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

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

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.

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.

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

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).

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

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

Promotor: S.J. Edixhoven, A. Iovita

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

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

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

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.

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

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

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

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.

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.

Promotor: S.J. Edixhoven

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.

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.

Fundamental research in the ALgebra, Geometry And Number Theory

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

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.

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

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

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.

Deze tweejarige opleiding heeft twee componenten. De eerste is een meer analysegerichte component, met onderwerpen als dynamische systemen, differentiaalvergelijkingen, kansrekening en stochastiek, percolatie of wiskunde in de life sciences. De andere betreft een meer algebra- of meetkundegerichte component,…

De 21e eeuw is getuige van een revolutie in ons begrip van rationale punten op oppervlakken en hoger-dimensionale variëteiten, en het is binnen dit vakgebied dat dit project zich bevindt.

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…

Promotor: Peter Stevenhagen

Promotores: S.J. Edixhoven, F. Andreatta

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

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…

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.

Het onderzoek in de cluster Algebra, meetkunde en getaltheorie slaat bruggen tussen abstracte theorie en de wereld van algoritmen en toepassingen.

Promotor: A. Kros

This thesis investigates how cell shape and collective behavior influence the dynamics and structure of biological tissues, which are crucial for understanding processes like embryonic development, tissue regeneration, and metastasis.

Sewer pipes are an essential infrastructure in modern society and their proper operation is important for public health. To keep sewer pipes operational as much as possible, periodical inspections for defects are performed.