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The Fields Institute

One goal of this workshop is to facilitate the exchange of novel ideas and results in mathematical ecology and to showcase the importance of the field in the face of many challenges from invasive species to climate change. Another goal is to celebrate and honour the exceptional achievements in the area of mathematical ecology of Prof Mark Lewis (Alberta) on the occasion of his 60th birthday (December 5, 2022).

The Fields Institute

‘Investors’ are broadly defined and includes retail and institutional investors as well as financial advisors and brokers. Behavioural finance is the study of how the psychology of investors affects personal investment and market outcomes. Based on investment behaviours, there is a need for investment dealerships and banks to develop tools that provide automated support for retail investors and financial advisors in selecting, managing, and evaluating investment portfolios. The difficulty in designing these tools lies in the specification of the complex mathematical structure that models investor behaviour in the presence of market conditions. Machine learning offers a data-driven approach with less specification of the structure of the data generating process.

Economics, Business and Marketing,    Mathematical Economics and Finance

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

The workshop "Compensated Compactness and Applications to Materials" will bring together experts from the theory of compensated compactness with researchers in material science. Classical compensated compactness is a theory that allows to study the limit of solutions of some partial differential equations with strongly oscillating coefficients. A particular focus is on the very recent developments in the compensated compactness theory involving concentration effects and formation of singularities. These developments have enabled many new results, for instance in the theories of microstructure, shape optimization, dislocation theory, fracture, and plasticity, and they also hold much promise for future applications. To facilitate further breakthroughs, this workshop aims to balance theoretical and more applied talks to give the participants the opportunity to exchange the latest ideas, learn new methods, and start new collaborations.

Calculus, Differential Equations and Integration,    Condensed Matter Physics and Materials

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

Present day biology generates a wealth of data from which tumor biology and tumor evolution can be inferred, and therapeutic strategies can be developed. Most clinical (and research) samples are comprised of a mixture of different cells, including multiple different populations of cancer cells (‘subclones’) and a variety of normal cell types. Effective use of these data thus requires data from individual cell types to be deconvolved. A number of subfields are independently developing mathematical and statistical deconvolution techniques. While at first glance these subfields are largely disparate, there are clear opportunities for synergies to be developed. This workshop will fill this gap by bringing together researchers from several of these fragmented subfields across a wide range of backgrounds (computational biology, mathematics, statistics, computer science, biomedicine, etc.) to provide a synergistic forum for cross-disciplinary learning, discussion and collaboration.

Banff International Research Station (BIRS) / UBCO

Recent remarkable advances in learning-based methods are revolutionizing the field of image analysis resulting in a paradigm shift towards data-driven approaches. These methods have already shown tremendous success in a wide range of applications from computer vision such as object detection and object category classifications. To perform efficiently, such methods typically require a large number of training sample and this requirement is highly impractical or impossible in applications from medical imaging where it is very laborious and expensive to generate labeled data. Another drawback of learning-based method is that they do not come with provable performance guarantees. One remedy to such limitations is to combine data-driven methods with prior knowledge through mathematical and/or physical models in such a way to optimize processing, reconstruction and analysis of medical imaging data without the need of extensive training. This workshop will bring together researchers with a different background ranging from optimization, inverse problem, numerical and harmonic analysis and machine learning to advance state-of-the-art methods combining data- and model-driven approaches for medical imaging. To create a more engaging and productive environment, participants are selected from a diverse pool of researchers from multiple institutions, geographic regions, ethnic background and at different career levels.

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 the geometric and combinatorial rigidity and global rigidity of structures, distance geometry and semidefinite programming and applications, for example in soft matter physics and in protein conformation determination.

Banff International Research Station (BIRS) / UBCO

This workshop will study this question for systems of geometric origin. One example of this is a particle bouncing inside a region -- think of a ball bouncing around a billiard table, or a light beam bouncing around a room whose walls are mirrors. If the walls are flat then the behavior is fairly predictable, but if they are curved then one often observes random-looking behavior in the long run. Or imagine walking in a straight line along a surface; if the surface is flat then changing the starting point a little will lead to a predictable change in the trajectory. However, if the surface is curved like a saddle then different trajectories will spread out and your location after walking for a long time will eventually seem to be random. The task of giving precise descriptions of systems such as these requires a more complete development of the theory of thermodynamic formalism for systems of geometric origin, which is precisely the goal of this workshop.

Banff International Research Station (BIRS) / UBCO

Minimal surfaces have inspired scientists and mathematicians for centuries and remain a central area of study with a vast number of pure and applied research outputs relating directly to their study. From art and architecture, to fluid dynamics and general relativity, they have an impressive list of applications. The main reason that they remain so popular amongst mathematicians is the fact that they are mysterious, beautiful, and lead to the resolution of challenging and abstract problems, not necessarily in obviously related fields. They can be created in the home by dunking a metal hoop into soapy water - the resulting soap film is a minimal surface (no matter how you bend the hoop). Equally they are integral to, for example, certain proofs of the positive mass theorem from general relativity. A surface is minimal if it is locally stretched tight, so that if you were to focus on a small region of the surface, any perturbation of that small region will increase surface area. In abstract terms, minimal surfaces are critical "points'' of the energy - in this case the energy of a surface is given by its area.

A large quantity of physical phenomena admit such a description - they are critical with respect to some energy, or in other words ``nature always tries to optimise energy''. For example the shape of cell membranes, event horizons of black holes and the behaviour of fundamental particles all fit within this regime. This workshop brings together young and experienced researchers in the mathematical/theoretical study of these problems. It mainly utilises the theory of differential geometry and partial differential equations, or broadly Geometric Analysis. This field has enjoyed popular notoriety in recent years with one of the modern progenitors of the subject, Karen Uhlenbeck, being awarded the Abel Prize. Similarly Perelman's proof of the Poincare conjecture, a question that took 100 years (and many contributors) to answer fully, for which Perelman famously turned down the $1,000,000 award.

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.

Mathematics and Computation Division of the American Nuclear Society

The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2023) is a part of a series of topical meetings organised by the Mathematics and Computation Division of the American Nuclear Society. The M&C conferences, held every two years, represent a series of international forums organised and sponsored to bring together worldwide expertise related to nuclear science or technology including mathematical and computational methods, numerical analysis, computer codes, computer architectures, and benchmarks for computationally solving problems in all disciplines encompassed by the Society.

Nuclear Energy,    Computational Physics and Numerical Simulation

AMMCS-2023 is a major international forum and interdisciplinary conference focused on mathematical and computational sciences, with their applications to modeling natural, social, and engineering systems.

The conference provides a unique opportunity for in-depth technical discussions and exchange of ideas in all areas involving mathematical and computational sciences, modeling and simulation, as well as their applications in natural and social sciences, engineering and technology, industry and finance. It offers to researchers, industrialists, engineers and students to present their latest research, to interact with the experts in the field, and to foster interdisciplinary collaborations required to meet the challenges of modern science, technology, and society.