相关论文: Index Calculus in the Trace Zero Variety

Recent results suggest that boundaries of coherent fluid vortices (elliptic coherent structures) can be identified as closed null-geodesics of appropriate Lorentzian metrics defined on the flow domain. Here we derive an automated method for…

We introduce a modification of the Fast Marching Algorithm, which solves the generalized eikonal equation associated to an arbitrary continuous riemannian metric, on a two or three dimensional domain. The algorithm has a logarithmic…

In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…

In this note we investigate the $p$-degree function of elliptic curves over the field $\mathbb{Q}_p$ of $p$-adic numbers. The $p$-degree measures the least complexity of a non-zero $p$-torsion point on an elliptic curve. We prove some…

We study an inverse problem associated with an eddy current model. We first address the ill-posedness of the inverse problem by proving the compactness of the forward map with respect to the conductivity and the non-uniqueness of the…

We provide an algorithm, running in polynomial time in the number of vertices, computing the unique solution to the biased infinity Laplacian Boundary Problem on finite graphs. The algorithm is based on the general outline and approach…

In this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system $|L|$ of an ample line bundle on a complex abelian variety. We prove an effective result on their (continuous) global generation, after…

Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate…

We establish a congruence formula between $p$-adic logarithms of Heegner points for two elliptic curves with the same mod $p$ Galois representation. As a first application, we use the congruence formula when $p=2$ to explicitly construct…

As a subproduct of the Schoof-Elkies-Atkin algorithm to count points on elliptic curves defined over finite fields of characteristic p, there exists an algorithm that computes, for l an Elkies prime, l-torsion points in an extension of…

We describe a computation of rational points on genus 3 hyperelliptic curves $C$ defined over $\mathbb{Q}$ whose Jacobians have Mordell-Weil rank 1. Using the method of Chabauty and Coleman, we present and implement an algorithm in Sage to…

We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…

In this paper we investigate linear dependence of points in Mordell-Weil groups of abelian varieties via reduction maps. In particular we try to determine the conditions for detecting linear dependence in Mordell-Weil groups via finite…

We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The method is then applied to the Schr\"{o}dinger equation in…

In this paper we develop an algebraic theory to study the problem of finding the minimum distance point from an algebraic variety with respect to the Hermitian distance function. The theory generalizes the Euclidean Distance degree…

Motivated by finding an effective way to compute the algebraic complexity of the nearest point problem for algebraic models, we introduce an efficient method for detecting the limit points of the stratified Morse trajectories in a small…

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value…

Let $R$ be the maximal order in a quadratic imaginary field $K$. We give an equivalence of categories between the category of polarized abelian varieties isomorphic to a product of elliptic curves over $\mathbb{C}$ with complex…

In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the solutions. We…

We consider families of smooth projective curves of genus 2 with a single point removed and study their integral points. We show that in many such families there is a dense set of fibres for which the integral points can be effectively…