2019

Le programme de l’école de recherche est orienté de façon à faire profiter les auditeurs des dernières avancées dans le domaine du Machine Learning, Deep Learning et d’autres techniques de réduction de modèles. La communauté de l’intelligence artificielle et des statistiques, et celle du calcul scientifique se sont retrouvées ces dernières années pour donner naissance à de nouveaux algorithmes utiles aux deux thématiques.

The notion of a group describes symmetry in mathematics. In recent decades, certain quantum mathematical objects have appeared whose symmetries are better described by group-like objects called tensor categories. Examples of areas of mathematics where tensor categories play a key role include subfactors, quantum groups, Hopf algebras, quantum topology and topological quantum computation. The aim of this is school is to introduce graduate students to tensor category theory and their applications to Topological Quantum Field theory, Subfactor theory and Hopf algebras.

This school is about a smooth transition from classical graph theory to modern approaches. At first extension of coloring results to homomorphisms of digraphs are presented. Next lectures would be on algorithmic graph theory with classic approaches such as LexBFS ordering being combined with modern ideas. Mixing algorithms with applications, there will be lectures on distributed algorithms. School will conclude by lectures on how to use power of randomness, which is a rather new modern and powerful method.

The school aims at presenting some of the current approaches in PDE modelling and mathematical analysis of biological phenomena or related domains. It aims at allowing the researchers and the students of Master’s degree level and talented undergraduate students to acquire a basic training in that field and to have an overview of what is the current research status of these types of problems.

Application of Dynamical Systems to Biology is nowadays an important challenge. The goal of this school is, on the one hand to present the basic tools in Dynamical Systems to solve ODE's, and, on the second hand, to present how these tools can be used in Biology. The school will comprise two series of lectures. One theoretical one and one for applied mathematics. A large part will be devoted to exercises sessions.