Work
Exotically knotted surfaces (2024). My master's thesis in mathematics advised by Prof. Peter Teichner and Dr. Isaac Sundberg.
Exotic embeddings (2024). Notes for the seminar talk on 4-manifolds I gave at the University of Bonn. The seminar is led by Dr. Roberto Ladu and Dr. Laura Wakelin.
On Groups of Homotopy Spheres (2024). Notes for the Advanced Homotopy Theory seminar talk I gave at the University of Bonn. The seminar was led by Prof. Dr. Stefan Schwede and Dr. Jack Davies.
Bezout's Theorem and Varieties of Minimal Degree (2023). Notes for the Classical Algebraic Geometry seminar talk I gave at the University of Bonn (2023). The seminar was led by Dr. Yajnaseni Dutta.
Exotic smooth structures on spheres (2022). My bachelor's thesis in mathematics advised by Dr. Ricardo García López
Abstract: The main goal of this work is to prove the existence of exotic smooth spheres. These are smooth manifolds that are homeomorphic but not diffeomorphic to the standard sphere. This was first shown in the 7-dimensional case by John Milnor in his influential paper [Mil56], and this work replicates his construction. In order to state and prove this result, though, a journey through some background is needed. This includes singular homology and cohomology theory, Morse theory and characteristic classes. Hence, we also slightly develop these topics here.
A quantum annealing protocol to solve the maximum clique problem (2022). My bachelor's thesis in physics advised by Prof. Dr. Bruno Juliá-Díaz.
Abstract: We give a short introduction to quantum annealing in the transverse Ising model and formulate the maximum clique problem in this setting. We then briefly show how problems are actually implemented in D-Wave’s annealers through the idea of minor-embeddings and chains. We also provide simulations for a small problem and actual results on D-Wave’s annealers for larger instances as well as the dependence of the success rate on different parameters.
Apunts d'Anàlisi Matemàtica (2018). Notes of Real Analysis with solved exercises (in Catalan).