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.

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.

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

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

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).

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

Fundamental research in the ALgebra, Geometry And Number Theory

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.

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,…

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.

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

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.

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.

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

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…

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

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

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

Artful Mathematics: The Heritage of M. C. Escher

Promotor: S.J. Edixhoven, A. Iovita

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.

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

In analogy to mathematical proofs, the goal of a proof system is for a prover to convince a verifier of the correctness of a claim.

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

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.

Een geheimschrift waarmee we nu veilig e-mails versturen is gebaseerd op wiskunde van honderd jaar geleden. De meetkundige oppervlakken die Dino Festi bestudeerde tijdens zijn promotieonderzoek worden wellicht in toekomstige geheimschriften of nieuwe natuurkunde toegepast. Promotie 5 juli.

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.

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