Promotor: Prof.dr. P. Stevenhagen, Co-Promotor: 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: V. Vitelli

Het onderzoek binnen het Algebra, Geometry and Number Theory programma varieert van fundamentele wiskundige theorie tot algoritmes en toepassingen.

In de masterspecialisatie Algebra, Geometry and Number Theory verbreed je je kennis van de zuivere wiskunde met onderwerpen als getaltheorie, algebraïsche meetkunde, algebraïsche topologie en cryptologie.

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

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

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

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).

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.

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: H.W. Lenstra

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

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.

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.

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

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

Promotores: P. Stevenhagen, E. Fouvry (Univeriste Paris Saclay)

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.

Promotor: S.J. Edixhoven

Quantum critical metals at vanishing fermion flavor number.

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.

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…

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.

Promotor: Prof.dr. P. Stevenhagen, Prof.dr. K. Belabas (Univ. de Bordeaux)

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

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

Promotor: S.J. Edixhoven, A. Iovita

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

Artin L-functions associated to continuous representations of the absolute Galois group G_K of a global field K capture a lot of information about G_K as well as arithmetic properties of K.

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

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.

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 unit residue group, to which the present thesis is devoted, is defined using the norm-residue symbol, which Hilbert introduced into algebraic number theory in 1897.

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.

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

Promotor: Peter Stevenhagen

This thesis consists of three chapters, the first two of which concern division points of elements of the multiplicative group of a number field.

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.

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.

Promotores: S.J. Edixhoven, F. Andreatta

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

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.

Op 3 september promoveert Adrian Stenton. Het Leiden University Centre for Linguistics feliciteert Adrian!

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.

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.

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.

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