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- James Ruffo, Yuval Sivan, Evgenia Soprunova, Frank Sottile
- Experimental Mathematics
- 2006

The Shapiro conjecture in the real Schubert calculus, while likely true for Grassmannians, fails to hold for flag manifolds, but in a very interesting way. We give a refinement of the Shapiro conjecture for the flag manifold and present massive computational experimentation in support of this refined conjecture. We also prove the conjecture in some special… (More)

- JAMES RUFFO
- 2008

The Drinfel’d Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural projective embedding arising from the canonical embedding of the Lagrangian Grassmannian. We show that the defining ideal of any Schubert subvariety of the Drinfel’d Lagrangian… (More)

- Luis David García-Puente, Nickolas Hein, +4 authors Zach Teitler
- Experimental Mathematics
- 2012

We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for… (More)

- James Ruffo
- ISSAC
- 2007

The Drinfel'd Lagrangian Grassmannian compacties the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural projective embedding arising from the highest weight embedding of the ordinary Lagrangian Grassmannian. We show that the defining ideal of any Schubert subvariety is generated by polynomials… (More)

- Christopher Hillar, Luis Garćıa-Puente, +4 authors Frank Sottile
- 2009

We describe the setup, design, and execution of a computational experiment utilizing a supercomputer that is helping to formulate and test conjectures in the real Schubert calculus. Largely using machines in instructional computer labs during off-hours and University breaks, it consumed in excess of 350 GigaHertz-years of computing in its first six months… (More)

- VINCENT RUFFO, LAGRANGIAN GRASSMANNIAN, +9 authors Alexander Woo
- 2007

A Straightening Law for the Drinfel’d Lagrangian Grassmannian. (August 2007) James Vincent Ruffo, B.A.;B.S., University of Rochester; M.A., University of Massachusetts-Amherst Chair of Advisory Committee: Dr. Frank Sottile The Drinfel’d Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the… (More)

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