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

Mathematics has a wide range of different disciplines, from algebra to geometry and from analysis to topology, etc. Some discoveries, however, are able to link several disciplines together and open a field of interplay. Two of such recent discoveries are self-similar group representations and projective spectrum of linear operators. The goal of this workshop is bring together scholars in spectral theory, representation theory, complex dynamics and other related fields to exchange and examine some recent discoveries on self-similarity and projective spectrum.

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

Mathematics of collective behavior and the subject of fluid dynamics undergo a rapid merger where most fascinating breakthroughs have been discovered in recent years. These breakthroughs are based on our novel understanding of collective phenomena from the viewpoint of the laws of fluid motion. Pattern formations in animal swarms or clustering in social networks or even technological applications to decentralized control of unmanned vehicles are just a few examples that can be studied with the new techniques. This workshop will bring together a diversified group of researches from both fields to share the knowledge and promote collaboration in this emerging and fascinating area.

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

Fluids are ubiquitous in the nature, but equations of fluid mechanics are among the most difficult PDEs to analyze. The question of global regularity v.s. finite time blow-up remains open for many fundamental fluid equations, and there are also many other interesting open questions on other aspects of properties. Recently, the study of fluid equations has witnessed multiple breakthrough results, such as non-existence of type-one singularity, rigorous proofs for small scale formation and finite-time blow-up for various equations, non-uniqueness of weak solutions to the Euler and Navier-Stokes equation via convex integration, as well as the non-uniqueness of the law of the 3D stochastic Navier-Stokes equations. With these exciting developments in the last decade, this workshop is a timely event to capitalize on this momentum. In this workshop, we aim to bring together leading experts and junior researchers covering complementary areas in fluid equations to share new ideas, discuss emerging problems, and identify promising research directions for the future. When inviting participants to the workshop, preferences will be given to junior researchers and researchers from underrepresented groups.

Centre de recherches mathématiques (CRM)

While network models have been studied as independent systems, efforts in neuroscience in recent years has been put towards inferring networks of the brain from imaging data. Using probabilistic methods and inverse models, recurrent networks across populations and their change with disease have been characterized based on input from electrophysiological and functional imaging.

This sub-theme will cover the notions of network dynamics, discuss conceptual frameworks to model brain network topology and provide the latest progress in neural network inference from imaging data and associated methodological approaches at modeling networks of the brain.