Rigidity and flexibility of microstructures
November 4 to November 8, 2019
American Institute of Mathematics,
San Jose, California
and Meera Sitharam
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
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.