Elections often take place in districts that divide up a
country or region. Sometimes these are relatively fixed, like the
cantons of Switzerland. What if you could re-draw the districts
regularly and try to get advantage for one group over another group in
the election? I'll discuss some mathematical ideas to sample
districting plans with a random walk through the space of graph
partitions. This leads to beautiful questions about the geometry of
graphs and spanning trees. And it lets you see whether a plan is
normal or extreme compared to the alternatives created through a
neutral process. I'll tell you how the logic has been received by
lawyers and judges in the United States.