Scientific Series

In the Scholium in Newton's Principia which contains the discussions about absolute space, time, and the bucket experiment, Newton also posed a problem that Julian Barbour has denoted the "Scholium problem". Newton writes there "But how are we to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it". This problem was clearly considered very important by Newton who claims he wrote the Principia dedicated to this problem. Interestingly Newton never returned to the problem. In this talk we are going to give a mathematical precise formulation of the Scholium problem. A subpart of the Scholium problem consists of determining how accurate the observers clock is. We are going to start from that end and see that the problem of defining duration is inseparately intertwined with the full scholium problem.

We report on a new class of fast-roll inflationary models. In a part of its parameter space, inflationary perturbations exhibit quite unusual phenomena such as scalar and tensor modes freezing out at widely different times, as well as scalar modes reentering the horizon during inflation. One specific point in parameter space is characterized by extraordinary behavior of the scalar perturbations. Freeze-out of scalar perturbations as well as particle production at horizon crossing are absent. Also the behavior of the perturbations around this quasi-de Sitter background is dual to a quantum field theory in flat space-time. Finally, the form of the primordial power spectrum is determined by the interaction between different modes of scalar perturbations.

I will review the progress made in our understanding of the QCD phase diagram within an RG approach to QCD and effective QCD models. In particular this includes a discussion of the confinement-deconfinement phase transition/cross-over, the chiral phase transition/cross-over, as well as their interrelation.

The concept of renormalization lies at the heart of fundamental physics. I introduce in this talk the Connes-Kreimer algebraic approach for expressing renormalizability in quantum field theories as well as the extension of these notions to the manifestly non-local framework of noncommutative quantum field theories. Finally, I will present an attempt to further generalize these concepts to quantum gravity models. based on: 0909.5631 [gr-qc], Class. Quant. Grav. (in press)

In recent years the characterization of many-body ground states via the entanglement of their wave-function has attracted a lot of attention. One useful measure of entanglement is provided by the entanglement entropy S. The interest in this quantity has been sparked, in part, by the result that at one dimensional quantum critical points (QCPs) S scales logarithmically with the subsystem size with a universal coefficient related to the central charge of the conformal field theory describing the QCP. On the other hand, in spatial dimension d > 1 the leading contribution to the entanglement entropy scales as the area of the boundary of the subsystem. The coefficient of this "area law" is non-universal. However, in the neighbourhood of a QCP, S is believed to possess subleading universal corrections. In this talk, I will present the first field-theoretic study of entanglement entropy in dimension d > 1 at a stable interacting QCP - the quantum O(N) model. Our results confirm the presence of universal corrections to the entanglement entropy and exhibit a number of surprises such as different epsilon -> 0 limits of the Wilson-Fisher and Gaussian fixed points, violation of large N counting and subtle dependence on replica index.

Self-assembly refers to any thermodynamic process in which a bunch of particles (molecules, biomolecules, polymers, colloids) come together in solution to form an ordered structure. In living things it is a widely used and robust manufacturing tool: DNA, RNA and proteins spontaneously form three dimensional structures, and supramolecular structures emerge from protein aggregates with staggering degrees of ordering and specificity. By contrast, most synthetic systems in soft condensed matter do not assemble robustly. In this talk I will discuss experiments on simple systems that allow us to probe the physics and thermodynamics of self-assembly. We use systems consisting of small numbers (N ⇐ 12) of confined spherical colloidal particles to understand what physical parameters (interactions) determine how a system will assemble. We find that the probability of self-assembling a particular configuration can be understood in terms of the geometry of sphere packings. The geometrical model gives some insights into how phase transitions emerge as N approaches the bulk limit. At the same time, it yields some general insights into the design principles for robust self-assembly.

Primordial non-Gaussianity has been traditionaly constrained using three-point function of the cosmic microwave background. Two years ago, however, Dalal et al have shown that non-Gaussianity of the local type induces a scale dependent bias for biased tracers of the underlying dark matter structure. This allows constraining of the primordial non-Gaussianity from measurements of large-scale structure provided by redshift surveys. I will discuss the technique, its theoretical aspects, it surprising resilience towards systematics and current results from the real data. I will also show some preliminary new results: extension to the two field inflationary models and the analogue of the Dalal effect in the Lyman alpha forest.

F-theory based vacua provide a potentially promising starting point for realizing Grand Unified Theories (GUTs) in string theory. In minimal realizations of this framework based on a point of E8 unification, this turns out to be quite constraining, and leads to specific expectations for the form of supersymmetry breaking. We discuss how the parameters of the F-theory GUT determine the sparticle spectrum, and possible signatures at the LHC.

We show that when a volume of quark matter rotates, there is an axial current flowing along the rotation axis. This effect has been overlooked in all previous treatments of relativistic fluids until calculations using gauge/gravity duality indicate it existence. The effect is a manifestation of triangle anomalies, and may exhibit itself in heavy ion collisions with nonzero impact parameter.

Binary neutron stars are among the most important sources of gravitational waves which are expected to be detected by the current or next generation of gravitational wave detectors, such as LIGO and Virgo, and they are also thought to be at the origin of very important astrophysical phenomena, such as short gamma-ray bursts. In order to describe the dynamics of these events one needs to solve the full set of general relativistic magnetohydrodynamics equations through the use of parallel numerical codes. I will report on some recent results obtained with the use of the fully general relativistic magnetohydrodynamic code Whisky in simulating binary neutron stars which inspiral and merge forming an hypermassive neutron star which eventually collapses to form a black hole surrounded by a torus. I will in particular describe how mass, equation of state and magnetic fields can affect the dynamics and consequently the gravitational waves emitted by these systems and discuss about their possible connection with the formation of short gamma ray bursts.

"Extended" topological field theory generalizes ordinary TQFT to include spacetimes with boundary. Starting from a gauge theory of flat G-connections, and its boundary restriction, I will describe a plan for constructing an extended topological field theory, for any compact Lie group G. This is based on work-in-progress with Jeffrey Morton.