Lecture notes
During my time as a student I liked to type lecture notes à la Gilles Castel. You can find some of them below.
Functional Analysis II
Lecture notes for a semester course given by Prof. Marc Burger at ETH during spring semester 2022. Contents include Banach algebras, spectral theory and Fourier analysis on locally compact abelian groups.
Harmonic Analysis
Lecture notes for a semester course by Prof. Joachim Krieger at EPFL during spring semester 2024. Topics include Fourier theory, aspects in number theory and the Calderón-Zygmund theory.
Algebraic Topology
Lecture notes for a semester course on algebraic topology by Prof. Will J. Merry at ETH during autumn semester 2021. Topics include the fundamental group, singular homology and cohomology.
Theses & semester projects
Master's Thesis
On the stability of the Faber-Krahn inequality for both the short-time Fourier transform and the wavelet transform. Awarded with an ETH medal for outstanding master's thesis. Supervised by Alessio Figalli and João P.G. Ramos.
Bachelor's Thesis
On Hausdorff measures, Hausdorff dimension, self-similar sets and their relationship with the Fourier transform. Awarded with honors at Universidad Autónoma de Madrid. Supervised by Ana Vargas.
The Faber-Krahn inequality for the STFT
A semester paper written while obtaining my master's degree at ETH on the original uncertainty principle for the short-time Fourier transform by F. Nicola and P. Tilli. Supervised by João P.G. Ramos.
Stability of isoperimetric inequalities
A semester paper written during my master's degree at ETH on the classical (N. Fusco, F. Maggi, A. Pratelli) and anisotropic (A. Figalli, F. Maggi, A. Pratelli) sharp quantitative isoperimetric inequality. Supervised by Alessio Figalli.