Goals: use of Schubert calculus as a laboratory to study
illunderstood topics in algebraic geometry, including questions of
reality,
improvement of methods in computational algebraic geometry.
Method: development and implementation of software on
networks of computers,
organization of such software to facilitate similar experiments in
the future.
Projects: Galois groups of Schubert problems,
lower bounds and lacunae for numbers of real solutions in Schubert calculus,
Monotone Secant Conjecture for typeA flag manifolds,
Secant Conjecture for Grassmannians,
Monotone Conjecture for typeA flag manifolds,
Shapiro Conjecture for Grassmannians.


