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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.

Angewandte Mathematik (allgem.),    Mathematische Physik

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

The study of geometric properties of convex bodies based on information about sections or projections of these bodies belongs to the area of geometric tomography and has important applications to many areas of mathematics and science, in general. In recent years, there has been a significant increase in the interaction between harmonic analysis and convex geometry, leading to solutions for several longstanding open problems, the discovery of new phenomena, and many new intriguing open questions. The goal of this workshop is to bring together young and established researchers to discuss recent developments and advance applications of harmonic analysis to convex geometry and geometric tomography.

Analysis,    Geometrie und Topologie

Fields Institute, Toronto, Canada

Kurse und Veranstaltungen für Physikstudenten,    Angewandte Mathematik (allgem.)

Fields Institute, Toronto, Canada

Fields Institute, Toronto, Canada

Fields Institute, Toronto, Canada

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.

Fields Institute, Toronto, Canada

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.

Angewandte Mathematik (allgem.),    Angewandte Physik (allgemein)

Fields Institute, Toronto, Canada

The three core objectives of the event are: (i) Accelerating research by crossing disciplinary boundaries between chemistry, physics, math, computer science and engineering, theory and experiment, quantum information processing and its "hardware" materials. (ii) Training junior researches in QIS with tutorials, research talks, and by providing them with opportunities to interact directly with leaders in the field. (iii) Strengthening QIS research in Canada by promoting collaborations and increasing the visibility of Canadian contributions to the field. QIS has evolved into a broad field encompassing numerous subfields. The primary goal of this conference is to foster interactions and collaborations among researchers working across diverse areas of QIS. Unlike many conferences that focus on one specific subfield of QIS, this event aims to bring to the same room researchers from a wide spectrum of QIS topics, and including theory and experimental work. The event will cover the study of foundations and applications in QIS and various prominent physical platforms: photons, atoms, molecules, and solid-state systems. The second objective of the conference is to train the next generation of QIS researchers including senior undergraduates, graduate students, postdoctoral fellows, and early-career researchers. The event will provide Canadian and international trainees with knowledge on the current state of the field and an understanding of key challenges in QIS.

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

The mathematical modeling of biological systems with partial differential equations has a long and successful history. Many results on species invasion or extinction, pattern formation and species interactions have been derived and used to better understand the biology around us. Applications cover a vast scale of sizes, from protein movement in the cell nucleus, to cell movement to tissue structure, organ structure, up to species interactions on the population level. Recently, a new model class arose that include finite distance interactions into the partial differential equation (PDE) framework. Non-local interactions relate to different sensing mechanisms, starting with sensing through sight and smell, to sensing through touch, cell-cell contact and cell protrusions to more abstract concepts such as learning and memory. In this workshop we aim to bring together established and young researchers to push the frontiers of research into non-local partial differential equations and their applications to biological problems.

Simulation,    Systembiologie und mathematische Biologie

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

The analysis of nonlinear diffusion PDEs is a wide field of research that not only encompasses elliptic and parabolic equations, but also includes several functional-analytic tools that proved successful in the deep understanding of such equations: just to mention a few, we recall Hardy, Poincaré and Sobolev inequalities. The corresponding rigorous theory, at least in the Euclidean setting, has reached extremely high levels, both in the local and the nonlocal case, with many sharp results available by now. The general interest for such equations is motivated by the fact that they are of paramount importance in the description and modeling of a number of real-world phenomena (e.g., the flow of gases through a porous medium, water infiltration, heat dispersion, population dynamics, etc...).

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.

Angewandte Mathematik (allgem.),    Numerische Analysis