238,996 research outputs found
Quantum Communication and Quantum Multivariate Polynomial Interpolation
The paper is devoted to the problem of multivariate polynomial interpolation
and its application to quantum secret sharing. We show that using quantum
Fourier transform one can produce the protocol for quantum secret sharing
distribution.Comment: 7 pages, no figure, LaTeX2
Some remarks on the Cegrell's class
In this paper, we study the near-boundary behavior of functions
in the case where is strictly pseudoconvex.
We also introduce a sufficient condition for belonging to in the
case where is the unit ball.Comment: 8 page
Automorphic Representations of \SL(2,\mathbb R) and Quantization of Fields
In this paper we make a clear relationship between the automorphic
representations and the quantization through the Geometric Langlands
Correspondence. We observe that the discrete series representation are realized
in the sum of eigenspaces of Cartan generator, and then present the automorphic
representations in form of induced representations with inducing quantum bundle
over a Riemann surface and then use the loop group representation construction
to realize the automorphic representations. The Lanlands picture of automorphic
representations is precised by using the Poisson summation formula
Poisson Summation and Endoscopy for SU(2,1)
In this paper we analyze the endoscopy for . The new results are a
precise realization of the discrete series representations (in Section 2), a
computation of their traces (Section 3) and an exact formula for the Poisson
summation and endoscopy for this group (in Section 4).Comment: Minor misprint changes. arXiv admin note: substantial text overlap
with arXiv:1407.681
Poisson Summation and Endoscopy for
The group is interesting as the first example of split rank 2 semisimple
group, all the irreducible unitary representations of which are known. We make
a precise realization of the discrete series representations (in Section 2) by
using the Orbit Method and Geometric Quantization, a computation of their
traces (Section 3) and an exact formula for the noncommutative Poisson
summation and endoscopy of for this group (in Section 4).Comment: arXiv admin note: substantial text overlap with arXiv:1407.690
Extending Erd\H{o}s- Beck's theorem to higher dimensions
Erd\H{o}s-Beck theorem states that points in the plane with at most
points collinear define at least lines for some positive constant .
In this paper, we will present two ways to extend this result to higher
dimensions. Our result has application to point-hyperplane incidences and
potential application to the point covering problem
Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes
Moduli spaces of hyperbolic surfaces may be endowed with a symplectic
structure via the Weil-Petersson form. Mirzakhani proved that Weil-Petersson
volumes exhibit polynomial behaviour and that their coefficients store
intersection numbers on moduli spaces of curves. In this survey article, we
discuss these results as well as some consequences and applications.Comment: 37 pages - submitted to Handbook of Moduli (edited by G. Farkas and
I. Morrison
The asymptotic Weil-Petersson form and intersection theory on M_{g,n}
Moduli spaces of hyperbolic surfaces with geodesic boundary components of
fixed lengths may be endowed with a symplectic structure via the Weil-Petersson
form. We show that, as the boundary lengths are sent to infinity, the
Weil-Petersson form converges to a piecewise linear form first defined by
Kontsevich. The proof rests on the observation that a hyperbolic surface with
large boundary lengths resembles a graph after appropriately scaling the
hyperbolic metric. We also include some applications to intersection theory on
moduli spaces of curves.Comment: 22 page
On a 1D transport equation with nonlocal velocity and supercritical dissipation
We study a 1D transport equation with nonlocal velocity. First, we prove
eventual regularization of the viscous regularization when dissipation is in
the supercritical range with non-negative initial data. Next, we will prove
global regularity for solutions when dissipation is slightly supercritical.
Both results utilize a nonlocal maximum principle
On the quantum graph spectra of graphyne nanotubes
We describe explicitly the dispersion relations and spectra of periodic
Schrodinger operators on a graphyne nanotube structure.Comment: Three footnotes and one reference added, minor revisions. Accepted to
Analysis and Mathematical Physics Journa
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