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

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.

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.

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

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.

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).

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

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

Promotor: S.J. Edixhoven

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.

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.

Promotor: S.J. Edixhoven

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.

Promotie

Fundamental research in the ALgebra, Geometry And Number Theory

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

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

This PhD thesis concerns the topic of arithmetic geometry. We address three different questions and each of the questions in some way is about counting how big some set is or can be.

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

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,…

Promotor: Peter Stevenhagen

Promotores: S.J. Edixhoven, F. Andreatta

Promotor: R. Cramer

Promotor: M.T.M. Koper, Co-promotor: J.B.F. Juurlink

Promotor: K.J. Batenburg

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

Promotor: A. Kros

Arithmetic geometry concerns the number-theoretic properties of geometric objects defined by polynomials. Mathematicians are interested in the rational solutions to these geometric objects.

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.

Promotor: Prof.dr. W.Th.F. den Hollander, Co-promotor: R. Fernandez.

Na het afronden van de bacheloropleiding volgen verreweg de meeste studenten de masteropleiding.

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.

The key purpose of this project is to study tautological relations on the level of closed differential forms or even integral cochains (i.e. we don't take classes in cohomology).

Promotor: Bas Edixhoven, Promotor: Qing Liu

A tidal basin is an inland sea which is almost entirely enclosed by land and connected to the open sea by a tidal inlet. Through the tidal inlets interaction takes place between the tidal basin and the open sea.

Hoe kun je vergelijkingen oplossen die niet ‘slechts’ een curve beschrijven, maar ook tweedimensionale oppervlaktes of zelfs objecten met nog meer dimensies? Dat is de grote vraag die wiskundige Martin Bright en zijn team gaan proberen te beantwoorden. Ze krijgen hiervoor een NWO Science-XL subsidie…

Het onderzoekscluster Geometry and Quantum Theory (GQT) heeft aan Björn de Rijk, in augustus 2012 afgestudeerd bij Marcel de Jeu en huidig MI promovendus, de GQT Student Prize 2011-2012 toegekend voor zijn masterscriptie “The Order Bicommutant”.

In het raamwerk van de nationale clusters in de wiskunde heeft NWO zeven voorstellen voor een tenure track positie goedgekeurd. Een van deze voorstellen is: 'Moduli, metrics, models, and arithmetic of Shimura varieties' door Bas Edixhoven van het Leidse Mathematische Instituut.

15 veelbelovende Leidse onderzoekers kunnen de komende jaren hun onderzoeksplan realiseren dankzij een Veni-financiering van NWO, waaronder de chemici dr. Wangyang, dr. Calle-Vallejo en dr. Chiodo en de astronoom dr. Tobin. Veni-onderzoekers zijn maximaal drie jaar geleden gepromoveerd. 15 onderzoekers…