Het onderzoek binnen het Algebra, Geometry and Number Theory programma varieert van fundamentele wiskundige theorie tot algoritmes en toepassingen.

In de masterspecialisatie Algebra, Geometry and Number Theory verbreed je je kennis van de zuivere wiskunde met onderwerpen als getaltheorie, algebraïsche meetkunde, algebraïsche topologie en cryptologie.

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 Mordell-Weil group of the jacobian of the curve and s is…

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

Promotor: H.W. Lenstra

We show that Kirchhoff ’s law of conservation holds for non-commutative graph flows if and only if the graph is planar. We generalize the theory of (Euclidean) lattices to infinite dimension and consider the ring of algebraic integers as such a lattice.

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

This thesis consists of three chapters. Each chapter is on a different subject. However, all three chapters address issues that arise in counting arithmetically interesting objects.

Promotor: S.J. Edixhoven, Co-promotor: R.S. de Jong

Promotor: S.J. Edixhoven Co-promotor: L. van Geemen, P. Parent

Promotores: P. Stevenhagen, E. Fouvry (Univeriste Paris Saclay)

Promotor: P. Stevenhagen, Co-promotor: R.M. van Luijk

Promotor: Prof.dr. P. Stevenhagen, Jan-Hendrik Evertse, Co-promotor: Pascal Autissier

Promotor: S.J. Edixhoven

Promotores: P. Stevenhagen, A. Enge Co-Promotor: T.C. Streng

Het onderzoeksprogramma Probability Theory richt zich op kansrekening en op operationeel onderzoek.

This thesis provides explicit expressions for the density functions of absolutely continuous invariant measures for general families of interval maps, that include random maps and infinite measure transformations, not necessarily number systems.

Promotor: H.W. Lenstra, Jr., Co-promotor: B. de Smit

In analogy to mathematical proofs, the goal of a proof system is for a prover to convince a verifier of the correctness of a claim.

Promotor: Robert Tijdeman, Co-promotor: Cornelis Kraaikamp

Promotor: Prof.dr. P. Stevenhagen, Prof.dr. K. Belabas (Univ. de Bordeaux)

To an algebraic curve C over the complex numbers one can associate a non-negative integer g, the genus, as a measure of its complexity.

This dissertation consists of two parts, each of which considers a different research area related to random interval maps. In the first part we are interested in random interval maps that are critically intermittent.

The unit residue group, to which the present thesis is devoted, is defined using the norm-residue symbol, which Hilbert introduced into algebraic number theory in 1897.

Promotoren: R. Tijdeman, A.K. Lenstra, Co-promotor: H.J.J. te Riele

The thesis mainly contributes to the characterization of Majorana fermions as they appear in the Condensed Matter context.

In this thesis three different topics in number theory are studied.

De masteropleiding Cultural Analysis: Literature and Theory van de Universiteit Leiden richt zich op de studie van literatuur vanuit een vergelijkend en theoretisch perspectief, en onderzoekt de literatuur van een breed spectrum van talen en culturen uit de hele wereld.

My PhD research is devoted to studies of the conjectural cluster-algebraic symmetry in the theory of topological string, which is the simplest, however already non-trivial sector in the theory of string.

In deze masterspecialisatie houd je je bezig met twee kernthema’s in de politieke filosofie: legitimiteit en rechtvaardigheid. Je verdiept je in theoriën, methoden en complexe casus en maakt de stap van opinie naar analyse.

Promotor: K.E. Schalm, Co-promotor: S.S. Lee

This six-weeks online course delves into the research behind terrorism as it unpacks the assumptions and impacts of both terrorism and counterterrorism.

Most of current public-key cryptography is considered insecure against attacks from sufficiently powerful quantum computers. Post-quantum cryptography studies methods to secure information resistant against such attacks. One proposal is isogeny-based cryptography, which bases its security on computational…

In this thesis, rational points on K3 surfaces are studied. In the first part of Chapter 1 the Brauer group and the the Brauer-Manin obstruction are introduced.

Fundamental research in the ALgebra, Geometry And Number Theory

Quantum critical metals at vanishing fermion flavor number.

In deze studie onderzoeken we of 2-3-jarigen in staat zijn te anticiperen op het gedrag van een personage door rekening te houden met wat dit personage wel of niet weet over de situatie. Het kind zit op schoot en krijgt animaties te zien met twee personages, waarbij de ene zich verstopt en de andere…

Promotor: Peter Stevenhagen

Promotor: J. Zaanen

In this work we describe three methods to improve the performance of Quantum Field Theory calculations.

Op 16 april 2020 verdedigde Andrew Fink zijn proefschrift 'The Importance of Conspiracy Theory in Extremist Ideology and Propaganda'. Het promotieonderzoek is begeleid door promotor prof.dr. A. Ellian.

Systems with local constraints is a new finding in recent researches on complex systems. The heterogeneous spatial interactions and the temporal dependencies among those numerous units make it difficult to describe by traditional statistical physics.

Femke Bakker, Hawks and Doves: Democratic Peace Theory Revisited

The next generation of high-contrast imaging instruments on space-based observatories requires sophisticated wavefront sensing and control in addition to a high-performance coronagraph.

Seminar

Seminar

Seminar

Hoe kunnen we de mysteries van quantummaterie verklaren?

Professor Edwin Bakker, directeur van het Centrum voor Terrorisme & Contraterrorisme heeft zijn nieuwe boek getiteld 'Terrorism and Counterterrorism Studies: Comparing Theory and Practice' bij Leiden University Press uitgebracht.