2020

The concept of a group is central to essentially all of modern mathematics. In number theory and geometry where groups take central stage in various shapes such as symmetry groups, Galois groups, fundamental groups, reflection groups and permutation groups, the conceptual unification that it provides is most strikingly illustrated. In this school, we present groups and the natural objects they act on in a variety of arithmetic and geometric contexts. Special emphasis will be given to concrete examples, and practical and computational aspects of groups and their actions will be stressed.

The research school will provide a useful background to understand several of the very active research subjects in the wide area of functional analysis. This includes Riesz spaces and Stochastics processes, function theory, differential operators, operator theory on various and natural Banach spaces, some notions of geometry of Banach spaces, semigroup theory and its links with applications, without omitting an introduction to harmonic analysis.

Numeration is an active and developing field of study that encompasses different areas of mathematics and theoretical computer science. The goal of the research school is to introduce graduate students and young researchers to the fundamentals of the geometric, combinatorial, and dynamical aspects of numeration systems as well as to topics of current research. The basic courses of the research school will include lectures on beta expansions, canonical number systems, formal languages, substitutions, and others.