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Society for Industrial and Applied Mathematics (siam)

Society for Industrial and Applied Mathematics (siam)

Society for Industrial and Applied Mathematics (SIAM)

Numerical Analysis and Computational Mathematics,    Algorithms and Data Structures

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

A tensor category is a category with a tensor product that satisfies properties similar to the tensor product of vector spaces. A typical example is given by the representation category of a group with the usual tensor product. While the most important examples of tensor categories arise from representation theory, the theory has outgrown its origins and has emerged into a vast and complex theory on its own, providing a unified language for many phenomena in different fields. Tensor categories are now ubiquitous in areas such as representation theory, invariants of links and 3-manifolds, algebraic geometry, higher category theory, quantum computing and mathematical physics. All in all the abstract theory of tensor categories along with its applications has seen a rapid growth over the last 10 - 20 years.

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

Symbiotic relationships are ubiquitous on our planet, and a necessary component of life in all its forms. Symbioses have been identified in ecological contexts ranging from forests, to coral reefs, to the microbiota of humans. Despite their importance, the main body of theory largely neglects key features of host-symbiont relationships, such as their interdependent fitness and the fluctuating abundance of symbionts within a hosts’ lifetime. This lack of mathematical theory limits our predictive understanding of the ecological and evolutionary dynamics of these communities, and is affecting our ability to successfully manage and conserve them. During this workshop, biologists and mathematicians will come together to discuss the current challenges and opportunities for the mathematical modelling of symbiotic systems. Participants will develop the foundations of a new class of ‘eco-evolutionary’ models that explicitly accounts for host-symbiont intertwined ecology and evolution, and for the consequences of this interdependence. The developed models will help advance our mechanistic understanding of host-symbiont community dynamics, with implications ranging from forestry management, to coral reef conservation, to human health.

Modeling and Simulation,    Systems Biology and Computational Biology

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

In-host modelling is a burgeoning field at the intersection of biology, mathematics, and computational science, dedicated to unravelling the intricate dynamics of disease and the immune system within individual hosts. The field has evolved significantly over time, driven by the need to understand how pathogens interact with the immune system and how interventions like treatments and vaccines can alter disease or infection outcomes. More work needs to be done to understand how genetic, environmental, and physiological factors affect how individuals respond to infections, vaccines, and treatments, influenced by variations in age, comorbidities, sex, ethnicity, immune-related genes, exposure histories, and overall health. Understanding these differences is crucial for advancing personalized and group-targeted medicines or vaccines, developing new drugs and vaccines, and optimizing public health programming for all populations. A workshop focus will be on key questions from industry and government through large and small group discussions. Industry and government reports will result.

Modeling and Simulation,    Systems Biology and Computational Biology

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

Mathematically, the characterization of localization and delocalization is a rich and delicate problem. Many disciplines, including probability, the analysis of partial differential equations, and mathematical physics, offer tools to tackle localization questions. This workshop will convene researchers from across these fields to share new techniques, explore common questions, and initiate novel lines of research. Moreover, the workshop is designed to nurture a community of early-career researchers who are comfortable communicating and collaborating across disciplines.

Calculus, Differential Equations and Integration,    Mathematical Physics

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

The vaccine development pipeline is a time, cost and labour-intensive process. Mathematical and computational methods can alleviate challenges related to this intensive process as well as providing further insights into the efficacy and safety of vaccines. These methods are key components of model-informed vaccine development (MIVD) and quantitative systems pharmacology/toxicology (QSP/T). MIVD and QSP/T can be used in tandem to better understand the biological processes and outcomes from vaccination administration, spurring future research. This workshop will strengthen and contribute to the ongoing development of this interdisciplinary community of biologists, mathematicians and vaccinologists.

Modeling and Simulation,    Pharmacology and Drug Development

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

This workshop explores problems in mathematical political science, focusing on recent developments in the study of alternative voting methods and the creation of district electoral maps. Over the last 20 years, many jurisdictions in Canada and the United States have adopted or have considered adopting alternative voting methods such as ranked-choice voting for electing mayors, representatives, city council members, etc. There are many questions about such methods which can be analyzed mathematically. For example, does ranked-choice voting tend to elect candidates who are more centrist than candidates elected by more commonly-used methods like plurality? How can we best achieve proportional representation on a legislative body? What makes an election fair? There are many open problems around such questions, and this workshop hopes to make some progress on them using mathematical tools.

Political science,    Sociology

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

The landscape of drug design is rapidly evolving, with computational methods and artificial intelligence (AI) playing an increasingly important role. This workshop aims to explore cutting-edge mathematical approaches that are transforming the field of computational drug design. We will delve into multiscale modeling techniques that bridge the gap between molecular and macroscopic levels, providing a comprehensive understanding of drug interactions and dynamics. Additionally, we will highlight the integration of generative AI and machine learning (ML) algorithms in predicting drug efficacy, optimizing molecular structure, speeding up drug repurposing, understanding potential toxicity, and thus accelerating the drug discovery and development process. By bringing together diverse experts from academia, industry, and innovation support organizations, and adding early career researchers to the mix, this workshop will foster interdisciplinary collaboration and innovation. Participants will gain insights into the latest developments, discuss challenges, and explore future opportunities in the quest for more effective and efficient drug design.

