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Rational number

Related publications (29)

Rational Points in the Noether-Lefschetz Locus of Moduli Spaces of K3 Surfaces

We give a characterization of rational points lying on the Noether-Lefschetz locus of moduli spaces of K3 surfaces by studying their lifting properties under some natural coverings of the ambient space. We then prove that the Bombieri-Lang conjecture impli ...

Oxford Univ Press2024

Lattice packings through division algebras

Nihar Prakash Gargava

In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...

SPRINGER HEIDELBERG2023

Ultra long turbulent eddies, magnetic topology, and the triggering of internal transport barriers in tokamaks

Stephan Brunner, Justin Richard Ball, Arnas Volcokas

Local nonlinear gyrokinetic simulations of tokamak plasmas demonstrate that turbulent eddies can extend along magnetic field lines for hundreds of poloidal turns when the magnetic shear is very small. By accurately modeling different field line topologies ...

IOP Publishing Ltd2023

On rationally connected varieties over C1 fields of characteristic 0

Marta Pieropan

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...

MATHEMATICAL SCIENCE PUBL2022

The Completion Of Covariance Kernels

Victor Panaretos, Kartik Waghmare

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...

INST MATHEMATICAL STATISTICS-IMS2022

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Daniel Kressner, Alice Cortinovis, Marcel Schweitzer

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

SIAM PUBLICATIONS2021

Global Frobenius liftability I

Maciej Emilian Zdanowicz

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...

2021

Two-dimensional nanochannel membranes for molecular and ionic separations

Guangwei He, Shaoyu Wang, Yifan Li, Zheyu Jiang

Two-dimensional (2D) nanosheets have emerged as promising functional materials owing to their atomic thickness and unique physical/chemical properties. By using 2D nanosheets as building blocks, diverse kinds of two-dimensional nanochannel membranes (2DNCM ...

Royal Society of Chemistry2020

Presymplectic convexity and (ir)rational polytopes

Tudor Ratiu

In this paper, we extend the Atiyah-Guillemin-Sternberg convexity theorem and Delzant's classification of symplectic toric manifolds to presymplectic manifolds. We also define and study the Morita equivalence of presymplectic toric manifolds and of their c ...

2019

Moving on: Is Existenzminimum Still Relevant?

Bruno Marchand

In the inter-war period, progressive architects confronted the building of mass housing with an analogy with rational and functional workplaces. At the 2nd CIAM (Congres Internationaux d'Architecture Moderne), held in Frankfurt in 1929, this was tested aga ...

2019

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

An Automatic, Data-Driven Definition of Atomic-Scale Structural Motifs

Piero Gasparotto

Structure-property relationships at the atomic scale are usually understood in terms of recurrent structural motifs formed by atoms and molecules, and how they transform and interact with each other. We introduce with this thesis a novel analysis approach, ...

EPFL2018

Low Frequency Sound Field Reconstruction in Non-rectangular Room: A Numerical Validation

Hervé Lissek, Etienne Thierry Jean-Luc Rivet, Vu Thach Pham

Characterization of sound fields in rooms has always been a challenging task. A faithful reconstruction of sound fields in rooms generally would require an impractically high number of microphones. At low frequencies, where sound field can be modeled as a ...

2018

Rationally isomorphic hermitian forms and torsors of some non-reductive groups

Eva Bayer Fluckiger

Let R be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an R-algebra with involution, which are rationally isomorphic and have isomorphic semisimple coradicals, are in fact isomorp ...

Academic Press Inc Elsevier Science2017

Some consequences of Masser's counting theorem on elliptic curves

Valéry Aurélien Mahé

We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...

Springer Heidelberg2017

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

Motivic Classes of Nakajima Quiver Varieties

Dimitri Stelio Wyss

We prove that Hausel’s formula for the number of rational points of a Nakajima quiver variety over a finite field also holds in a suitable localization of the Grothendieck ring of varieties. In order to generalize the arithmetic harmonic analysis in his pr ...

2016

Inhomogeneous minima of mixed signature lattices

Eva Bayer Fluckiger, Martino Borello, Peter Simon Jossen

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Academic Press Inc Elsevier Science2016

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