181 search results for “elliptic curves” in the Public website

Constructing elliptic curves of prescribed order
Promotor: Peter Stevenhagen

Galois representations of elliptic curves and abelian entanglements
Prof.dr. P. Stevenhagen, Prof.dr. K. Belabas (Universite Bordeaux I)

Universal adelic groups for imaginary quadratic number fields and elliptic curves
Promotor: Prof.dr. P. Stevenhagen & Prof.dr. K. Belabas (Univ. de Bordeaux)

Torsion points on elliptic curves over number fields of small degree
Promotor: S.J. Edixhoven Copromotor: L. van Geemen, P. Parent

Split Jacobians and Lower Bounds on Heights
This thesis deals with properties of Jacobians of genus two curves that cover elliptic curves.

Models of curves: The Birch and SwinnertonDyer conjecture & ordinary reduction
Chapter 1,contains the numerical verification of the Birch and SwinnertonDyer conjecture for hundreds of Jacobians of hyperelliptic curves of genus 2, 3, 4 and 5.

Faster number theory, safer cryptography
Developing a method to simplify polynomials in complex curves

Images of Galois representations
Promotores: S.J. Edixhoven, P.Parent

Modular curves, Arakelov theory, algorithmic applications
Promotor: S.J. Edixhoven, Copromotor: R.S. de Jong

Arakelov invariants of Belyi curves
Promotores: Bas Edixhoven, JeanBenoit Bost, Copromotor: Robin de Jong

Inverse Jacobian and related topics for certain superelliptic curves
To an algebraic curve C over the complex numbers one can associate a nonnegative integer g, the genus, as a measure of its complexity.

Kummer theory for commutative algebraic groups
This dissertation is a collection of four research articles devoted to the study of Kummer theory for commutative algebraic groups.

The CM class number one problem for curves
Promotores: P. Stevenhagen, A. Enge CoPromotor: T.C. Streng

Deterministic equation solving over finite fields
Promotor: H.W. Lenstra

Division points in arithmetic
This thesis consists of three chapters, the first two of which concern division points of elements of the multiplicative group of a number field.

Tautological differential forms on moduli spaces of curves
In this thesis we study the moduli space of genus g curves, and the differential forms that occur naturally on this moduli space.

Geometry and arithmetic of del Pezzo surfaces of degree 1
This thesis contains results on the arithmetic and geometry of del Pezzo surfaces of degree 1.In Chapter 1 we give the necessary background, assuming the reader is familiar with algebraic geometry.

Exploring structure dependencies of gassurface interactions with curved single crystals
Curved single crystals provide variable, but welldefined surface structures.

Refined tautological relations on moduli spaces of curves
Robin de Jong

Néron models in high dimension: nodal curves, Jacobians and tame base change
We describe certain birational modifications of nodal relative curves over a regular base of arbitrary dimension.

Arakelov inequalities and semistable families of curves uniformized by the unit ball
The main object of study in this thesis is an Arakelov inequalitywhich bounds the degree of an invertible subsheaf of the direct image ofthe pluricanonical relative sheaf of a semistable family of curves.

Programme structure
The Algebra, Geometry and Number Theory specialisation offers you the opportunity to spend two full years on training in research to develop a thorough theoretical basis and become an independent scientist.

On the geometry of demixing: A study of lipid phase separation on curved surfaces
Like a mixture of oil and water, lipid membranes separate into two liquid phases.

On shape and elasticity: biosheets, curved crystals, and odd droplets
Because thin systems can deform along the thickness with relative ease, the interplay between surface mechanics and geometry plays a fundamental role in sculpting their threedimensional shape.

Lasers, lenses and light curves: adaptive optics microscopy and peculiar transiting exoplanets
Promotores: Prof.dr. C.U. Keller, Prof.dr. H.C. Gerritsen

Geometric quadratic Chabauty and other topics in number theory
This thesis is is made of three parts. The first part describes a generalization of the Chabauty's method, that can be used to determine the rational points of a curve such that s+g>r+1, where g is the genusof the curve, r is the rank of the MordellWeil group of the jacobian of the curve and s is…

Studying abstract mathematical equations using tangible surfaces
On January 5, Rosa Winter will obtain her doctorate in arithmetic geometry. She researched solutions of equations that define socalled ‘del Pezzo surfaces’. ‘I like geometry because I can imagine and draw the shapes and objects,’ says Winter. ‘That makes abstract mathematics feel more tangible.’

