Conferences  >  Mathematics  >  Modeling and Simulation  >  Canada

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.

Calculus, Differential Equations and Integration,    Analysis

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

In this workshop, we will explore how the research realms of generative modelling and 3D neural representations can benefit from each other, as well as explore novel applications in different areas of science and technology.

Neural Networks and Artificial Intelligence, Machine Learning,    Scientific Computing and Data Science

The Fields Institute

This workshop will showcase advances related to the Fields thematic program on geometric constraint systems, framework rigidity and distance geometry. Particular topics of interest include matrix and tensor product completions, kinematics and flexibility, polynomial constraint systems, structured polynomials including sums of squares, matrix factorizations, Euclidean distance minimization and maximum likelihood estimation.

Centre de recherches mathématiques (CRM)

While brain function originates in neuron, its energy is supported by the vascular system. With the recent development of anatomically detailed synthetic network models of the entire cerebral circulation, it is now possible to perform detailed simulations of physiology in realistic brains of small animals and humans on the computer. Modeling microcirculatory blood flow as a biphasic suspension of red-blood-cell and plasma, blood pressure, flow and hematocrit can be simulated in whole brains on the computer. Combining Poiseuille’s hemodynamic simulations with advection/diffusion equations describing oxygen diffusion, the human brain metabolism can now be modeled in-silico, by integrating tissue oxygen consumption and differential equations describing compartments associated with neural and glial brain cells. In parallel, energy metabolism regulation in the brain and its modeling has greatly progressed over the past few decades. This workshop will thus be focused on digital human brains, and their use to predict critical metabolic functions namely blood flow, oxygen extraction and cellular metabolism across all length scales down to the level of individual capillaries and cells. Courses and conferences will be combined with research presentations and practical workshops.

Applied Mathematics (in general),    Systems Biology and Computational Biology

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

What have we learned from the COVID-19 pandemic, and how can we be better prepared for the next global outbreak? This workshop brings together collaborative teams of modellers, statisticians, epidemiologists, genomics experts, public health decision-makers, and those implementing and delivering interventions who have been working together in a research network, aiming to increase Canada’s capacity for data-driven emerging infectious disease modelling to directly support future public health decisions. This BIRS meeting is an important opportunity for network members and collaborators to share the outcomes of their research over the two years since the network was launched with funding from the federal government. The questions being tackled at this workshop are grounded in public health needs and generated in partnership between research investigators and knowledge users – public health leaders, health administrators and policy-makers.

Epidemiology & Public Health,    Systems Biology and Computational Biology