Tropical Interpolation

Frank Sottile
Texas A&M University

  Many people in algebraic geometry geoemtry know that there are
12 different ways to pass a rational cubic through 8 points in the
plane.  It is not as well-known that if the 8 points are real,
then at least 8 of the 12 solutions to this interpolation problem
are real.  This is part of an unfolding story that ties together
many recent developments in real algebraic geometry, including
Enumerative Real Algebraic Geometry, Tropical Geometry, and
Applications.  In my talk (which does not assume you knew the
problem of the first sentence) I will present this intriguing story.
(For more, see http://www.math.tamu.edu/~sottile/stories/MSRI04/index.html.)