Colloquium

Some of the speculations on new physics, beyond what is in the standard model are reviewed. Particular attention is paid to ideas that try to address the hierarchy puzzle, i.e., why is the weak scale so much smaller than the Planck scale. These new theories will be tested at the large hadron collider in the near future.

Neural circuits exhibit complex patterns of spontaneous activity. I will discuss how neural network models can reproduce this activity and how it interacts with responses evoked by sensory stimuli. This work involves analytic, mean-field and computer analyses of large systems of nonlinear differential equations with random parameters.

Experimentalists at the Relativistic Heavy Ion Collider create exploding droplets of quark-gluon plasma, the stuff which filled the universe for the first microseconds after the big bang. I'll give one theorist's perspective on what we are learning about the properties of quark-gluon plasma from these experiments, including the conclusion that it is closer to an ideal liquid than to an ideal gas and the observation that it "quenches" high energy quarks ("jets") trying to plow through it. The static properties of quark-gluon plasma can be calculated from first principles, but we have no rigorous calculations of what QCD predicts for the viscosity and jet quenching ability of the evidently very strongly interacting quark-gluon plasma that RHIC has discovered. In desperation, theorists are resorting to calculating the properties of quark-gluon plasma in theories other than QCD, wherein difficult dynamical questions like how does a strongly interacting plasma quench jets can be answered by doing easy string theory calculations. I will discuss two examples where such calculations have been compared quantitatively to inferences drawn from existing RHIC data, and close with one prediction for data to come.

Soon after Quantum Chromodynamics (QCD) was shown to exhibit asymptotic freedom at short distances, it was realized that it might be possible to create a new form of matter at high temperatures (T „d 150 MeV) in which hadrons dissolve and quarks and gluons become locally deconfined. Experiments have been carried out for the last two decades attempting to create this new form of matter, called ¡§quark-gluon plasma¡¨ (QGP), via high-energy collisions of large nuclei. In 2000, the Relativistic Heavy Ion Collider (RHIC) started operation at Brookhaven National Laboratory in the US and results obtained from the first five years of RHIC operation provide the first convincing evidence for creation of the quark-gluon plasma in the laboratory. Measurements at RHIC show that the QGP is opaque to the passage of high-energy quarks and gluons and that interactions between the quarks and gluons in the QGP appears to be much stronger than initially expected. The estimated viscosity to entropy ratio of the QGP has been interpreted as showing that the QGP produced at RHIC is the most perfect fluid ever observed in the laboratory. Measurements from RHIC also suggest that the strong, coherent gluon fields in the incident nuclei play a significant role in the initial particle production and early evolution of the quark gluon plasma. Within the next few years, the large hadron collider will provide Pb+Pb collisions at a nucleon-nucleon center of mass energy of 5.5 TeV, thus opening a new frontier in the study of the QGP. I will provide a summary of the key experimental observables at RHIC, a discussion of their canonical interpretation and then discuss how measurements at the LHC can be used to test these interpretations.

With a cosmic flight simulator, we'll take a scenic journey through space and time. After exploring our local Galactic neighborhood, we'll travel back 13.7 billion years to explore the Big Bang itself and how state-of-the-art measurements are transforming our understanding of our cosmic origin and ultimate fate. We then turn to the question of whether this can all be described purely mathematically, and discuss implications ranging from standard physics topics like symmetries, irreducible representations, units, free parameters and initial conditions to broader issues like parallel universes, simulations and and Goedel incompleteness.

Understanding magnetic reconnection is one of the major challenges of plasma physics. It plays an essential role in a wide range of physical systems such as stellar flares, accretion disks, active galactic nuclei, astrophysical dynamos and closer to home, intense magnetic energy releases in the Earth's magnetosphere. It is a phenomena which can be created in the laboratory. Magnetic reconnection occurs when oppositely directed components of field lines are broken and re-connected resulting in destruction of magnetic flux and topological rearrangement of magnetic field lines on very small scales. This can induce the release of magnetic energy on large scales resulting in high speed flows, heating and energetic particle production. There is a strong connection between formation of singular structures in flows and magnetic reconnection which I will discuss and tie this into some of the laboratory and natural physical systems under recent study. In addition to giving a contemporary overview on this subject I will discuss some open questions.

If spacetime is "quantized" (discrete), then any equation of motion compatible with the Lorentz transformations is necessarily non-local. I will present evidence that this sort of nonlocality survives on length scales much greater than Planckian, yielding for example a nonlocal effective wave-equation for a scalar field propagating on an underlying causal set. Nonlocality of our effective field theories may thus provide a characteristic signature of quantum gravity.

A full analysis of QCD, the fundamental theory of subnuclear structure and interactions, relies upon numerical simulations and the lattice approximation. After being stalled for almost 30 years, recent breakthroughs in lattice QCD allow us for the first time to analyze the low-energy structure of QCD nonperturbatively with few-percent precision. This talk will present a non-technical overview of the history leading up to these breakthroughs, and survey the wide array of applications that have been enabled by them. It will focus in particular on the impact of these new techniques on experiments that explore such areas as heavy-quark and Standard Model physics.

In this talk I describe a possible connection between quantum computing and Zeta functions of finite field equations that is inspired by the \'spectral approach\' to the Riemann conjecture. This time the assumption is that the zeros of such Zeta functions correspond to the eigenvalues of finite dimensional unitary operators of quantum mechanical systems. To model the desired quantum systems I use the notion of universal, efficient quantum computation. Using eigenvalue estimation, such quantum systems should be able to approximately count the number of solutions of the specific finite field equations with an accuracy that does not appear to be feasible classically. For certain equations (Fermat hypersurfaces) one can indeed model their Zeta functions with efficient quantum algorithms, which gives some evidence in favor of the proposal. In the case of equations that define elliptic curves, the corresponding unitary transformation is an SU(2) matrix. Hence for random elliptic curves one expects to see the kind of statistics predicted by random matrix theory. In the last part of the talk I discuss to which degree this expectation does indeed hold. Reference: arXiv:quant-ph/0405081

A nonrotating black hole placed in a tidal environment (that is, subjected to the gravitational interactions produced by other nearby bodies) is not described by the Schwarzschild solution to the Einstein field equations. Instead, its metric is given by a perturbed version of this exact solution, and the spacetime is no longer stationary nor spherically symmetric. After reviewing the situation in Newtonian theory, I shall describe how the metric of a tidally distorted black hole is calculated. Special attention will be placed on the general description of the tidal environment, the choice of a good coordinate system to describe the perturbed black hole, and the consequences on the structure of the event horizon