Publications related to Elliptic curve

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Generating Calligraphic Trajectories with Model Predictive Control

Sylvain Calinon

We describe a methodology for the interactive definition of curves and motion paths using a stochastic formulation of optimal control. We demonstrate how the same optimization framework can be used in different ways to generate curves and traces that are g ...

2017

Elliptic curves over a finite field and the trace formula

Ian Nicholas Petrow

We prove formulas for power moments for point counts of elliptic curves over a finite field k such that the groups of k-points of the curves contain a chosen subgroup. These formulas express the moments in terms of traces of Hecke operators for certain con ...

Wiley2017

Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration

Dimitri Stelio Wyss, Michael Gröchenig

We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type

SL_n

and

PGL_n

. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generica ...

2017

Distinct Distances on Algebraic Curves in the Plane

János Pach, Frank de Zeeuw

Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...

Cambridge Univ Press2017

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Michaël Unser, Julien René Pierre Fageot, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that interpolate the shape ...

2017

Characterization methodology for lead zirconate titanate thin films with interdigitated electrode structures

Paul Muralt, Robin Nigon, Trygve Magnus Raeder

The accurate evaluation of ferroelectric thin films operated with interdigitated electrodes is quite a complex task. In this article, we show how to correct the electric field and the capacitance in order to obtain identical polarization and CV loops for a ...

Amer Inst Physics2017

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

Height of rational points on quadratic twists of a given elliptic curve

Pierre Francis André Le Boudec

We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can prove only partial resul ...

Oxford Univ Press2016

A Singular Elliptic System with Higher Order Terms of p-Laplacian Type

Linda Maria De Cave

We use variational techniques to prove existence and nonexistence results for the following singular elliptic system: {div(vertical bar del u vertical bar(p-2)del u) = theta z(q)/u(1-0), u > 0 in Omega is an element of W-0(,1p) (Omega), -div(vertical bar d ...

Walter De Gruyter Gmbh2016

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Isogeny graphs of ordinary abelian varieties

Generating Calligraphic Trajectories with Model Predictive Control

Elliptic curves over a finite field and the trace formula

Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration

Distinct Distances on Algebraic Curves in the Plane

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Characterization methodology for lead zirconate titanate thin films with interdigitated electrode structures

Computational Aspects of Jacobians of Hyperelliptic Curves

Height of rational points on quadratic twists of a given elliptic curve

A Singular Elliptic System with Higher Order Terms of p-Laplacian Type

Isogeny graphs of ordinary abelian varieties

Generating Calligraphic Trajectories with Model Predictive Control

Elliptic curves over a finite field and the trace formula

Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration

Characterization methodology for lead zirconate titanate thin films with interdigitated electrode structures

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Distinct Distances on Algebraic Curves in the Plane

Height of rational points on quadratic twists of a given elliptic curve

A Singular Elliptic System with Higher Order Terms of p-Laplacian Type

Computational Aspects of Jacobians of Hyperelliptic Curves