Promotor: Prof.dr. P. Stevenhagen, Co-Promotor: Dr. J.H. Evertse

One of the effects of climate change is the phenomenon of desertification, a process that occurs in semi-arid and arid areas and causes land degradation as well as vegetation loss. Due to the lack of resources, vegetation self-organizes to sustain itself by forming large-scale spatial patterns.

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

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

Like a mixture of oil and water, lipid membranes separate into two liquid phases.

Promotor: V. Vitelli, Co-promotor: J. Paulose

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

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.

Knowledge and culture subproject 2:

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…

Knowledge and culture subproject 3:

We live in a data-drenched society awash with numbers. An inhabitant of the democratic polis of Athens (5th and 4th centuries B.C.E.) increasingly found himself surrounded by numerical data. This project aims to analyze the communicative functions and the political meaning(s) ascribed to these public…

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.

The key characteristic of active matter is the motion of an emergent collection (such as a flock of birds), which is driven by the consumption of energy by its active components (i.e. individual birds).

The dissertation offers new tools and insights to computation and modelling of topological phases, with an emphasis on the aperiodic setting.

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.

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.

A semi-empirical version of the specific reaction parameter approach to density functional theory (SRP-DFT) has been remarkably successful at predicting dissociative chemisorption probability vs. incidence energy curves for reactions on metal surfaces. New quantum Monte Carlo (QMC) calculations on the…

Dynamical systems describe the evolution of objects in a space over time and may be used to model physical phenomena. Due to this, much research is dedicated to understanding the mathematics of dynamical systems.

Knowledge and culture subproject 3:

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.

Knowledge and culture subproject 2:

Promotor: S.J. Edixhoven, A. Iovita

Promotor: S.J. Edixhoven

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 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.

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.

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.

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.

Promotores: S.J. Edixhoven, F. Andreatta

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.

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…

Promotor: H.W. Lenstra

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

Promotor: S.J. Edixhoven, L.D.J. Taelman

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

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

In the first part of this thesis we study the geometry of folding patterns.

This PhD-thesis presents a study on micron-sized particles, so-called colloids. By controlling the chemical and physical properties of these particles, such as the interparticle interaction and the particles’ shape, colloids can act as building blocks that self-assembly into larger structures.

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 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.

This thesis is comprised of three chapters covering the theme of studying semistable varieties by looking at their dual combinatorial objects.

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

This work is dedicated to interpreting in cohomological terms the special values of zeta functions of arithmetic schemes.

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.