Lambda-Medial Axis
            Yuriy Mileyko 

For any bounded open subset $O$ of a Euclidean space one can look at 
points in $O$ that are "in the middle" of at least two points on the 
boundary of $O$; more precisely, look at points $x$ in $O$ that have at 
least two points on the boundary of $O$ with the same distance to $x$.  
Such points form a  geometric object called Medial Axis, which has various 
applications in computer science. Unfortunately, a medial axis is an 
unstable configuration.  That is, small perturbations of an initial set 
may yield large distortions of its medial axis. In a recent paper, Chazal 
and Lieutier introduced a subset of a medial axis which retains its nice 
topological and geometric properties and is stable under Hausdorff 
distance pertubations for 'most' values of a parameter $\lambda$  on which 
it depends.

In this talk, I will define the Lambda-Medial Axis,  show some of its 
properties, and discuss benefits that it provides for practical 
applications. First, though, I will introduce several other interesting 
and useful concepts which are closely related to the lambda-medial axis.