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.

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.

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.

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.

Bruin

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

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.

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

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.

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.

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

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.

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.

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.

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.

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.

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…

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

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.

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.

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

Promotor: S.J. Edixhoven

Within the Mathematical Institute, the Algebra, Geometry and Number Theory research group organises a seminar.

In the Algebra, Geometry and Number Theory specialisation you dive deep into pure mathematics. You explore both the fundamentals and how mathematics is applied in other sciences, society and industry. As a master’s student you join a multidisciplinary research team at the Mathematical Institute and…