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.

The defense will be followed by drinks at IRIF, on the 4th floor of the same building.

The manuscript is available via: https://www.samvangool.net/hdr.html

The focus of this habilitation thesis is on secure computation, an area of cryptography that lets multiple parties distributively compute a function on their private data. After providing a high-level introduction to my work in cryptography, the manuscript provides a gentle introduction to secret-sharing-based secure computation, which is aimed at a general audience. Then, the last chapter covers some of my contributions to secure computation through the introduction and construction of pseudorandom correlation generators (PCG), a cryptographic primitive that enables considerable efficiency improvements for a wide variety of secure computation protocols. I provide a step-by-step introduction to the notion of PCG and its security properties, outline the challenges in building them, and present a general framework for constructing PCGs. The chapter also contains extensive efficiency considerations and covers various optimizations, as well as extensions and generalizations of the notion of PCGs. Altogether, this provides a unified introduction to the work on pseudorandom correlation generators developed in my work over the past five years, aimed at a broad cryptography audience.

Jury:
Michel Abdalla, reviewer, DR CNRS at ENS Paris
Benny Applebaum, reviewer, professor at Tel-Aviv University
Ivan Damgård, examiner, professor at Aarhus University
Carmit Hazay, reviewer, professor at Bar-Ilan University
Sophie Laplante, examiner, professor at Université Paris-Cité