Welcome to Vincent's IRIF page PhD topic I am a PhD student at IRIF under the supervision of Paul-André Melliès and Sam van Gool since September 2021, at the École doctorale de Sciences Mathématiques de Paris Centre (ED 386). I belong to the three following teams: Automata and applications from the Automata, structures and verification pole Algebra and computation from the Proofs, programs and systems pole Picube/$\pi r^2$, an Inria project-team hosted by IRIF. The title of my thesis is, in French: Une approche topologique et fibrationnelle de la théorie des automates d'ordre supérieur Our ambition is to connect profinite spaces and Stone-type dualities, codensity monads, linear logic and higher-order automata within a categorical framework. If you have access to the GitLab of Sophie Germain, you can see what I have been recently working on by clicking here. We may have met I have attended the following events outside of IRIF: Linear Logic Winter School, CIRM in Luminy, from the 24th to the 28th of January 2022. Chocola seminar, ENS de Lyon, the 31th of March 2022. Midlands Graduate School, University of Nottingham, from the 10th to the 14th of April 2022. Duality and More workshop, Université Côte d'Azur, from the 16th to the 20th of May 2022. TYPES 2022, including the first Dedukti school, from the 20th to the 25th of June 2022. Contact Nom Moreau Prénom Vincent Téléphone Bureau 4033 Mail moreau@irif.fr Page web https://www.irif.fr/~moreau/