133 citations · 554 across the 117 of their papers we have counts for
8 papers · 1 filter
Cofree compositions of coalgebras (extended abstract)
Stefan Forcey, Aaron Lauve, Frank Sottile
We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and the theory of species. We prove that the composition of two cofree…
Cofree compositions of coalgebras
Stefan Forcey, Aaron Lauve, Frank Sottile
We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and in the theory of species. We prove that the composition of two cofr…
alphaCertified: certifying solutions to polynomial systems
Jonathan D. Hauenstein, Frank Sottile
Smale's alpha-theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to a squ…
Dense Fewnomials
Korben Rusek, Jeanette Shakalli, Frank Sottile
We derive new bounds of fewnomial type for the number of real solutions to systems of polynomials that have structure intermediate between fewnomials and generic (dense) polynomial…
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…
Toric degenerations of Bezier patches
Luis David Garcia-Puente, Frank Sottile, Chungang Zhu
The control polygon of a Bezier curve is well-defined and has geometric significance---there is a sequence of weights under which the limiting position of the curve is the control…
Arithmetic toric varieties
E. Javier Elizondo, Paulo Lima-Filho, Frank Sottile +1
We study toric varieties over a field k that split in a Galois extension K/k using Galois cohomology with coefficients in the toric automorphism group. Part of this Galois cohomolo…
Solving Schubert Problems with Littlewood-Richardson Homotopies
Frank Sottile, Ravi Vakil, Jan Verschelde
We present a new numerical homotopy continuation algorithm for finding all solutions to Schubert problems on Grassmannians. This Littlewood-Richardson homotopy is based on Vakil's…