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.

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.

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

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

Modeling and analysis of cyber-physical systems are still challenging. One reason is that cyber-physical systems involve many different parts (cyber or physical), of different nature (discrete or continuous), and in constant interaction via sensing and actuating.

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.

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.

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

Promotie

Fundamental research in the ALgebra, Geometry And Number Theory

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).

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

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

Het belangrijkste doel van dit onderzoek was het bevorderen van de aspecten van de symbol sense die studenten in staat stellen algebraïsche formules te doorzien en niet-standaard algebra problemen aan te pakken.

In dit onderzoek worden orde isomorfismen en orde antimorfisme bestudeerd in het algemene kader van partieel geordende vector ruimten.

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

Promotor: S.J. Edixhoven, A. Iovita

Promotor: S.M. Verduyn Lunel, Co-promotoren: M.F.E. de Jeu, S.D. Silvestrov

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.

Veel leerlingen hebben problemen met het lezen van algebraische formules. Grafieken kunnen betekenis geven aan deze algebraische formules. Wat efficiënte methoden zijn om bij deze formules globale grafieken te maken is tot dusver onbekend.

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.

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

Prof. dr. Bart de Smit benoemd tot hoogleraar Algebra en Getaltheorie bij het Mathematisch Instituut van de Universiteit Leiden.

Promotor: S.J. Edixhoven

Promotores: H.W. Lenstra, B. Erez, Co-promotor: L. Taelman

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.

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

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

With tomography it is possible to reconstruct the interior of an object without destroying.

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.

Promotor: S.M. Verduyn Lunel, Co-promotores: M.F.E. de Jeu, B. de Pagter

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.

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.

Het Mathematisch Instituut heeft een lichte managementstructuur. Taken zijn gespreid over de staf. Belangrijke beslissingen worden genomen per consensus. Hieronder worden diverse organisatieonderdelen toegelicht.