Frontiers of Reality in Schubert Calculus

Goals: use of Schubert calculus as a laboratory to study ill-understood 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 type-A flag manifolds,
Secant Conjecture for Grassmannians,
Monotone Conjecture for type-A flag manifolds,
Shapiro Conjecture for Grassmannians.

DMS-1001615 DMS-0922866 DMS-0915211 DMS-0701050
DMS-0538734 DMS-0134860 DMS-0079536 DMS-0070494