Related papers: Dynamical Invariants from Asymptotic Composants
It is known that the asymptotic invariant manifolds around an unstable periodic orbit in conservative systems can be represented by convergent series (Cherry 1926, Moser 1956, 1958, Giorgilli 2001). The unstable and stable manifolds…
Attempts at building an unified description of the strong, weak and electromagnetic interactions usually involve several stages of spontaneous symmetry breaking. We consider the effects of such symmetry breaking during an era of primordial…
We argue that all the necessary ingredients for successful inflation are present in the flat directions of the Minimally Supersymmetric Standard Model. We show that out of many gauge invariant combinations of squarks, sleptons and Higgses,…
While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…
In models of cosmological inflation motivated by dynamical supersymmetry breaking, the potential driving inflation may be characterized by inverse powers of a scalar field. These models produce observables similar to those typical of the…
Going beyond the cohomological invariants attached to tiling spaces via inverse limit constructions, Clark and Hunton introduced shape group invariants, and showed these invariants in dimension one give new information. We show for…
We investigate the emergence of large, localized, pseudo-stable configurations (oscillons) from inflaton fragmentation at the end of inflation. We predict the number density of large oscillons, and the conditions necessary for their…
The purpose of this paper is to define and study systematically some asymptotic invariants associated to base loci of line bundles on smooth projective varieties. We distinguish an open dense subset of the real big cone, called the stable…
Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…
We show that a moduli space of the form predicted by string theory, lifted by supersymmetry breaking, gives rise to successful inflation for large regions of parameter space without any modification or fine tuning. This natural realization…
The dimer problem arose in a thermodynamic study of diatomic molecules, and was abstracted into one of the most basic and natural problems in both statistical mechanics and combinatoric mathematics. Given a rectangular lattice of volume V…
It is proved that whenever two aperiodic repetitive tilings with finite local complexity have homeomorphic tiling spaces, their associated complexity functions are asymptotically equivalent in a certain sense (which implies, if the…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
We introduce Dehn invariants as a useful tool in the study of the inflation of quasiperiodic space tilings. The tilings by ``golden tetrahedra'' are considered. We discuss how the Dehn invariants can be applied to the study of inflation…
Consider an asymptotically flat Riemannian manifold $(M,g)$ of dimension $n \geq 3$ with nonempty compact boundary. We recall the harmonic conformal class $[g]_h$ of the metric, which consists of all conformal rescalings given by a harmonic…
In this paper we give an asymptotic formula for a matrix integral which plays a crucial role in the approach of Diaconis et al. to random matrix eigenvalues. The choice of parameter for the asymptotic analysis is motivated by an invariant…
We place functional constraints on the shape of the inflaton potential from the cosmic microwave background through a variant of the generalized slow roll approximation that allows large amplitude, rapidly changing deviations from…
We analyse the behaviour of thin composite plates whose material properties vary periodically in-plane and possess a high degree of contrast between the individual components. Starting from the equations of three-dimensional linear…
Inflationary cosmologies, regarded as dynamical systems, have rather simple asymptotic behavior, insofar as the cosmic baldness principle holds. Nevertheless, in the early stages of an inflationary process, the dynamical behavior may be…
The class of Cyclotomic Aperiodic Substitution Tilings (CAST) is introduced. Its vertices are supported on the 2n-th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations.…