Phase transitions on one-dimensional symbolic systems
By Tamara Kucherenko
Approximating entropy/pressure for multidimensional shifts of finite type
By Ronnie Pavlov
Appears in collections : Jean-Morlet Chair - Doctoral school: Elliptic Methods and Moduli Spaces / Chaire Jean-Morlet - Ecole doctorale : Méthodes elliptiques et espaces de modules, Exposés de recherche
Theory of persistence modules is a rapidly developing field lying on the borderline between algebra, geometry and topology. It provides a very useful viewpoint at Morse theory, and at the same time is one of the cornerstones of topological data analysis. In the course I'll review foundations of this theory and focus on its applications to symplectic topology. In parts, the course is based on a recent work with Egor Shelukhin arXiv:1412.8277