40 citations · 76 across the 12 of their papers we have counts for
5 papers · 1 filter
The Secant Conjecture in the real Schubert calculus
Luis Garcia-Puente, Nickolas Hein, Christopher J. Hillar +4
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 i…
Experimentation at the Frontiers of Reality in Schubert Calculus
Christopher Hillar, Luis Garcia-Puente, Abraham Martin del Campo +4
We describe a general framework for large-scale computational experiments in mathematics using computer resources that are available in most mathematics departments. This framework…
Some geometrical aspects of control points for toric patches
Gheorghe Craciun, Luis Garcia-Puente, Frank Sottile
We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a Bézier curve or patch. In particular, we establish a ge…
Linear precision for parametric patches
Luis Garcia-Puente, Frank Sottile
We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the…
Algebraic Geometry of Bayesian Networks
Luis David Garcia, Michael Stillman, Bernd Sturmfels
We study the algebraic varieties defined by the conditional independence statements of Bayesian Networks. A complete algebraic classification is given for Bayesian Networks on at m…