Neural Networks and Artificial Intelligence, Machine Learning,    Pharmacology and Drug Development

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

Baryonic matter in the Universe is almost exclusively (99,9 \%) in the plasma state, which is one of the four common states (with solid, liquid and gas), having the specificity of being strongly affected by electrical and magnetic fields. Already three generations of plasma physicists have worked at understanding more precisely the dynamics of plasmas, unravelling their secrets and bringing order to what seems by nature chaotic. Still, the plasmas continue to preserve a part of their mystery. First, our project aims to gain more insight into the microscopic reactions induced by the presence of radiation. Secondly, it is to mathematically elucidate how inertial effects coming from the mixing of charged species (like electrons and ions) is able to stabilize the plasma dynamics at very small scales. Incidently, this would bring innovative insight about some specificities of (magnetohydrodynamics).

Number Theory, Arithmetic,    Mathematical Physics

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

According to recently published research study in Canada Medical Association Journal, in 2024, the number of new cancer cases and deaths from cancer were expected to reach 247 100 and 88 100, respectively. A key driver of cancer formation, development and its metastasis are single cancer cells. Understanding the biochemical processes that drive their force generation and polarisation and their mechanical properties might aid our understanding of how single cancer cells evolve over time and how they aid the formation of primary and secondary tumours. Cell migration is essential for many biological processes; e.g. immune response, embryogenesis, and cancer metastasis. The aim of this 5-day workshop is to bring applied mathematicians, cellular, molecular and developmental biologists, biophysicists, biostatisticians, biomechanical engineers and biotechnologists to deliberate on a roadmap towards developing 2- and 3-D mechanobiochemical models (MBMs) for single and collective cell migration through non-isotropic environments. The ultimate goal is to develop biophysically- and mathematically-engineered artificial cells that can be easily interrogated and perturbed for medical, biomedical, cancer and drug-delivery research at low cost, while reducing the use of animals in experiments.

Modeling and Simulation,    Systems Biology and Computational Biology

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

Plant productivity and resilience to environmental stresses such as climate change depends on the mechanisms that define cellular morphogenesis. This is largely governed by the mechanical properties of the plant cell wall, which is in turn dependent on the spatial organization of dynamic cytoskeletal polymers known as microtubules. In contrast to animal cells, where microtubule organization is controlled by organizing centres, plant cell microtubule arrays are self organized. Understanding this self-organization remains an active area of research where mathematical approaches have proven to be indispensable. This is done by simulating interacting microtubules in shapes representing an individual cell. Starting with simple simulations, different researchers have implemented their own computational models to study various aspects involved in this process. Building on this, these models are now employing increasingly sophisticated ideas. This workshop aims to give researchers the opportunity to understand each others' models and to foster stronger collaborations.

Modeling and Simulation,    Botany

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

Cost-effective monitoring of large transportation networks, combined with the collection of accurate and relevant data on transport, vehicle movements, and individual mobility through various technologies, is crucial for enhancing transportation service efficiency. As we have seen in the past decade, recent technological advancements have produced an enormous volume of data, which is invaluable for understanding, planning, and managing transport networks in large cities, while also addressing the limitations imposed by road network growth. The challenge of managing, analyzing, and interpreting the information collected is considerable. The objective of this workshop is to bring together statisticians and engineers, with the specific goal to share recent advances, identify pressing problems, spark productive collaborations, and ultimately advance the state of the art by developing methods for the statistical modeling of data in the field of transportation. We will foster these interactions through four theme-focused daily workshops on the following topics: network modeling, travel behavior and choice modeling, traffic flow modeling and accident and safety analysis.

Optimization Theory, Operational Research,    Transportation and Logistics

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

The subjects in this workshop are closely related to the world we live in. For example, the Einstein metrics - describing gravitational fields and mirror symmetry - a phenomenon discovered to describe our physical universe. To understand them, we need to find solutions to equations that involve many unknowns and their derivatives. It is highly challenging to construct solutions for these equations. Many basic questions remain open despite great efforts have been devoted and significant progress has been made. In attempts to solve the equations, a powerful way is the geometric flows. These are equations which evolve the key quantities that we try to understand along with time, and as time moves on the evolutions eventually get close to the true solutions. This approach has been fruitful and providing deep insights. It it timely to gather some of the leading experts and young talents to share their results and imitate new projects.

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

Catastrophic events, even though they happen rarely, have a significant impact when they occur. Disastrous climate, financial, insurance or complex network failure events can have devastating social and environmental consequences. A complete risk analysis for modelling and prediction purposes requires understanding how these extreme, rare events occur, and what are the main drivers causing them. Machine learning methods open the road for methodological developments to forecast these extreme events and discover their complex, possibly high-dimensional nature. The aim of this workshop is to bring together researchers contributing to closely related, but culturally disconnected research communities: extreme value theory and machine learning. The goal is to discuss new directions and open mathematical problems, and foster further collaboration. The leading experts will introduce young researchers, postdocs and graduate students to the state-of-the-art in the field.

