Experimentation in and around the Shapiro Conjecture

Outline: We peform large-scale computer experiments to study versions and generalizations of the Shapiro conjecture for flag varieties, both to find evidence, as well as to formulate these generalizations. A secondary goal is to create software tools to run our experiments autonomously.

Individual Projects:
Lower bounds and gaps for real solutions in Schubert calculus, Some preliminary data
Monotone Secant Conjecture for type-A flag manifolds, (computing)
Secant Conjecture for Grassmannians, Data
Monotone Conjecture for type-A flag manifolds (2005),
Shapiro Conjecture for Grassmannians On-line paper (2000).