On complex and real identifiability of tensors

We report about the state of the art on complex and real generic identifiability of tensors, we describe some of our recent results obtained in [6] and we present perspectives on the subject.Comment: To appear on Rivista di Matematica dell'Universit\`a di Parma, Volume 8, Number 2, 2017, pages 367-37

Measuring eccentricity in binary black-hole initial data

Initial data for evolving black-hole binaries can be constructed via many techniques, and can represent a wide range of physical scenarios. However, because of the way that different schemes parameterize the physical aspects of a configuration, it is not alway clear what a given set of initial data actually represents. This is especially important for quasiequilibrium data constructed using the conformal thin-sandwich approach. Most initial-data studies have focused on identifying data sets that represent binaries in quasi-circular orbits. In this paper, we consider initial-data sets representing equal-mass black holes binaries in eccentric orbits. We will show that effective-potential techniques can be used to calibrate initial data for black-hole binaries in eccentric orbits. We will also examine several different approaches, including post-Newtonian diagnostics, for measuring the eccentricity of an orbit. Finally, we propose the use of the ``Komar-mass difference'' as a useful, invariant means of parameterizing the eccentricity of relativistic orbits.Comment: 12 pages, 11 figures, submitted to Physical Review D, revtex

Families of fast elliptic curves from Q-curves

We construct new families of elliptic curves over \FF_{p^2} with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as Gallant-Lambert-Vanstone (GLV) and Galbraith-Lin-Scott (GLS) endomorphisms. Our construction is based on reducing \QQ-curves-curves over quadratic number fields without complex multiplication, but with isogenies to their Galois conjugates-modulo inert primes. As a first application of the general theory we construct, for every $p > 3$, two one-parameter families of elliptic curves over \FF_{p^2} equipped with endomorphisms that are faster than doubling. Like GLS (which appears as a degenerate case of our construction), we offer the advantage over GLV of selecting from a much wider range of curves, and thus finding secure group orders when $p$ is fixed. Unlike GLS, we also offer the possibility of constructing twist-secure curves. Among our examples are prime-order curves equipped with fast endomorphisms, with almost-prime-order twists, over \FF_{p^2} for $p = 2^{127}-1$ and $p = 2^{255}-19$