Probability and Statistics, Game Theory,    Neural Networks and Artificial Intelligence, Machine Learning

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

The Banff International Research Station will host the workshop "Recent Breakthroughs and New Perspectives on the Interplay between Fluid Mechanics and Kinetic Theory" in 2026. This event will bring together leading experts from two closely-related fields---fluid mechanics and kinetic theory---that have seen remarkable progress and growth in the last decade. The workshop aims to foster collaboration and the exchange of ideas between these communities, accelerating the proliferation of techniques and discovery of new research directions.

Calculus, Differential Equations and Integration,    Applied Physics (general)

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

Understanding the resilience of ecosystems will be critical for our future considering the multiple crises that we face. Current understanding of resilience relies largely on examining the consequences of disturbances in a deterministic framework. However, disturbances will be arguably stochastic in nature. Disturbances will be multifaceted, often repeated, and probably highly variable over time. Furthermore there is uncertainty and randomness in the processes that respond to the disturbances. Consequently, resilience is most naturally explored in the context of stochasticity: randomness in disturbances must be expected and prepared for. In this workshop, we aim to bring together stochastic and deterministic researchers studying the resilience of ecosystems and the resilience of human economic-ecosystem interactions.

Probability and Statistics, Game Theory,    Ecosystems, Environment and Sustainable Development

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

Most volcanic hazards --- from lava and pyroclastic flows to ash and gas clouds --- are fundamentally multiphase fluid flows. Predicting these fluid flows is of considerable importance in order to inform quantitative hazard assessment, including, for example, potential evacuation and exclusion zones during eruptions. Although recent advances in remote sensing offer some remarkable new insights into the dynamics, these hazardous fluid flows can be difficult to measure directly. Predictive mathematical models therefore play a vital role in allowing forecasters make robust operational decisions. This is the theme of our proposed workshop: the fluid mechanics of volcanic hazards.

Modeling and Simulation,    Geophysics and Geology

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

The 5-day workshop, "Space-time Approaches to PDE Solvers: Unlocking the Power of Co-Design'', will bring together a diverse group of leading international experts in numerical analysis, scientific computing, and hardware-software integration to review and explore the cutting-edge developments and challenges in the simulation of complex PDEs. The workshop will focus on three major themes: i) space-time discretization methods for PDEs; ii) co-design principles for the next generation of PDE solvers; and iii) real-world applications for these advanced solvers, ranging from fluid dynamics and Earth system modeling to plasma-based energy systems to biomedical simulations and personalized medicine.

Calculus, Differential Equations and Integration,    Numerical Analysis and Computational Mathematics

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

The upcoming workshop on the analysis of wastewater and environmental surveillance data aims to revolutionize how we handle and interpret wastewater data through advanced statistical methods. Participants will focus on newly developed statistical approaches and optimization of existing models, with a special emphasis on how to prioritize avenues of research that not only generate insightful academic results but are also feasible, impactful, and capable of addressing immediate public health needs. This thoughtful approach will help bridge scientific discovery and real-world implementation. The workshop will also work toward establishing a standardized framework to evaluate and enhance the performance of wastewater models. By fostering collaboration among statisticians, engineers, biologists, and public health experts, the event seeks to generate innovative, practical solutions. Additionally, it will provide public health decision-makers with reliable tools for interpreting wastewater data, helping them make informed decisions during health crises.

Hydrology,    Training in Waste Management and Environmental Protection

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

The mathematics of Design Theory traces its roots back to antiquity, with Latin squares appearing in medieval Islamic manuscripts and in the 17th and 18th century works of Choi Seok-jeong, Jacques Ozanam and Leonhard Euler. The subject is known for its longstanding open problems, many of which took over a century to resolve: Euler's 36 Officers Problem was posed in the 18th century and solved by Tarry in 1900; the Existence Problem for Combinatorial Designs was posed in the 19th century and solved for large orders by Keevash in 2014. The impetus for this workshop comes from the dramatic advances that have been made in Design Theory during the last decade since this breakthrough. This period has seen an explosion of solutions for large orders to high profile classical problems in Design Theory, based on the key new idea that probabilistic arguments, often in conjunction with algebraic constructions, can yield powerful new approaches for finding these solutions for large orders. The time is therefore ripe for bringing together experts in both the new and classical methods of Design Theory to share ideas, make new collaborations, solve problems and identify important directions for future research.

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

The rapid advances in the mathematical analysis of geometric nonlinear dispersive equations, from General Relativity, fluid dynamics, quantum mechanics, both on the deterministic and the probabilistic side, make this an opportune time for the proposed workshop. Our objective is to bring together leading experts with overlapping interests related to this wide range of problems and disseminate and exchange state of the art tools newly available.