for this workshop
Rigidity and flexibility of microstructures
American Institute of Mathematics, San Jose, California
Anthony Nixon, Brigitte Servatius, and Meera Sitharam
This workshop, sponsored by AIM and the NSF, will be devoted to problems in combinatorial and geometric rigidity theory arising from modeling of microstructures. Rigidity theory is concerned with the local and global uniqueness of congruence classes of frameworks as solutions to their underlying geometric constraint system. Intuitively, the framework is locally rigid if it cannot be continuously deformed in the ambient space while satisfying the constraints, and it is globally rigid if there is no other framework that is a solution or realization of the underlying constraint system. Frameworks are categorized by the types of geometric primitives and constraints. Example categories include bar-and-joint (point and distance), panel-and-hinge (e.g. polyhedra), and point-line-angle. When the constraints are inequalities, examples include tensegrities, as well as packings of discs and spheres. Such constraint systems are ubiquitous in nature (aperiodic and periodic structures in proteins, crystals, colloids and other materials), in 3D printing (microstructure and metamaterials design), and elsewhere.
Developments in the applications of rigidity theory to the modeling of microstructures are the starting point for the workshop goals, namely to investigate independently interesting rigidity and configuration space problems that arise in the scenarios of molecular and materials modeling as well as geometric and mechanical (computer aided) design at the micro/nano structural level.
The overall goal of this workshop is to formalize and start working on a graded set of problems arising from the applications, framed by specific focus topics on flexibility, tunnelling, stresses and periodicity, while connecting them with existing techniques and already formulated open problems.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than May 4, 2019. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email firstname.lastname@example.org