Linkages and their applicationsMisha KapovichUC Davis
March 31,

ABSTRACT


Historically, linkages appear as tools for tracing curves, they also have long been used in the mechanical engineering. One of the most famous examples is ``Watt parallelogram'', invented by James Watt to solve the problem of linking the piston of his steam engine to a point on the flywheel so that the straight line motion of the piston would convert to the rotation of the flywheel. In this talk I will concentrate on three, purely mathematical, aspects of the theory of mechanical linkages: 1. Universality theorems for moduli spaces of mechanical linkages. 2. Applications of linkages to the representation theory of finitely generated groups (Coxeter, Artin and 3manifold groups). 3. Applications of polygonal linkages to the representation theory of Lie groups: Saturation theorems for the decompositions of tensor products of irreducible representations, etc. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

