September 22, 11:40
Room N-130
Speaker: Herman Servatius (Worcester Polytechnic Institute)
Title: Rigidity and movability of configurations in the projective plane.
Abstract: Configurations of points and lines in the plane have a long history.
The Theorem of Pappus from the fourth century begins a classical
theory that has been advanced by Desargues, Pascal, Cayley, Steinitz,
Grassman and many others. The study of such objects and their
generalizations has deep roots in algebra, geometry, topology and
combinatorics.
In this talk we discuss recent work which is the result of regarding
these classical structures as geometric constraint systems. The objects
of interest then become the topology, geometry, and parameterizations
of the space of realizations of a configuration. Some of the tools
derive from those developed by civil and mechanical engineers in the
analysis of the statics of structures and the kinematics of linkages.