Integrability and Near-Integrability in Mechanics and Geometry (16w5017)
Boris Khesin (University of Toronto)
Sergei Tabachnikov (Pennsylvania State University)
Vadim Zharnitsky (University of Illinois at Urbana-Champaign)
The main goal of the workshop is to bring together mathematicians, physicists, and engineers working on various aspects of mechanics and geometry: on the one hand, researchers working on more applied problems--control theory, robotics, motion planning, etc., and on the other hand, researchers working on basic problems in dynamics (integrability, Arnold's diffusion, KAM, nonholonomic problems, etc.)
During the last several years there have been fast advances and important new developments in the classical areas of mutual interest for these communities. To mention just a few: new results on bicycle stability (A. Ruina's group in Cornell University), integrability of pentagram maps and their generalizations (R. Schwartz et al.), discovery and description of various geometric structures behind cluster algebras (M. Gekhtman et al.), a study of infinite-dimensional non-holonomic systems in mechanics and fluid dynamics (A. Agrachev et al.), nonholonomic approach to billiards (Yu. Baryshnikov et al.), etc.
We believe that bringing together researchers from these diverse domains to exchange ideas and to learn to speak the same language is particularly beneficial now. It has an additional feature: unlike many other workshops that put under one roof scientists in the same area but using different methods, this time researchers from different areas will be unified by similar methods. It is anticipated that this approach will serve to cross-fertilize these domains. Thus, problems coming from applications will generate new directions of research in dynamical systems. On the other hand, engineers will learn about new ideas and techniques in mathematical areas. The junior researchers participating in the workshop will be exposed to emerging areas of applications and new theoretical approaches.
An important rationale for this workshop is that people from these diverse communities rarely overlap, and BIRS is an ideal place to have an effective interaction of these groups. We feel that it is important to have a full size workshop of 42 participants to have a broad cross section of all mentioned communities. We believe that the majority of our colleagues in the list will be willing to participate in the workshop and we have an informal confirmation of possible participation from about a quarter of them already, should this workshop be approved.