Topics In Multiple Time Scale Dynamics
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Topics in Multiple Time Scale Dynamics
Author: Maximilian Engel
language: en
Publisher: American Mathematical Society
Release Date: 2024-10-21
This volume contains the proceedings of the BIRS Workshop "Topics in Multiple Time Scale Dynamics," held from November 27? December 2, 2022, at the Banff International Research Station, Banff, Alberta, Canada. The area of multiple-scale dynamics is rapidly evolving, marked by significant theoretical breakthroughs and practical applications. The workshop facilitated a convergence of experts from various sub-disciplines, encompassing topics like blow-up techniques for ordinary differential equations (ODEs), singular perturbation theory for stochastic differential equations (SDE), homogenization and averaging, slow-fast maps, numerical approaches, and network dynamics, including their applications in neuroscience and climate science. This volume provides a wide-ranging perspective on the current challenging subjects being explored in the field, including themes such as novel approaches to blowing-up and canard theory in unique contexts, complex multi-scale challenges in PDEs, and the role of stochasticity in multiple-scale systems.
Multiple Time Scale Dynamics
This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Convex and Complex: Perspectives on Positivity in Geometry
Author: Robert J. Berman
language: en
Publisher: American Mathematical Society
Release Date: 2025-01-28
This volume presents a collection of research articles arising from the conference on “Convex and Complex: Perspectives on Positivity in Geometry,” held in Cetraro, Italy, from October 31–November 4, 2022. The conference celebrated the 70th birthday of Bo Berndtsson and the vitality of current research across complex and convex geometry, as well as interactions between the two areas, all united by the overarching concept of positivity. Positivity plays a central role in complex and convex geometry. It arises from a range of complementary perspectives, as illustrated by the breadth of the papers appearing in this volume, including existence Kähler–Einstein edge metrics, Santaló-type inequalities, curvature of direct images of bundles, extension theorems for holomorphic functions, optimal transport and Hessian manifolds, interpolation and Brunn–Minkowski theory, and non-Archimedean geometry. The format of the workshop was innovative compared to standard conferences in mathematics, with focused 30-minute talks, aimed at stimulating lively discussions and a “flipped classroom” where the audience becomes more engaged and the speaker is not expected to transmit more information than listeners can possibly absorb. Lengthy breaks between talks and a relatively small number of talks allowed for useful time blocks for collaboration. This volume reflects the spirit of the conference, showcasing the vitality of current research in these areas as well as the profound impact of Bo Berndtsson's contributions to the field.