Goals: use of Schubert calculus as a laboratory to study
ill-understood topics in algebraic geometry, including questions of
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
Projects: Galois groups of Schubert problems,
lower bounds and lacunae for numbers of real solutions in Schubert calculus,
Monotone Secant Conjecture for type-A flag manifolds,
Secant Conjecture for Grassmannians,
Monotone Conjecture for type-A flag manifolds,
Shapiro Conjecture for Grassmannians.