The Western Algebraic Geometry Seminar


Speaker: Bernd Sturmfels
Title: Tropical Algebraic Geometry
In tropical algebraic geometry, the zero sets of polynomial equations
are piecewise-linear. The tropical variety of a polynomial ideal is
the "logarithmic limit set" which was introduced by Bergman in 1971
and studied further by Bieri and Groves in the 1980's. We show that it
is embedded as a polyhedral subcomplex in the Gröbner fan of the
ideal. Our main example is the Grassmannian of lines in tropical
projective space. We interpret tropical lines as phylogenetic trees,
and we identify the Grassmannian with the space of trees of Billera,
Holmes and Vogtmann. The references are math.AG/0306366 and
math.AG/0304218 .