The 21st century is witnessing a revolution in our understanding of rational points on surfaces and higher-dimensional varieties, and it is in this field that this project lies.

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.

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: S.J. Edixhoven

We find ourselves in an era of transition, not just towards a more computing- and data-driven society but also away from unsustainable fossil fuels as an energy source.

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…

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.

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.

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 three-dimensional shape.

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.

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…

Morality, mathematics, geometry, geography, music, navigation, and language are traditionally viewed as uniquely human cultural achievements and abilities. The study of their development and variation is classified as part of the humanities and social sciences. These fields have been mainly studied…

In this thesis, we investigate how deep generative models (AI models that can create new designs) can be better utilized for technical and industrial design. Our goal is to generate designs that are not only realistic (plausible), but also efficient, reliable, and usable in complex 2D and 3D applica…

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…

How can you figure out which points lie on a certain curve? And how many possible curves do you count by a given number of points? These are the kinds of questions Pim Spelier of the Mathematical Institute studied during his PhD research. Spelier received his doctorate with distinction on June 12.

Fundamental research in the ALgebra, Geometry And Number Theory

Promotor: W. Jaffe, Co-promotor: K. Meisenheimer

On 30 September 2013 Ronald Cramer, head of the Cryptology group of Centrum Wiskunde & Informatica (CWI) and a professor of cryptology at the Mathematical Institute of Leiden University, was inaugurated as a member of the Royal Netherlands Academy of Arts and Sciences (KNAW).

Within the Mathematical Institute, the Algebra, Geometry and Number Theory research group organises several meetings.

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In this thesis, we show that we can use Shimura’s CM theory to explicitly compute the Hilbert class field of any primitive quartic CM field.

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

How can you solve equations that define not ‘just’ curves, but also two-dimension surfaces or even higher-dimensional objects? That’s the big question that mathematician Martin Bright and his team will be trying to answer. They’ve received a NWO Science-XL grant of 2.8 million euros.

We are interested in understanding the mechanics of soft materials, of which biological materials are prominent examples.

During the development of the (human) body from a single fertilized egg, organs and structures must form. The development and growth of biological forms is called morphogenesis.

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

Promotor: Peter Stevenhagen

PhD defence

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.

Promotores: S.J. Edixhoven, F. Andreatta

We study the dynamics of individual emitters in micro cavities.

The main topic of this PhD thesis is the Arakelov ray class group of a number field, an algebraic object that contains both the ideal class group structure and the unit group structure.

This thesis explores interfacial conductance and electric field-effects in LaAlO3/SrTiO3 heterostructures.

The Mathematics master’s programme provides a solid theoretical foundation and prepares you to work in multidisciplinary and international environments. With a Leiden Mathematics degree, you’ll have the tools to pursue opportunities worldwide in research, industry, and beyond.

The Mathematics and SCS master specialisation gives you the opportunity to combine Mathematics research with different aspects of science communication.

The two-year research programme Applied Mathematics offers courses at an advanced level. There is a large degree of freedom in choosing one’s own topics. Some of the courses are given at national level, in the Dutch Mastermath programme. The programme concludes with the preparation of a master’s the…

We prove a p-adic version of the work by Gross and Zagier on the differences between singular moduli by proving a set of conjectures by Giampietro and Darmon, who investigated the factorisation of a rational invariant associated to a pair of CM-points on a genus zero Shimura curve, obtained as the ratio…

As an alternative to the diving board shaped force sensor, we are now developing a magnetically levitated small superconducting particle – or ‘Lead Zeppelin'' – as our mechanical resonator. We explore routes towards detection of gravity between small objects.

The first book ever on information-theoretically secure multiparty computation

In this thesis, we address two problems concerning the tautological rings of the moduli space of curves.

In Chapter 1 we provide some background information about modular forms, describe the correspondence between half-integral and integer weight modular forms and explain how the coefficients of half-integral weight modular forms encode the central values of L-functions of twisted modular forms.

The Mathematics and Education master specialisation gives you the opportunity to combine Mathematics research with an excellent education in becoming a Mathematics teacher.

The MSc Mathematics programme offers a dynamic and flexible curriculum that allows you to shape your own path—whether you're aiming for a research career in mathematics or looking to apply your skills in education, industry, business, or science communication.

Located in the friendly small city of Leiden in the centre of the Netherlands, Leiden University has for centuries been at the forefront of developments in science and mathematics and that excellent continues today, with world-leading department of mathematics, physics, astronomy, chemistry and computer…

Combine training in Mathematics research with different aspects of business studies. Learn to build bridges between science and business.