2 citations · 2 across the 6 of their papers we have counts for
9 papers
The Euler-Betti Algorithm to identify foliations in Hilbert Scheme
P. Rubí Pantaleón-Mondragón, Abraham Martín del Campo
Foliations in the complex projective plane are uniquely determined by their singular locus, which is in correspondence with a zero-dimensional ideal. However, this correspondence i…
Classification of Schubert Galois groups in Gr(4,9)
Abraham Martin del Campo, Frank Sottile, Robert Williams
We classify Schubert problems in the Grassmannian of 4-planes in 9-dimensional space by their Galois groups. Of the 31,806 essential Schubert problems in this Grassmannian, there a…
Numerical Schubert Calculus via the Littlewood-Richardson Homotopy Algorithm
Anton Leykin, Abraham Martin del Campo, Frank Sottile +2
We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric…
Experimentation in the Schubert Calculus
Abraham Martin del Campo, Frank Sottile
Many aspects of Schubert calculus are easily modeled on a computer. This enables large-scale experimentation to investigate subtle and ill-understood phenomena in the Schubert calc…
Galois groups of Schubert problems of lines are at least alternating
Christopher J. Brooks, Abraham Martin del Campo, Frank Sottile
We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. This constitutes the largest family of enumerative problem…
An inequality of Kostka numbers and Galois groups of Schubert problems
Christopher J. Brooks, Abraham Martin del Campo, Frank Sottile
We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument…
Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals
Christopher J. Hillar, Abraham Martin del Campo
We study chains of lattice ideals that are invariant under a symmetric group action. In our setting, the ambient rings for these ideals are polynomial rings which are increasing in…
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…