133 citations · 554 across the 117 of their papers we have counts for
136 papers
A quantum Murnaghan--Nakayama rule for the flag manifold
Carolina Benedetti, Nantel Bergeron, Laura Colmenarejo +2
In this paper, we give a rule for the multiplication of a Schubert class by a tautological class in the (small) quantum cohomology ring of the flag manifold. As an intermediate ste…
Some problems at the interface of approximation theory and algebraic geometry
Frank Sottile
We sketch an assortment of problems that were posed -- and not yet solved -- during problem sessions at the conference ``Approximation Theory and Numerical Analysis meet Algebra, G…
Numerical Nonlinear Algebra
Daniel J. Bates, Paul Breiding, Tianran Chen +3
Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equation…
Real solutions to systems of polynomial equations in Macaulay2
Jordy Lopez Garcia, Kelly Maluccio, Frank Sottile +1
The Macaulay2 package RealRoots provides symbolic methods to study real solutions to systems of polynomial equations. It updates and expands an earlier package developed by Grayson…
Critical points of discrete periodic operators
Matthew Faust, Frank Sottile
We study the spectra of operators on periodic graphs using methods from combinatorial algebraic geometry. Our main result is a bound on the number of complex critical points of the…
Galois Groups in Enumerative Geometry and Applications
Frank Sottile, Thomas Yahl
As Jordan observed in 1870, just as univariate polynomials have Galois groups, so do problems in enumerative geometry. Despite this pedigree, the study of Galois groups in enumerat…