.06940.  

The observed deviations from the laws of gravity of Newton and Einstein in galaxies and clusters can logically speaking be either due to the presence of unseen dark matter particles or due to a change in the way gravity works in these situations. Until recently there was little reason to doubt that general relativity correctly describes gravity in all circumstances. In the past few years insights from black hole physics and string theory have lead to a new theoretical framework in which the gravitational laws are derived from the quantum entanglement of the microscopic information that is underlying space-time. An essential ingredient in the derivation is of the Einstein equations is that the vacuum entanglement obeys an area law, a condition that is known to hold in Anti-de Sitter space due to the work of Ryu and Takayanagi. We will argue that in de Sitter space due to the positive dark energy, that the microscopic entanglement entropy also contains also a volume law contribution in addition to the area law. This volume law contribution is related to the thermal properties of de Sitter space and leads to a total entropy that precisely matches the Bekenstein-Hawking formula for the cosmological horizon. We study the effect of this extra contribution on the emergent laws of gravity, and argue that it leads to a modification compared to Einstein gravity. We provide evidence for the fact that this modification explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

 I will present several studies showing a surprising pattern. Not only can preschoolers learn abstract higher-order principles from data, but younger learners are actually better at inferring unusual or unlikely principles than older learners and adults. This pattern also holds for children in Peru and in Headstart programs in Oakland, California. I relate this pattern to computational ideas about search and sampling, to evolutionary ideas about human life history, and to neuroscience findings about the negative effects of frontal control on wide exploration. My hypothesis is that our distinctively long, protected human childhood allows an early period of broad hypothesis search, exploration and creativity, before the demands of goal-directed action set in.

The modeling of pulsar radio and gamma-ray emission suggests that in order to interpret the observations one needs to understand the field geometry and the plasma state in the emission region. In recent years, significant progress has been achieved in understanding the magnetospheric structure in the limit of abundant plasma supply. However, the very presence of dense plasma everywhere in the magnetosphere is not obvious. Even the region where the observed emission is produced is subject to debate. To address this from first principles, we constructed global kinetic simulations of pulsar magnetospheres using relativistic Particle-in-Cell codes, which capture the physics of plasma production and particle acceleration. In this talk I will describe how plasma is produced in magnetospheres of pulsars and show that effects of general relativity are crucial for the activity of pulsars with low inclination angles. I will present modeling of high-energy lightcurves, calculated self-consistently from particle motion in the pulsar magnetosphere. I will also show evidence that observed radio emission is powered by non-stationary discharge at the polar cap. Finally, I will argue that giant radio pulses in the Crab are produced by coherent plasma currents, which appear at the interfaces of merging plasmoids in the current sheet beyond the light cylinder.

Over the past several years, our understanding of topological electronic phases of matter has advanced dramatically.   A paradigm that has emerged is that insulating electronic states with an energy gap fall into distinct topological classes.   Interfaces between different topological phases exhibit gapless conducting states that are protected topologically and are impossible to get rid of.   In this talk we will discuss the application of this idea to the quantum Hall effect, topological insulators,  topological superconductors and the quest for Majorana fermions in condensed matter.   We will then show that similar ideas arise in a completely different class of problems.    Isostatic lattices are arrays of masses and springs that are at the verge of mechanical instability.   They play an important role in our understanding of granular matter, glasses and other 'soft' systems.  Depending on their geometry, they can exhibit zero-frequency 'floppy' modes localized on their boundaries that are insensitive to local perturbations.   The mathematical relation between this classical system and quantum electronic systems reveals an unexpected connection between theories of hard and soft matter.

The existence of a deconfined quantum-critical point [1] between the standard antiferromagnet
and a valence-bond solid in 2D S=1/2 quantum magnets has been controversial, in part due to
anomalous finite-size scaling behaviors observed in quantum Monte Carlo simulations interpreted by some as signs of a first-order transition. I will discuss a new finite-size scaling hypothesis in which a scaling function of two divergent length scales [the standard correlation length and a length-scale related to an emergent U(1) symmetry of the valence-bond solid] has a limiting form implying unconventional finite-size scaling behaviors, while maintaining conventional scaling in the thermodynamic limit [2]. This proposal goes beyond the standard scenario of a dangerously irrelevant perturbation as a source of the second length scale in, e.g., classical 3D clock models. Quantum Monte Carlo simulations of the J-Q model (a spin-1=2 Heisenberg model extended with certain multi-spin interactions) are in full agreement with the proposed scaling form, suggesting that deconfined quantum-criticality is an even richer phenomenon than initially imagined. Since finite temperature T plays the role of a finite imaginary-time dimension in quantum systems, the anomalous scaling behavior impacts also the scaling in the quantum-critical \fan" at T > 0. This is also observed in the J-Q model.

[1] H. Shao, W. Guo, and A. W. Sandvik, Science 352, 213 (2016).
[2] T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, M. P. A. Fisher, Science 303, 1490 (2004).

An overview will be given of recently discovered connection between asymptotic symmetries in general relativity  and soft theorems in quantum field theory together with their implications for the black hole information paradox.