Title: Voronoi diagrams with neutral zones 
Speaker: Jiri Matousek (Charles University and ETH Zurich)

Abstract:

Given n points in the plane, we want to assign a region R_i
to each point p_i, with the following property: For every i,
the region R_i is the set of all points whose distance to p_i
is not greater than the distance to the union of R_j for all j
distinct from i. This definition looks circular, and indeed,
formally the n-tuple of regions is defined as a fixed
point of the "dominance" operator. This definition
apparently gives rise to nontrivial mathematical
and computational challenges. Partial results in various directions
will be discussed. Many of them are work in
(slow) progress.

(joint work with Tetsuo Asano, Tomas Kaiser, and Takeshi Tokuyama)