Mathematics

Configuration spaces model the collective motions of several objects,
such as cars on a road, packets across a network, robots in a factory, or
molecules in a solution.  They also arise naturally in mathematics, and
topologists have studied them for decades.

In some contexts it is natural to approximate continuous motions by
discrete ones, thereby constructing a corresponding discretized
configuration space.  We can then employ combinatorial techniques,
in addition to topological ones, for their study.

In this talk I will describe one way to carry out this discretization process,
and I will give some examples and applications in topology, geometry,
combinatorics, group theory, and robotics.