Knowledge and culture subproject 3:

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

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.

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.

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…

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

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

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.

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.

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).

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

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

Knowledge and culture subproject 3:

Promotor: S.J. Edixhoven, A. Iovita

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 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.

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

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

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

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

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.

Professor of Computer Science Joost Batenburg has received half a million euros from the Dutch Research Council (NWO) to improve the conservation of historical paintings with 3D X-ray imaging.

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

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…

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

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.

n this thesis we study curves. In the first half, we study moduli spaces of curves and Gromov-Witten invariants, certain kinds of curves counts. We employ logarithmic geometry for this.

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

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.

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.

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.

Alumnus Pim Spelier is one of the two winners of the ASML Graduation prizes for mathematics students. He used a new method to solve single polynomial equations. Bachelor student Jorre The wins one of the ORTEC Incentive prizes for the best study results during the first year. On 30 November, the Royal…