<style> .boxed { background: #F2F2F2; color: black; border: 3px solid #535353; margin: 0px auto; width: 80%; padding: 10px; border-radius: 10px; } </style> <meta charset="utf-8"> **Habilitation 脿 Diriger des Recherches (HDR)** **Sam van Gool** **[IRIF](https://www.irif.fr), [Universit茅 Paris Cit茅](https://www.u-paris.fr)** **Manuscript.** [Logical reflections: Profinite monoids, propositional quantifiers, and temporal operators](https://www.samvangool.net/hdr.pdf). **Abstract.** My HDR manuscript surveys some of the research in algebra, topology, logic, and the foundations of computer science that I have contributed to since completing my PhD in 2014, and suggests directions for further research in this field. The work I report on falls into three research themes: (1) profinite monoids and their relationship to automata and regular languages; (2) uniform interpolation and its relationship to model-complete theories; (3) axiomatization and unifiability for temporal logics. A thematic coherence between these topics lies in the recurring appearance of techniques from infinite model theory and universal algebra for studying finitary phenomena, and the use of projective limits of finite structures. This report aims to show how these techniques help with solving problems in all three of these, a priori different, research themes. **Jury.** + Val茅rie Berth茅, Directrice de Recherche, CNRS, Universit茅 Paris Cit茅, examinatrice + Jean Goubault-Larrecq, Professeur des Universit茅s, Universit茅 Paris-Saclay, rapporteur + Victoria Gould, University of York, rapporteure (absente 脿 la soutenance) + Dexter Kozen, Professor, Cornell University, rapporteur + Paul-Andr茅 Melli猫s, Directeur de Recherche, CNRS, INRIA, Universit茅 Paris Cit茅, examinateur + Carlos Simpson, Directeur de Recherche, CNRS, Universit茅 C么te d'Azur, examinateur + Christine Tasson, Professeure des Universit茅s, Institut Sup茅rieur de l'A茅ronautique et de l'Espace, examinatrice **Defense.** The defense will take place on **Friday, December 6th, 2024**, at **13h**, in room **2011** of the **Sophie Germain** building, 8 place Aur茅lie Nemours, Paris 13猫me. It will be followed by drinks at IRIF, on the 4th floor of the same building. **Contact.** For more information, please contact Sam van Gool, <vangool@irif.fr>. <!-- Markdeep: --> <style class="fallback">body{visibility:hidden;white-space:pre;font-family:monospace}</style> <script>window.markdeepOptions = {autoLinkImages: false, tocStyle: 'short'};</script> <script src="./markdeep.min.js" charset="utf-8"></script> <script>window.alreadyProcessedMarkdeep||(document.body.style.visibility="visible")</script>