Here are a few expository documents I wrote at some point, either for myself, for a talk, or for a class.
- Constructions of Morse-Bott Homology in Finite Dimension (2016), written when I was thinking about Morse-Bott contact homology. This is just a recollection of three approaches to Morse-Bott homology described in the literature: one uses the moduli spaces of cascades, one uses a spectral sequence that interpolates between the singular chain complex and the Morse-Smale complex, and the last one uses currents.
- Introduction aux Noeuds Legendriens (2013, in French), the outcome of an assignment for the class Compléments de Topologie Algébrique - Théorie des Noeuds (LMAT 2240).
- Structures Symplectiques sur les Fibrés Cotangents de Variétés Ouvertes de Dimension 4 (2013, in French), the outcome of my work for the class Initiation à la Recherche II (MATH-F405) in 2013, under the supervision of Mélanie Bertelson. The goal was to introduce the prerequisites to this paper by Knapp, and then to understand the paper.
- Sur les Groupes d'Homotopie et le Théorème de Périodicité de Bott (2012, in French), the outcome of my work for the class Initiation à la Recherche I (MATH-F404) in 2012, under the supervision of Joel Fine. This document has two parts. In the first one I expose the basics of homotopy groups following Hatcher's Algebraic Topology. In the second one I prove Bott's periodicity for unitary groups, following Bott's original paper The Stable Homotopy of the Classical Groups and Milnor's Morse Theory.
- Introduction à la Théorie des Noeuds (2012, in French), published in Notes de la cinquième BSSM (2012). These are the notes for a talk on knot theory I gave at the Brussels Summer School of Mathematics in 2012, where I was invited to speak after I apparently gave a particularly good talk in the class Travaux de Recherche Mathématique (MATH-F305) at the Université Libre de Bruxelles.