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The Fields Institute

Differential equations, in particular evolutionary differential equations, are used to model, often with uncanny effectiveness, a vast number of natural and social phenomena. The study of dynamical behaviors of the underlying models, e.g. their stabilities, robustness, bifurcations, and complexities, has become truly essential to understand the phenomena being modeled. It is precisely because of the modeling effectiveness of evolutionary differential equations that their dynamical study is among the fastest growing and most active multidisciplinary research fields today. Not only is the existing theory of dynamics of evolutionary equations closely intertwined with many areas of mathematics, but also the concepts, methods, and paradigms, introduced in the study have become an indispensible component of a multitude of works of more applied nature, in disciplines including chemistry, physics, material science, mechanics, electrical engineering, as well as in the emerging applications of social sciences, not to mention the explosion during the last several decades of applications related to the biological and life sciences. As we push the boundaries of applicability of the existing theory, we routinely discover that new mathematical and computational tools are needed, often symbiotically. To witness, it is widely accepted that an important factor contributing to the explosive growth in studying dynamics of evolutionary differential equations has been the availability of sophisticated and powerful computational tools. Yet, huge systems, systems with multiple time scales, multi-physics models, stochastic differential equations, non-smooth evolutionary problems, still transcend our collective understanding, and exhibit inherent complexities which are requiring the development of sophisticated new modeling and numerical techniques, and whose validity will need to be validated by rigorous mathematics.

Calcul infinitésimal, équations différentielles et intégrales,    Simulation

Centre de recherches mathématiques (CRM)

The main focus of the workshop will be to discuss new trends and techniques in the variational analysis of a wide range of mathematical problems, as well as to chart the current challenges in these models and to have in-depth discussions on possible routes towards overcoming these.

Centre de recherches mathématiques (CRM)

A two-week summer school in the summer 2023 that addresses the description/characterization/analysis and modeling of complex and/or scale-free temporal/spatial dynamics in functions, processes, images and fields..., under the light of several scientific fields, ranging from theoretical and methodological developments to real-world applications. The program will start from harmonic and fractal analysis as developed by mathematicians and will progressively introduce a variety of real-world applications (very different in nature, yet with a focus on neurosciences and neurophysiology towards the end of the workshop) via statistical signal and image processing and computer sciences.

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.

Cours et évènements pour étudiants en mathématiques,    Statistique, Théorie des jeux

Centre de recherches mathématiques (CRM)