21,448 research outputs found
Concept for using laser beams to measure electron density in plasmas
Concept is proposed for using laser beams as a means of measuring electron density at various points in flame or plasma exhausts. Measurement of the electron density is obtained by detecting reflected waves in the plasma that were activated by the laser
The rationality of quaternionic Darmon points over genus fields of real quadratic fields
Darmon points on p-adic tori and Jacobians of Shimura curves over Q were
introduced in previous joint works with Rotger as generalizations of Darmon's
Stark-Heegner points. In this article we study the algebraicity over extensions
of a real quadratic field K of the projections of Darmon points to elliptic
curves. More precisely, we prove that linear combinations of Darmon points on
elliptic curves weighted by certain genus characters of K are rational over the
predicted genus fields of K. This extends to an arbitrary quaternionic setting
the main theorem on the rationality of Stark-Heegner points obtained by
Bertolini and Darmon, and at the same time gives evidence for the rationality
conjectures formulated in a joint paper with Rotger and by M. Greenberg in his
article on Stark-Heegner points. In light of this result, quaternionic Darmon
points represent the first instance of a systematic supply of points of
Stark-Heegner type other than Darmon's original ones for which explicit
rationality results are known.Comment: 34 page
Quaternion algebras, Heegner points and the arithmetic of Hida families
Given a newform f, we extend Howard's results on the variation of Heegner
points in the Hida family of f to a general quaternionic setting. More
precisely, we build big Heegner points and big Heegner classes in terms of
compatible families of Heegner points on towers of Shimura curves. The novelty
of our approach, which systematically exploits the theory of optimal
embeddings, consists in treating both the case of definite quaternion algebras
and the case of indefinite quaternion algebras in a uniform way. We prove
results on the size of Nekov\'a\v{r}'s extended Selmer groups attached to
suitable big Galois representations and we formulate two-variable Iwasawa main
conjectures both in the definite case and in the indefinite case. Moreover, in
the definite case we propose refined conjectures \`a la Greenberg on the
vanishing at the critical points of (twists of) the L-functions of the modular
forms in the Hida family of f living on the same branch as f.Comment: Heavily revised and shortened version, to appear in Manuscripta
Mathematic
An irreducibility criterion for group representations, with arithmetic applications
We prove a criterion for the irreducibility of an integral group
representation \rho over the fraction field of a noetherian domain R in terms
of suitably defined reductions of \rho at prime ideals of R. As applications,
we give irreducibility results for universal deformations of residual
representations, with a special attention to universal deformations of residual
Galois representations associated with modular forms of weight at least 2.Comment: 11 page
How to add a boundary condition
Given a conformal QFT local net of von Neumann algebras B_2 on the
two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A
is a completely rational net on the left/right light-ray, we show how to
consistently add a boundary to B_2: we provide a procedure to construct a
Boundary CFT net B of von Neumann algebras on the half-plane x>0, associated
with A, and locally isomorphic to B_2. All such locally isomorphic Boundary CFT
nets arise in this way. There are only finitely many locally isomorphic
Boundary CFT nets and we get them all together. In essence, we show how to
directly redefine the C* representation of the restriction of B_2 to the
half-plane by means of subfactors and local conformal nets of von Neumann
algebras on S^1.Comment: 20 page
Data Driven Discovery in Astrophysics
We review some aspects of the current state of data-intensive astronomy, its
methods, and some outstanding data analysis challenges. Astronomy is at the
forefront of "big data" science, with exponentially growing data volumes and
data rates, and an ever-increasing complexity, now entering the Petascale
regime. Telescopes and observatories from both ground and space, covering a
full range of wavelengths, feed the data via processing pipelines into
dedicated archives, where they can be accessed for scientific analysis. Most of
the large archives are connected through the Virtual Observatory framework,
that provides interoperability standards and services, and effectively
constitutes a global data grid of astronomy. Making discoveries in this
overabundance of data requires applications of novel, machine learning tools.
We describe some of the recent examples of such applications.Comment: Keynote talk in the proceedings of ESA-ESRIN Conference: Big Data
from Space 2014, Frascati, Italy, November 12-14, 2014, 8 pages, 2 figure
A Remark on Quantum Group Actions and Nuclearity
Let H be a compact quantum group with faithful Haar measure and bounded
counit. If H acts on a C*-algebra A, we show that A is nuclear if and only if
its fixed-point subalgebra is nuclear. As a consequence H is a nuclear
C*-algebra.Comment: 12 pages, LateX 2
How to remove the boundary in CFT - an operator algebraic procedure
The relation between two-dimensional conformal quantum field theories with
and without a timelike boundary is explored.Comment: 18 pages, 2 figures. v2: more precise title, reference correcte
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