Multilinear Fourier multipliers of a locally compact group

In his paper "Group C*-algebras without the completely bounded approximation property", Haagerup proves several important results about the weak amenability of locally compact groups. Among these, is the result that a lattice in a second-countable, unimodular, locally compact group is weakly amenable if and only if the surrounding group itself...

On the Dual of the Lovász Theta Prime Number for the Disjunctive Product of Graphs

The Lovász theta function, and the variants of it given by Schrijver and Szegedy are upper bounds on the independence number of a graph. These functions play an important role in several optimization problems, such as the Cohn-Elkies bound for optimal sphere packing densities.<br/><br/>This thesis covers the properties of these functions. The...

The Asymptotic Behavior of a Random Walk Among a Field of Traps

We consider the problem of random walks moving around on a lattice Zd with an initial Poisson distribution of traps. We consider both static and moving traps. In the static case, we prove that the survival time has a decay of e−c t d /d +2 based on a heuristic argument. In the moving case we aim to prove the sub-exponential...

Real Equiangular Lines

A set of lines passing through the origin in Euclidean space is called equiangular if the angle between any two lines is the same. The question of finding the maximum number of such lines, N(d) in any dimension d is an extensively studied problem. Closely related, is the problem of finding the maximum number of lines, N_α(d), such that the...

Strain tests in low dimensional materials: Geometrical Phase Analysis

In the last decades there has been an increasing interest in computing the local strain at the atomic scale of materials. By knowing aspects of the local strain in a lattice, one has information about measurements of distortions of lattice parameters concerning shifts, deformations and defects computed with respect to a smooth, defect-free...

Controlling the behaviour of eigenvalues: The interlacing method

This thesis uses the method of interlacing polynomials to study the behaviour of eigenvalues of a matrix after a rank-one update. Specifically, interlacing polynomials, common interlacing and interlacing families are exhaustively studied. These are excellent tools to find bounds on the eigenvalues of updated matrices by keeping track of how they...

Een coördinaatvrije basis voor vectorvelden in de context van rotatiesymmetrische operatoren met behulp van sferisch harmonische functies

Vector spherical harmonics are a set of basis functions for vector fields derived from the spherical harmonic functions. They are commonly used in spectral methods in certain areas of applied mathematics. In most of the existing literature they are defined in a way that is heavily dependent on the used coördinate system. In this thesis we define...

Implementations of Quantum Random Walks

In this research, the implementations of quantum random walks in superconducting circuit-QED are studied. In particular, a walk that moves across the Fock states of a quantum harmonic oscillator by a Jaynes-Cummings model is investigated, which is difficult to implement because of different Rabi frequencies for different Fock states....

Noiseless clusters and perturbations in networks of coupled quantum harmonic oscillators

In this thesis, networks of coupled quantum harmonic oscillators are studied. The dynamics of these networks are determined by single-frequency vibrations of the entire network called normal modes. We study the behavior of the nor- mal modes when the network is coupled to a thermodynamical heat bath by looking at the Lindblad Master Equation of...

Classical Capacities of Classical and Quantum Channels

This thesis investigates two types of classical capacities of both classical and quantum channels, giving rise to four different settings. The first type of classical capacity investigated is the ordinary capacity of a channel to transmit classical information with a probability of error which becomes arbitrarily small as the channel is used...