Hendrik Lenstra honored Ridder in de Orde van de Nederlandse Leeuw
On Friday April 24th, after a day of festivities in honor of his 60th birthday, Hendrik Lenstra was awarded the distinction of `Ridder in de Orde van de Nederlandse Leeuw' by the mayor of the city of Leiden.

Theses
Below thesis archives will be moved shortly (work in progress) to the Leiden Repository. Once this is done, theses submitted by MI students (from 2008 onwards) can be accessed via the Repository and will be removed from this site.

Groups and fields in arithmetic
Promotor: Prof.dr. H.W. Lenstra

Focus and ellipsis
This project aims at investigating the syntactic role of focus in ellipsis across languages.

Sabine Auras
Science

The million dollar proof
PhD student Raymond van Bommel decided to pore upon one of the most complicated mathematical problems of our time; the solution of it is worth 1 million dollars! Van Bommel did not get that far yet. However, he wrote his own computer program to make new calculations. ‘It could just be that someone else…

Ellipsis licensing beyond syntax
Ellipsis is a frequently used sentenceshortening device. It allows us to leave out material that is evident from the (linguistic) context. Even though the elliptical material is not pronounced, elliptical sentences are not perceived as incomplete.

The syntax and licensing of Gapping and Fragmenting
This study investigates the syntax and distribution of the two elliptical phenomena Gapping and Fragments, as well as the movements involved in ellipsis contexts in general.

Some case studies of random walks in dynamic random environments
Promotor: Promotor: W.Th.F. den Hollander, Copromotor: V. Sidoravicius.

The unbearable lightness of clitics
On the 23rd of January, Anastasiia Ionova successfully defended her doctoral thesis and graduated. The Leiden University Centre for Linguistics congratulates Anastasiia on this achievement.

The Derivational Timing of Ellipsis
This volume explores the nature of ellipsis, the core phenomenon that results in various types of omission in sentences.

Dual Complexes of Semistable Varieties
This thesis is comprised of three chapters covering the theme of studying semistable varieties by looking at their dual combinatorial objects.

Structure dependence of molecular reactions on surfaces
The research presented in this thesis makes use of small molecules (as H2 , D2 and O2 ) on welldefined single crystal surfaces (flat Pt(111), flat Cu(211) and curved Pt(111)) to elucidate the role of surface structure and degrees of freedom in the reactant in specific surface reactions.

Computability of the étale EulerPoincaré characteristic
Promotor: S.J. Edixhoven, L.D.J. Taelman

Isogeny graphs, modular polynomials, and applications
This thesis has three main parts. The first part gives an algorithm to compute Hilbert modular polynomials for ordinary abelian varieties with maximal real multiplication. Hilbert modular polynomials of a given level b give a way of finding all of the abelian varieties that are bisogeneous to any given…

Dawn of the red and dead: stellar kinematics of massive quiescent galaxies out to z = 2
Promotores: Prof.dr. M. Franx, Prof.dr. M. Kriek (Univ. of California at Berkeley)

Gassurface reaction dynamics and surface science
The local ordering of atoms at the surface of a metallic particle determines its catalytic activity and selectivity. As energy systems of the future will be based on efficient catalytic conversion of small molecules in closed cycles, we study how structural effects of catalysts can be used to our ad…

Complex multiplication of abelian surfaces
Promotor: Peter Stevenhagen

Predicting the future: Predictive control for astronomical adaptive optics
The field of exoplanet research is rapidly advancing through the development of new technology, observing techniques, and postprocessing methods.

Inferno Worlds
A remarkable population of short period transiting rocky exoplanets with equilibrium temperatures on the order of 2,000 K has recently been discovered.

Periodic pulse solutions to slowly nonlinear reactiondiffusion systems
Promotor: A. Doelman, Copromotor: J.D.M. Rademacher

From supernovae to galaxy clusters: observing the chemical enrichment in the hot intracluster medium
Promotor: Jelle S. Kaastra Copromotor: Jelle de Plaa

Tapping into Semantic Recovery
On May 31st, Bobby Ruijgrok succesfully defended his doctoral thesis and graduated. The Leiden University Centre for Linguistics congratulates Bobby on this great result.