Investigating neutrino oscillations and diffuse cosmic neutrino fluxes with the KM3NeT neutrino telescope

KM3NeT is a neutrino telescope under construction in the Mediterranean Sea. Among the main goals is the discovery and subsequent study of sources of high-energy neutrinos. Furthermore, the determination of the mass ordering of the three known neutrino types is envisaged which is possible via oscillations of atmospheric neutrinos on their path through Earth. For these goals, two separate detectors are being built: the ARCA detector for high-energy neutrino astronomy, and the ORCA detector dedicated to the determination of the mass ordering. This work presents contributions to both detectors. Based on numerical calculations, neutrino oscillations in the Earth have been analysed in order to predict the susceptibility of the ORCA detector to systematic uncertainties both in the Earth model and in fundamental oscillation parameters describing the neutrino oscillations. Furthermore, the calculation of oscillation probabilities still represents a major bottleneck in the CPU time consumption of ORCA sensitivity studies. A dedicated interpolation algorithm has therefore been developed with the aim to reduce the corresponding computing time by calculating all needed oscillation probabilities in advance. The amount of data needed for these interpolations has been estimated as well. The final computing time needed to run the ORCA sensitivity studies is expected to be reduced by these measures by around three orders of magnitude. In order to increase the sensitivity of the ARCA detector to an isotropic high-energy cosmic neutrino flux, a machine learning algorithm for the classification of neutrino events has been developed. The studies achieve unprecedented sensitivity in the shower channel, a major neutrino event class. The "rediscovery" of the cosmic neutrino signal measured and published by the IceCube collaboration is possible within less than one year observation time. In particular, considering the strongest published signal flux, an observation with 5$\sigma$ significance is possible in less than 0.3 years with 50% observation probability, meaning that the chance for a random background fluctuation giving a similar signature is below 2.87 $\cdot$ 10${}^{-5}$ %. Compared to previous ARCA sensitivity analyses in the shower channel, the time needed for such a significant observation is reduced by at least 25% up to about 50% depending on the assumed signal flux hypothesis. Furthermore, besides the potential determination of the so-called prompt atmospheric neutrino flux, the capabilities of the ARCA detector to constrain the spectral shape of an isotropic cosmic neutrino flux has been analysed for the first time within the KM3NeT collaboration. In addition, part of the work performed during the doctoral studies included tutoring of diverse student classes, the maintenance and administration of a Mac client-server system (about 100 users) as well as the work with several Linux systems including an HPC system.