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.

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…

Central Limit Theorem associated to a particular case of ergodic total automorphisms. Finally, Chapter 6 proves that the isoperiodic foliation is connected for a meromorphic differential with three poles on a torus.

Within the context of the four national mathematics clusters, NWO has awarded seven proposals for tenure track positions. One of these was on 'Moduli, metrics, models, and arithmetic of Shimura varieties' by Bas Edixhoven from the Leiden Mathematical Institute.

Promotor: R. Cramer

Many students have difficulties to read and give meaning to algebraic formulas. In this study it is explored whether graphing formulas with pen and paper will improve students’ability to reason with algebraic formulas.

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.

This thesis studies operator-algebraic aspects of subproduct systems, a generalization of product systems of Hilbert spaces.

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.

We study the interplay of topology and geometry with chirality for several passive and active systems, employing both analytical and numerical methods.

In this thesis, we explore a Hochschild homology and cohomology-like notion for logarithmic schemes.

Knowledge and culture subproject 3:

This thesis discusses several questions regarding the double ramification cycle as a Chow class on the moduli space of stable n-pointed genus g curves using tools from so-called logarithmic geometry.

Promotores: H.W. Lenstra, B. Erez, Co-promotor: L. Taelman

Promotor: S.M. Verduyn Lunel, Co-promotoren: M.F.E. de Jeu, S.D. Silvestrov

Let A be a commutative algebraic group over a field K, and let G be a finitely generated subgroup of the K-rational points of A. The purpose of this thesis is to study the degrees of the Kummer extensions relative to A,K and G.

This thesis studies the geometry of representation varieties and character stacks. These are spaces parametrizing the representations of a finitely generated group, typically the fundamental group of a compact manifold, into an algebraic group G.

Promotor: Prof.dr. W.T.F. den Hollander, Prof. dr. E.A. Verbitskiy

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.

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.

If X is a locally compact Hausdorff space, then a representation of the complex C* algebra C_0(X) on a Hilbert space $H$ is given by a spectral measure that takes its values in the orthogonal projections on $H$.

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

Promotor: S.J. Edixhoven

Promotores: B. Erez, P. Stevenhagen, Co-Promotor: B. de Smit

Do you have any questions about the master’s specialisation Mathematics and Algebra, Geometry and Number Theory? Please contact us.

Find out how to apply for Algebra, Geometry and Number Theory at Leiden University by following our step-by-step guide.

In this thesis we examine certain phenomena in symplectic topology which are related to the theory of isolated singularities.

The Mathematics and Algebra, Geometry and Number Theory specialisation programme consists of 120 European Credit Transfer System (EC) points and includes a research project (40 EC), advanced courses (min 60 EC) and electives (maximum 20 EC). 30 EC are to be taken from the Dutch national Mastermath p…

From applied to fundamental research, and from algebra to data science, our master’s programme spans these fields entirely. You will be able to follow courses from the national Mastermath programme and write a thesis in one of our strong research groups in algebra, number theory and geometry; dynamical…

In this research we have studied how teaching graphing formulas by hand (i.e. sketching a graph of a formula) could promote grade 11- and 12-students’ symbol sense.

A secret code that we currently use to send e-mails securely is based on the maths of a century ago. The geometrical surfaces that Dino Festi studied during his PhD research will perhaps be used in future codes or new physics. PhD defence 5 July.

The Algebra, Geometry and Number Theory specialisation offers excellent preparation for a career in research and is a strong foundation for pursuing a PhD. At the same time, the skills you develop open doors to diverse career opportunities outside academia.

In this thesis integral points on affine del Pezzo surfaces are studied.

Promotor: Prof.dr. M.L. van Hecke, Co-Promotor: Prof. dr. V. Vitelli

Not all problems are easy to solve, but with enough bright minds, you make progress step by step. ‘The kind of problems I am interested in have been occupying mathematicians for over two millennia,’ says theoretical mathematician David Lilienfeldt. In September, he started at the Mathematical Institute…