Linkages and their applications

Misha Kapovich

UC Davis

March 31,
refreshments at 3:45pm


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 3-manifold 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.

Speaker's Contact Info: kapovich(at-sign)

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