2023

Recent years have witnessed the emergence of powerful semantic tools for non-classical logics. These semantic methods draw from web of mathematical formalisms at the intersection of ordered and universal algebra, topology, and category theory, and together provide a flexible and unifying framework for the study of logic across a host of domains. LIACT serves as a broad introduction to this dynamic and quickly growing area of modern mathematical research, and places particular emphasis on this area's deep interactions with/and applications to computer science.

Differential equations are typically considered to be a subject of mathematical analysis or, more generally, "continuous mathematics". However, algebraic and discrete methods have been successfully applied to questions about differential equations such as, for example, finding symmetries or closed-form solutions. Recent years have witnessed significant development of constructive aspects of algebraic geometry and tropical algebra including deep theory and efficient algorithms.

La cryptographie post-quantique a pour objectif de développer des algorithmes mathématiques assurant la sécurité et résistant à l’ordinateur quantique. En effet, il est établi que si un tel ordinateur est mis au point, alors il permettra de casser de nombreux cryptosystèmes largement utilisés aujourd’hui comme RSA, ElGamal et d'autres. La communauté cryptographique a identifié 5 grandes pistes pour construire des cryptosystèmes résistants à l'ordinateur quantique. Elles exploitent la difficulté présumée de problèmes portant sur :

Coding theory is a remarkable example of how various areas of mathematics can be used to solve problems in the storage and transfer of information. In this school, participants will be introduced to various techniques used in recent years to solve problems in coding theory. The aim is to motivate participants to do research in coding theory.