133 citations · 554 across the 117 of their papers we have counts for
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Certifiable Numerical Computations in Schubert Calculus
Jonathan D. Hauenstein, Nickolas Hein, Frank Sottile
Traditional formulations of geometric problems from the Schubert calculus, either in Plucker coordinates or in local coordinates provided by Schubert cells, yield systems of polyno…
Newton polytopes and witness sets
Jonathan D. Hauenstein, Frank Sottile
We present two algorithms that compute the Newton polytope of a polynomial defining a hypersurface H in C^n using numerical computation. The first algorithm assumes that we may onl…
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…
Discriminant coamoebas through homology
Mikael Passare, Frank Sottile
Understanding the complement of the coamoeba of a (reduced) A-discriminant is one approach to studying the monodromy of solutions to the corresponding system of A-hypergeometric di…