The Special Semester on Rigidity and Flexibility will be held at the
Johann Radon Institute for Computational and Applied Mathematics (RICAM) from February 26 to May 17, 2024.
Mechanics has a purely geometrical part, which investigates possible positional relations between rigid bodies in 3-space
or planar figures in 2-space. Traditionally, kinematics is concerned with moving parts, and combinatorial rigidity theory
is concerned with conditions that stabilize a potentially movable framework.
Both rigidity and flexibility have interested researchers for centuries. While in the 19th century Maxwell analyzed, for
instance, necessary condition for the rigidity of structures, Bricard classified the types of flexible octahedra.
Later, Pollaczek-Geiringer and Laman characterized combinatorially the rigidity of two dimensional structures and on the
other side new mechanisms exhibiting paradoxical mobility have been discovered and classified.
Nowadays, there are established communities whose research interests gravitate around these areas, with contaminations in
both directions and also outside (classically, in theoretical kinematics, robotics, and distance geometry, and more recently
in topics like algebraic statistics).
Both rigidity and flexibility theory have been drawing fully from several "abstract" mathematical disciplines, as for example
combinatorics (in particular, graph and matroid theory to encode various notions of rigidity), non-commutative algebras (in
particular, Clifford algebras and related topics to encode). Kinematics has major applications in machine theory and in
biomechanics, while combinatorial rigidity theory finds applications for instance in architecture and in molecular chemistry.
The intention of this special semester is to bring computational aspects of flexible and rigid structures together. Workshops 1
deals with systematical generation of rigid structures. In workshop 2, we want to compare existing software for simulating
rigid/flexible structures, and also join our efforts for software development. Workshop 3 explores applications of rigid
structures. Applications of flexible structures will be the topic of workshop 5, and workshop 6 will be concerned with various
constructions of flexible structures. The barcamp (Workshop 4) is an open space that we hope will be filled with ideas/problems
from researchers in rigidity theory, kinematics, and applications.