2018

The autumn school will show recent developments in index theory in connection with noncomuutative geometry and global analysis. The scientific programme will include topics related to Secondary index theory, index theory for manifolds with singularities, Lie groupoid’s techniques in index theory and methods from topological K-Theory and noncommutative geometry.

This will be a school on dynamical systems in a rather wide sense, including background results on invariant manifolds and symplectic geometry (Chaperon), weak Kolmogorov-Arnold-Moser (KAM) theory and Arnold diffusion (Cheng, Seara), weak solutions of Hamilton-Jacobi evolution equations (Cheng, Wei), small denominators and KAM theory (Eliasson, Kuksin), partial differential equations (Cheng, Eliasson, Wei, Kuksin) and ergodic theory (Cheng, Luzzatto). Complex dynamics will be represented by a mini-course and a talk by Anna Miriam Benini (Rome).

Topics of school include various aspects of the theory of non-associative algebras, their representations and applications, including Lie, Leibniz, Jordan and other classes of algebras.

Cette école de recherche est destinée à exposer les méthodes statistiques modernes de traitement et d’analyse des durées de vie. Un accent particulier sera mis sur la modélisation spatiale et la modélisation des extrêmes pour ce type de données. Les champs d’application de ces méthodes sont nombreux et variés : agronomie, changement climatique, épidémiologie et santé publique, hydrologie, industrie, météorologie...

The School encompasses various topics in contemporary algebra: non-associative algebras, graph algebras, computer algebra and category theory.

Stochastic models are present in many areas of theoretical and applied sciences. The interplay with other areas has been a rich source of challenges and inspiration for probabilists. The present school will have courses on (a) the limiting behavior of rescaled microscopic systems giving rise to macroscopic laws in Physics, (b) on the rescaling of random graphs appearing in Field Theory, and (c) on folding-unfolding transition in Biology.

The area of the school is number theory, broadly understood - analytic, algebraic, combinatorial, with links to groups and geometry.

The school aims to introduce graduate students and young researchers to the modern theory of dynamical systems and its applications, with a focus on geometric, topological, and numerical methods. The courses will be focused on some key topics in low and high dimensional dynamics, including Hamiltonian systems, Celestial Mechanics, statistical properties of dynamical sysyems and their relation with the underlying geometric structures. The participants will be provided with an introduction to the basic material with the necessary background, before proceeding with the more advanced topics.

Commutative algebra and its multiple applications have grown considerably in recent years. The main purpose of the school is to present both, basic aspects of commutative algebra as well as more advanced tools focused on applications to combinatorics, coding theory and statistics. Participants will be provided with the basics on the combinatorics of binomial ideals and its relations with coding theory and algebraic statistics problems through courses and talks on the following topics:

The topics of this school will be on geometric and homological methods in the representation theory of associative algebras, and their applications. This school will offer five short courses with an intensity of twelve hours each (six hours theoretical and six exercise hours). The lectures will run over the three following main topics:

• Geometric aspects of the representation theory ofalgebras.
• Homological aspects of the representation theory of algebras.
• Applications of the representation theory of posets and algebras.