Abstract:

This talk is concerned with motions for untangling polygonal 
linkages (open and closed chains) in 2 and 3 dimensions.
Unknotted linkages that cannot be untangled are called locked.
Recent results for different constraints on the input configurations 
and motions allowed, are discussed. In addition, the history of 
some special cases of the problem proposed by Cauchy in 1813 and Erdos
in 1935, are reviewed. These results enjoy a wide spectrum of applications
ranging from knot theory to bioinformatics, where knots and molecules, 
respectively, are modelled as closed 3-dimensional polygons.