An N-tiling of triangle ABC by triangle T is a way of writing ABC as a union
of N triangles congruent to T, overlapping only at their boundaries. The
triangle T is the "tile". The tile may or may not be similar to ABC. In this
paper we stud...
Random matrices: Universality of local spectral statistics of
non-Hermitian matrices
June 8, 2012
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Mathematics
Probability
It is a result of Ginibre that the normalized bulk k-point correlation
functions of a complex n×n Gaussian matrix with independent entries of
mean zero and unit variance are asymptotically given by the determinantal point
process ...
Triangle Tiling V: Tilings by a tile with integer sides
June 4, 2012
Mathematics
Metric Geometry
An N-tiling of triangle ABC by triangle T is a way of writing ABC as a union
of N triangles congruent to T, overlapping only at their boundaries. The
triangle T is the "tile". The tile may or may not be similar to ABC. We wish to
understand...
Generalized Minkowski spacetime with geometric algebra
May 23, 2012
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Physics
Mathematics
Mathematical Physics
Mathematical Physics
Classical Physics
We begin from the generalised eight-dimensional Minkowski spacetime
structure, previously developed in Clifford geometric algebra Cℓ(ℜ3).
We propose that this is the correct algebraic representation for physical
three-dimensional ...
Dark Energy in F(R,T) Gravity
May 23, 2012
Physics
General Physics
General Relativity and Quantum Cosmology
Since the discovery of cosmic acceleration, modified gravity theories play an
important role in the modern cosmology. In particular, the well-known
F(R)-theories reached great popularity motivated by the easier formalism and by
the prospect...
Lectures on AKSZ Sigma Models for Physicists
April 17, 2012
Physics
Mathematics
High Energy Physics - Theory
Mathematical Physics
Differential Geometry
Mathematical Physics
Symplectic Geometry
This is an introductory review of topological field theories (TFTs) called
AKSZ sigma models. The AKSZ construction is a mathematical formulation for the
construction and analyses of a large class of TFTs, inspired by the
Batalin-Vilkovisky...
Riemannian Metrics and Harmonic Sections of Spinor Bundles
April 15, 2012
Mathematics
Differential Geometry
Functional Analysis
We study the clustering of the lowest non negative eigenvalue of the Dirac
operator on a general Dirac bundle when the metric structure is varied. In the
classical case we show that any closed spin manifold of dimension greater than
or equa...
On Isomorphisms of Grassmann Spaces
April 14, 2012
Mathematics
Algebraic Geometry
We exhibit isomorphisms of Grassmann spaces and their relationship with
collineations and embeddings of the underlying projective spaces....
A Central Limit Theorem for Repeating Patterns
April 12, 2012
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Mathematics
Combinatorics
Probability
We prove a central limit theorem for the length of the longest subsequence of
a random permutation which follows one of a class of repeating patterns. This
class includes every fixed pattern of ups and downs having at least one of
each, suc...
On the behaviour of \gamma\Log p modulo 1
March 8, 2012
Mathematics
Number Theory
We prove non-trivial lower bounds for sums of type \sum_{p\sim
P}g(\gamma\Log p), where g is a non-negative 2π-periodical function and
γ is a given parameter. As an application we prove that
$\zeta(1+it)^{\pm1}\ll\Log\Log (9+...