While the national Mastermath program allows you to follow courses all across the country, the master thesis project should make the difference in your choice of university. Have a look at a list of exciting thesis topics that you could explore at the Vrije Universiteit Amsterdam.
Project: Patterns and Uncertainty Quantification in Brain dynamics
Supervisor: Daniele Avitabile
Short Description: models of brain activity have a special structure: the activity at a certain position in the brain changes as a consequence of the interaction with nearby neurons, as well as contributions from distant areas of the brain. The mathematical structure of such equations is special, in that it contains integrals as well as differential operators. This project aims to investigate the occurrence of patterns in the brain using a variety of techniques which, depending on the student’s preference and study path, may be drawn from dynamical systems, numerical methods, statistical analysis, functional analysis, or a combination thereof.
Project: Periodic orbits of relativistic particles
Supervisor: Gabriele Benedetti
Short description: This project studies the periodic motions of a charged particle hit by an electromagnetic wave in the presence of symmetry. We investigate the number of such motions and their relation with the underlying geometry of the space.
Project: Networks, Symmetry, and Synchrony
Supervisor: Christian Bick
Short description: Synchronization is one of the most fascinating emergent dynamical phenomena when you couple oscillatory units (such as metronomes). The goal of this project is to determine possible synchronization patterns, whether they are stable, and how they can be controlled based on network properties such as symmetry or the existence of nontraditional 'higher-order' interactions.
Project: Computer Assisted Proofs
Supervisor: Jan Bouwe van den Berg
Short Description: Computers are often used in mathematical research to perform experiments and simulations. In this project we use computers to help us prove theorems,in particular about the interesting, complex dynamics described by solutions of nonlinear (ordinary, partial) differential equations.
Project: Stochastic electrodynamics
Supervisor: Oliver Fabert
Short description: In the classical atom model the electron would constantly lose energy to the electromagnetic field due to its own acceleration. Stochastic electrodynamics aims at explaining quantum mechanical phenomena of charged particles by employing the existence of the zero-point field (vacuum fluctuations of the electromagnetic field) which can be treated as a random classical field.
Project: On the Study of Feed Forward Network Dynamics
Supervisor: Fahimeh Mokhtari
Short Description: Numerous phenomena are described by the dynamics that are occurring on a set of nodes in a network that are connected to each other along edges (links) in some nontrivial fashion. Network dynamics is a research field focused on analyzing how the states of these networks change over time.
One class of network dynamical systems is feed forward networks. These networks are characterized by loop-free node connections and cells receive input only from the cells below. In this project, we aim to conduct a bifurcation analysis of these systems near nilpotent singularities, considering versal deformation parameters.
Project: Turán problem and eigenvalues of hypergraphs
Supervisor: Raffaella Mulas
Short description: Given integers n>= k > r >= 2, the Turán problem consists of determining or estimating the largest integer t such that there exists an r-uniform hypergraph on n vertices and t edges that does not contain any complete r-uniform hypergraph on k vertices as a sub-hypergraph. In this project, we aim to investigate the spectral properties of optimal solutions to this problem and its variants.
Project: Thriving or surviving: how bacteria manage to stay alive in an ever-changing world
Supervisor: Bob Planqué
Short Description: Bacteria thrive in diverse and hostile environments by balancing growth during favorable conditions and survival in adverse ones, despite having limited information to guide these decisions. This project will use dynamical systems theory, linear programming, convex analysis and control theory to model how cells manage their internal chemical networks and optimize their behavior with incomplete information.
Project: Periodic orbits of mathematical billiards
Supervisor: Bob Rink
Short description: The classical billiard problem posed by Birkhoff considers the motion of a point mass through a convex planar domain, such that when the point mass hits the boundary of the domain, it changes its direction obeying the rule “angle of incidence equals angle of reflection”. This simple problem defines a dynamical system given by a so-called symplectic twist map on the 2-dimensional annulus. Mathematicians have studied the billiard problem for over a century now, and surprisingly there still are many open problems. In this project we exploit that the orbits of the billiard map correspond to extremal points of an action function. We will use this variational principle to find unknown periodic orbits in billiards and hopefully prove that certain billiards support chaotic dynamics.
Project: Dimension reduction for networks of coupled oscillators
Supervisors: Bob Rink and Christian Bick
Short description: Synchronization occurs in many networks of coupled oscillators across physics (e.g., coupled metronomes), biology (e.g., flashing fireflies) and neuroscience (e.g., brain rhythms). Predicting and computing synchrony is important to understand the function of these systems. But direct computations of synchrony patterns is often infeasible since most natural oscillator systems are high-dimensional. In this project we will develop and apply phase reduction techniques that can greatly reduce the dimension of an oscillator network. This makes an explicit analysis of these systems feasible and allows to determine which types of interactions between oscillators lead to global synchronization.