Rigidity and flexibility of microstructures

November 4 to November 8, 2019

at the

American Institute of Mathematics, San Jose, California

organized by

Anthony Nixon, Brigitte Servatius, and Meera Sitharam

Original Announcement

This workshop 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.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop Videos