Abstract:
Although the scalar nonlinear Schrodinger equation has provided valuable insights into how quantum mechanics might modify the classical general relativistic description of space-time, a detailed understanding of space-times with matter has remained elusive. In this paper, we propose generalizing the nonlinear Schrodinger equation theory of Einstein spaces to include matter by transplanting the 3 + 1 dimensional theory to the 24-dimensional Leech lattice plus 1 time dimension. The scalar wave function and Chern-Simons gauge potential which encode the classical Kahler potential become 11 × 11 complex matrices belonging to a 195,442 dimensional representation of the Mathieu group M_{11}. This theory describes gravity coupled to internal degrees of freedom which include a supersymmetric E_{6} × E_{6} Yang-Mills theory of matter.

Abstract:
Attention is drawn to the possibility that self-organizing biological neural networks could spontaneously acquire the capability to carry out sophisticated computations. In particular it is shown that the effective action governing the formation of synaptic connections in models of networks of feature detectors that encorporate Kohonen-like self-organization can spontaneously lead to structures that are topologically nontrivial in both a 2-dimensional and 4-dimensional sense. It is suggested that the appearance of biological neural structures with a nontrivial 4-dimensional topology is the fundamental organizational principle underlying the emergence of advanced cognitive capabilities.

Abstract:
As developed previously the physical behavior of space-time near to an event horizon can be surmised from the behavior of a superfluid near to a critical point where the speed of sound vanishes. In this talk we note that this critical behavior can be given a geometrical interpretation by regarding the tuning parameter as a radial coordinate for anti-de Sitter space. We also draw attention to a mathematical model for a layered conductor with strong spin-orbit interactions which provides a physical explanation for why the behavior of space-time near an event horizon is related to the behavior of high Tc superconductors.

Abstract:
The theory of dark energy stars illustrates how the behavior of matter near to certain kinds of quantum critical phase transitions can be given a geometrical interpretation by regarding the criticality tuning parameter as an extra dimension. In the case of a superfluid with vanishing speed of sound, the implied geometry resembles 5-dimensional anti-de-Sitter. In a dark energy star this geometry applies both inside and outside the horizon radius, so the AdS-CFT correspondence is consistent with the idea that the surface of a compact astrophysical object represents a quantum critical phase transition of space-time. The superfluid transition in a chiron gas, which was originally proposed as a theory of high temperature superconductivity, may provide an exact theory of this transition.

Abstract:
An initial state for the observable universe consisting of a finite region with a large vacuum energy will break-up due to near horizon quantum critical fluctuations. This will lead to a Friedmann-like early universe consisting of an expanding cloud of dark energy stars and radiation. In this note we point out that this scenario provides a simple explanation for the present day density of dark matter as well as the level of CMB temperature flucuations. It is also predicted that all dark matter will be clumped on mass scales ~ 10E3 solar masses.

Abstract:
Recent hints from observations of distant supernovae of a positive cosmological constant with magnitude comparable to the average density of matter seem to point in the direction of a two fluid model for spacetime; where the "normal" component consists of ordinary matter, while the "superfluid" component is a zero entropy condensate. Such a two fluid model for spacetime provides an immediate and simple explanation for why information seems to be lost when objects fall into a classical black hole.

Abstract:
Low temperature measurements of the magnetic susceptibility of LSCO suggest that the superconducting transition is associated with the disappearance of a vortex liquid. In this note we wish to draw attention to the fact that spin-orbit-like interactions in a poorly conducting layered material can lead to a new type of quantum ground state with spin polarized soliton-like charge carriers as the important quantum degree of freedom. In 2-dimensions these solitons are vortex-like, while in 3-dimensional systems they are monopole-like. In either case there is a natural mechanism for the pairing of spin up and spin down solitons, and we find that at low temperatures there is a cross-over transition as a function of carrier density between a state where the solitons are free and a condensate state where the spin up and spin down solitons in neighboring layers are paired.

Abstract:
The pattern of duality symmetries acting on the states of compactified superstring models reinforces an earlier suggestion that the Monster sporadic group is a hidden symmetry for superstring models. This in turn points to a supersymmetric theory of self-dual and anti-self-dual K3 manifolds joined by Dirac strings and evolving in a 13 dimensional spacetime as the fundamental theory. In addition to the usual graviton and dilaton this theory contains matter-like degrees of freedom resembling the massless states of the heterotic string, thus providing a completely geometric interpretation for ordinary matter.

Abstract:
In the dark energy star picture a compact object is transparent at radio and optical frequencies, and acts as a defocusing lens. Thus the object itself appears as a luminous disk whose surface brightness reflects the surface brightness of the background. In the case of rotating dark energy stars the image will also contain background independent emission features. In this note we provide simple analytic formulae for the separation of these features as a function of angular momentum and viewing angle. In the case of rapid rotation these features will appear to lie within the shadow expected if the compact object were a black hole.

Abstract:
In this paper we suggest a novel explanation for the alpha-delta transition in plutonium based on an analogy between the evolution of the actinide ground state as a function of spin orbit coupling and the behaviour of thin film superconductors in a magnetic field. The key point is that in metals with a low carrier density spin-orbit interactions give rise to low energy monopole-like solitons with quantized spin currents, which play much the same role as Abrikosov vortices in thin film superconductors. In alpha-plutonium these solitons form an ordered solid, while in impurity stabilized delta-plutonium they form a pair condensate.