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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The workshop will bring together some of the world's top experts and early career mathematicians working at the interface of Stochastics and Geometry, broadly understood. Through expository talks and research presentations, the workshop will give a vibrant overview of the most recent developments in the interaction between analysis, geometry and stochastic analysis. The focus of the workshop will be different approaches to random processes in geometric settings, with emphasis on problems on heat kernel analysis on finite- and infinite-dimensional manifolds, often equipped with degenerate geometries, as well as random matrices and non-commutative probability and geometric rough paths. Another objective of the workshop is to identify fundamental open problems in this area that are motivated by mathematical physics and other potential applications. We plan to maintain geographic diversity and invite many promising early career mathematicians.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

High-quality randomness is a valuable commodity in computation, experimentation, and discovery. This workshop focuses on randomness as a resource within real and complex algebraic geometry. The program highlights three current research trends: understanding the statistical properties of fundamental geometric invariants, developing randomized algorithms for symbolic and numerical calculations in algebraic geometry, and exploring the synergies between algebraic geometry and data analysis. This workshop will, for the first time, bring together a wide range of mathematicians interested in random algebraic geometry.

The Fields Institute

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Particle Physicists study matter at its smallest and most fundamental scale. The well-known proton, neutron and similar particles are composed of quarks. Atoms also contain electrons; together with the two heavier versions of the electron (the muon and tau), each with its associated neutrino, they make up the group of leptons. Another ingredient of the catalogue of particles is the Higgs Boson, discovered at the CERN Lab's Large Hadron Collider (LHC) in 2012. Experiments studying these and other particles require large accelerators and detectors: the circumference of the LHC is 27 km and one of the detectors to study the collisions is 25 meters high and 45 meters long. Building and running these machines is expensive, in terms of money and human effort. It is therefore important to use the best statistical techniques to extract the maximum amount of information from the hard-won data. This workshop brings together Statisticians and experimental Particle Physicists to discuss how best to achieve this.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

A distinguished feature of the last few decades is the increasing availability of technological innovations to an everyday broader spectrum of society. This phenomenon has rapidly paved the way for the development of new economies such as e-commerce, sharing economies and online advertising. These activities are characterised by, for instance, a higher number of agents from both the supply and demand side, and an unprecedentedly large menu of tailor-made and personalised services. Naturally, this has led to more intricate behaviours and interactions at all levels of the economy. Consequently, there is a pressing need for the creation of economic theories that are able to explain the rationale of the participants, the way their actions are aggregated in society, and which are compatible with documented evidence. This workshop will unite specialists of stochastic control and economic theory, who will work and explore how recent theoretical developments in their respective fields can be applied to these newly identified problems.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The study of random growth models connects to a large number of areas in probability theory such as integrable probability, homogenization, percolation, disordered systems, interacting particle systems, random matrices, SPDEs, random polymer measures, random dynamical systems, and random walk in random environment. The last two decades have seen rapid advances in all these directions, with a significant acceleration in progress in several of these subfields recently, including solutions of several long-open problems. This is an exciting time for the subject, with new possibilities in extending universality, new geometric approaches, and more. The main objective of this workshop will be to bring together a number of top experts on these various subfields to disseminate these recent developments and exchange ideas that will fertilize the ground for yet another leap forward. This opportunity will also be used to celebrate the work of Timo Seppalainen in the field.

American Statistical Association

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.

Courses and Events for Math Students and Early Career Researchers,    Analysis

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

What could be a bigger source of "big data" than the entire Universe? Researchers in statistics and computer science are developing new methods to analyse the "big data" that companies and governments want to understand. To test out these methods they need big datasets that everyone can share --- and new astronomical telescopes just happen to be gearing up to generate observations of billions of stars and galaxies that fit the bill. Insights from statistics will help astrophysicists to get the most out of these observations. The Astrostatistics 2023 workshop will bring together statisticians and astrophysicists to learn the technical languages of the two fields and identify how to work together to combine the excitement of space with big data.

Astronomy, Astrophysics and Cosmology,    Scientific Computing and Data Science

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications