Abstract:
Matrix theory and the AdS/CFT correspondence provide nonperturbative holographic formulations of string theory. In both cases the finite N theories can be thought of as infrared regulated versions of flat space string theory in which removing the cutoff is equivalent to letting N go to infinity. In this paper we consider the nature of this limit. In both cases the holographic mapping becomes completely nonlocal. In matrix theory this corresponds to the growth of D0-brane bound states with N. For the AdS/CFT correspondence there is a similar delocalization of the holographic image of a system as N increases. In this case the limiting theory seems to require a number of degrees of freedom comparable to large N matrix quantum mechanics.

Abstract:
We provide the first evidence for a holographic correspondence between a gravitational theory in flat space and a specific unitary field theory in one dimension lower. The gravitational theory is a flat-space limit of topologically massive gravity in three dimensions at Chern-Simons level k=1. The field theory is a chiral two-dimensional conformal field theory with central charge c=24.

Abstract:
We present a new
model of cosmology which appears to show great promise. Our flat space cosmology
model, using only four basic and reasonable assumptions, derives highly
accurate Hubble parameter H_{0},
Hubble radius R_{0} and total
mass M_{0} values for our observable
universe. Our model derives a current Hubble parameter of , in excellent
agreement with the newly reported (lower limit) results of the 2015 Planck
Survey. Remarkably, all of these derivations can be made with only these basic
assumptions and the current CMB radiation temperature

Abstract:
Hawking and the author have proposed a class of singular, finite action instantons for defining the initial conditions for inflation. Vilenkin has argued they are unacceptable. He exhibited an analogous class of asymptotically flat instantons which on the face of it lead to an instability of Minkowski space. However, all these instantons must be defined by introducing a constraint into the path integral, which is then integrated over. I show that with a careful definition these instantons do not possess a negative mode. Infinite flat space is therefore stable against decay via singular instantons.

Abstract:
Regular tesselations of space are characterized through their Schlafli symbols {p,q,r}, where each cell has regular p-gonal sides, q meeting at each vertex, and r meeting on each edge. Regular tesselations with symbols {p,3,3} all satisfy Plateau's laws for equilibrium foams. For general p, however, these regular tesselations do not embed in Euclidean space, but require a uniform background curvature. We study a class of regular foams on S^3 which, through conformal, stereographic projection to R^3 define irregular cells consistent with Plateau's laws. We analytically characterize a broad classes of bulk foam bubbles, and extend and explain recent observations on foam structure and shape distribution. Our approach also allows us to comment on foam stability by identifying a weak local maximum of A^(3/2)/V at the maximally symmetric tetrahedral bubble that participates in T2 rearrangements.

Abstract:
Flat space-time has not heretofore been thought a suitable locus in which to construct model universes because of the presumed necessity of incorporating gravitation in such models and because of the historical lack of a theory of gravitation in flat space-time. It is here shown that a Lorentz-invariant theory of gravitation can be formulated by incorporating in it the mass-energy relation. Such a theory correctly predicts the well-known relativistic effects (advance of perihelion, gravitational refraction, gravitational red shift, echo delay of sun-grazing radio signals, and others). The equations of motion, properly stated, are also seen to be identical to those of electromagnetism and lead to the correct prediction of gravitational radiation. Therefore Milne's kinematic model of the universe, mappable into his dynamical (or Newtonian) model, offers a unique alternative to the general relativistic models which are encumbered with both theoretically and observationally objectionable features.

Abstract:
We propose a Lie geometric point of view on flat fronts in hyperbolic space as special omega-surfaces and discuss the Lie geometric deformation of flat fronts.

Abstract:
We shall investigate flat surfaces in hyperbolic 3-space with admissible singularities, called `flat fronts'. An Osserman-type inequality for complete flat fronts is shown. When equality holds in this inequality, we show that all the ends are embedded. Moreover, we shall give new examples for which equality holds.

Abstract:
Let $G_0=K\ltimes\mathfrak p$ be the Cartan motion group associated with a noncompact semisimple Riemannian symmetric pair $(G, K)$. Let $\frak a$ be a maximal abelian subspace of $\mathfrak p$ and let $\p=\a+\q$ be the corresponding orthogonal decomposition. A flat horocycle in $\p$ is a $G_0$-translate of $\q$. A conical distribution on the space $\Xi_0$ of flat horocycles is an eigendistribution of the algebra $\mathbb D(\Xi_0)$ of $G_0$-invariant differential operators on $\Xi_0$ which is invariant under the left action of the isotropy subgroup of $G_0$ fixing $\q$. We prove that the space of conical distributions belonging to each generic eigenspace of $\mathbb D(\Xi_0)$ is one-dimensional, and we classify the set of all conical distributions on $\Xi_0$ when $G/K$ has rank one.

Abstract:
We investigate the evolution of infinite strings as a part of a complete cosmic string network in flat space. We perform a simulation of the network which uses functional forms for the string position and thus is exact to the limits of computer arithmetic. Our results confirm that the wiggles on the strings obey a scaling law described by universal power spectrum. The average distance between long strings also scales accurately with the time. These results suggest that small-scale structure will also scale in expanding universe, even in the absence of gravitational damping.