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CRM / Université de Montréal

This mini-school focuses on “huge” groups, such as the Cremona group and its subgroups, the homeomorphism group of a surface, the mapping class group of an infinite-type surface, a general Artin group. They can be studied through non-proper actions on nonpositively or negatively curved combinatorial spaces.

Centre de recherches mathématiques (CRM)

The focus of these activities will be on the algebraic and dynamical aspects of ordered group theory. Introductory mini-courses will be given in the first week by Adam Clay (Manitoba), Tyrone Ghaswala (Waterloo), Thomas Koberda (Virginia) and Andrés Navas (Santiago). The second week will be devoted to research talks covering recent advances in both the theory of ordered groups and their applications in group theory, dynamics and low-dimensional topology.

This two week school will focus on spectral theory of periodic, almost-periodic, and random operators. The study of periodic problems is one of the most classical subjects of spectral theory. Many of the basic properties of periodic operators are now well understood due to the powerful method known as the Floquet-Bloch decomposition which performs a partial diagonalisation of the operator. Another type of problems mathematicians and physicists have been interested in is known under the broad name of ergodic problems; the most prominent among them being almost-periodic and random problems. These problems are much more complicated because no straightforward partial diagonalisation is known for them. The study of the spectral properties for ergodic problems developed to a large extent independently of the periodic theory, although occasionally periodic results were used in almost-periodic or even random settings. The interplay between almost-periodic and random problems has been more significant, but still, most of the methods have been specific to each of these two types. In the last few years however there emerged a number of methods which originated in one type of these problems but were successfully used to tackle problems from neighbouring areas (periodic methods used to deal with almost-periodic or random problems, etc). This suggests that these three lines of research have more in common than previously believed. The main aim of this school is to teach the students who work in one of these areas methods used in parallel problems, explain the similarities between all these areas and show them the ‘big picture’.

Centre de recherches mathématiques (CRM)

The mini-courses and research talks will address several themes, including: nonpositively-curved cube complexes, median spaces, (coarsely) Helly spaces and groups, and various combinatorial notions of nonpositive curvature. The first week of the workshop involves mini-courses by Elia Fioravanti (MPI Bonn), Thomas Haettel (Université de Montpellier), Nima Hoda (ENS Paris), Nir Lazarovich (Technion). The second week will be devoted to research talks.

Graph Theory and Combinatorics,    Geometry and Topology

Centre de recherches mathématiques (CRM)

Robert Langlands est un des mathématiciens contemporains les plus influents. Il est surtout connu pour un ensemble de conjectures très profondes dont l'étude porte maintenant le nom de «programme de Langlands». Tout au long de sa carrière, de nombreux prix ont été décernés au professeur Langlands. En particulier, ses travaux lui ont valu de recevoir le prix Wolf en 1996 et le prix Abel en 2018. Au-delà des mathématiques, le professeur Langlands s'intéresse à l'apprentissage des langues et à la poursuite de la recherche mathématique dans ces langues. En plus de l'anglais, il parle couramment le français, le turc et l'allemand. En 2019 il a créé un Fonds de dotation au CRM dont le but est de soutenir les activités scientifiques de recherche et de formation en français.  Trois mini-cours s’adressant aux étudiants de premier cycle sont présentés à l’édition 2023 de cette école d’été francophone. Ils sont appuyés par le Fonds de dotation Langlands.

Analysis,    Probability and Statistics, Game Theory