Numerical Schubert Calculus

The Schubert calculus is a well-understood and fundamental class
of geometric problems that are formulated as intersections of
Schubert varieties on a Grassmannian.  The importance of these problems
lies in their use as a testing ground for new ideas and that they
are universal for certain classes of problems expressed as degeneracy
loci of maps between bundles.   While highly-structured, they are
far from being complete intersections and standard numerical methods
do not perform well when solving Schubert problems.

Numerical Schubert calculus consists of algorithms tailored to the
geometry of these Schubert problems, including specialized homotopy
algorithms, reformulation as square systems of equations, and
notions of witness sets and regeneration.   This talk will survey
the developments just sketched that comprise this numerical Schubert
calculus.