Projects

This master thesis delves into the exploration of Meta-Learning through a PAC-Bayesian lens, introducing the PACOH algorithm as a new class of meta-learners with probabilistic performance guarantees. It bridges the gap between empirical success and theoretical foundations in Meta-Learning, offering a comprehensive analysis and numerical experiments to demonstrate the efficacy of these approaches.

This Bachelor Thesis presents a numerical analysis of zero-dimensional Fabry-Pérot micro-cavities, emphasizing the impact of integrating hexagonal Boron Nitride (hBN) freeforms to manipulate electric field distributions. Through the development and application of numerical models, the study explores the effects of various hBN lens shapes and configurations within Fabry-Pérot cavities, revealing significant insights into the dependence of transverse confinement on lens curvature and the behavior introduced by multiple lenses. This research contributes to the understanding of optical micro-cavities and lays the groundwork for further exploration of arbitrary hBN shapes in optical device engineering.

This project explores the development and implementation of a real-time data processing system using the Spectrum M4i.4420-x8 digitizer card and SCAPP framework to enhance data acquisition in ultrafast laser experiments. By leveraging the computational power of GPUs, the system processes large data volumes from high-resolution spectroscopy and rapid pump-probe measurements more efficiently than traditional methods. The study demonstrates significant improvements in flexibility and data processing speed, offering a new approach to handling the demanding data analysis requirements of cutting-edge laser research.

This document outlines the Analysis II exam preparation course conducted by Klemens Flöge for Prof. Tristan Rivière’s class in the Spring semester of 2021. The course, delivered in German, aimed to deepen students’ understanding of multivariable calculus, covering topics such as topology, differential calculus in multiple dimensions, optimization, implicit functions and diffeomorphisms, multiple integrals, and major integral theorems like Green’s, Gauss’s, and Stokes’s theorem. The script reflects an effort to bring theoretical concepts closer to students, fostering intuition in Analysis.