The research of the Algebra, Geometry and Number Theory programme ranges from fundamental mathematical theory to algorithms and applications.

The research of the Algebra, Geometry and Number Theory cluster tries to bridge the gap between abstract theory and the world of algorithms and applications.

Developing a method to simplify polynomials in complex curves

Bruin

The master’s specialisation Algebra, Geometry and Number Theory at Leiden University is aimed at students who wish to acquire a profound knowledge of one of the areas within pure mathematics. There is a strong theme dealing with algebra and number theory as well as a strong theme dealing with topology…

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…

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.

Leiden Professor of Number Theory Manjul Bhargava has been awarded a Fields Medal, widely regarded as the Nobel Prize for Maths. Bhargava is a professor in Princeton, and since 2010 has also been the holder of the Stieltjes chair in Leiden.

On Tuesday 15 September 2015, Bart de Smit has been appointed as professor of Algebra and Number Theory at the Mathematical Institute of Leiden University.

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.

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

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

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

Promotor: H.W. Lenstra

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

The research programme Probability Theory focuses on probability theory and on operations research.

Many important topics in computer science, such as the correctness of software, the efficiency of algorithms and the modeling of complicated systems, depend on sound theoretical underpinnings. In the Theory group, we study these fundamental building blocks and develop verification methods to prove system…

Promotor: Robert Tijdeman, Co-promotor: Cornelis Kraaikamp

Many important topics in computer science, such as the correctness of software, the efficiency of algorithms and the modeling of complicated systems, depend on sound theoretical underpinnings. In the Theory group, we study these fundamental building blocks and develop verification methods to prove system…

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 book addresses the definition of history and how people are influenced by it.

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

Combining geometry and number theory. That is what Dr Jan Vonk of the Institute of Mathematics receives a Vidi grant for today. ‘By fusing these two disciplines we may be able to solve a century-old mathematical problem.’

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.

Subproject of

Leiden PhD student Peter Koymans has been declared ‘best mathematics PhD student’ by the Royal Dutch Mathematical Society (KWG). He received the prize at the Dutch Mathematical Congress (NMC) on 24 and 25 April. With his talk about his research into the Cohen-Lenstra conjecture, Koymans left eleven…

The Death of Archaeological Theory, edited by John Bintliff and Mark Pearce, addresses the provocative subject of whether it is time to discount the burden of somewhat dogmatic theory and ideology that has built up over the last 25 years.

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

On the brink of war, what influences decision makers to attack another country? Using innovative theoretical angles, Femke E. Bakker explores whether the basic assumptions of democratic peace theory are indeed correct. She stresses the microfoundations of conflict, questioning the assumptions on…

Majorana meets a mermaid

Sentencing is becoming increasingly complex for the courts. Legal scholars and criminologists from Leiden document the process of sentencing in the Netherlands. They use this knowledge to advise legislators and those who implement this legislation on how to make sentencing more consistent and effect…