Title: Geometry Meets the Traveling Salesman

Peter Jones (Yale)

The classical traveling salesman problem can be recast as a problem in
analysis. We describe a way to do this  that gives a surprising tie to
geometry as well as classes of  functions. One of the problems treated
is    the "traveling bandit problem",    where the bandit doesn't have
enough gas in his car to rob  all the banks  he wants to. Near optimal
strategies lead to  a multiscale theory   of paths and  are related to
classical  statistics.  These    results  can be   translated   via  a
"dictionary"  to  statements  about behavior  of  functions satisfying
different regularity conditions.