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

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

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

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