Publications (88)
Arithmetic toric varieties
E. Javier Elizondo, Paulo Lima-Filho, Frank Sottile +1
General isotropic flags are general (for Grassmannian Schubert calculus)
Frank Sottile
Gale duality for complete intersections
Frédéric Bihan, Frank Sottile
Certifiable Numerical Computations in Schubert Calculus
Jonathan D. Hauenstein, Nickolas Hein, Frank Sottile
The monotone secant conjecture in the real Schubert calculus
Nickolas Hein, Christopher J. Hillar, Abraham Martin del Campo +2
Skew Schubert polynomials
Cristian Lenart, Frank Sottile
The Horn recursion for Schur P- and Q- functions: Extended Abstract
Kevin Purbhoo, Frank Sottile
Hopf structures on the multiplihedra
Stefan Forcey, Aaron Lauve, Frank Sottile
Explicit Enumerative Geometry for the Real Grassmannian of Lines in Projective Space
Frank Sottile
Higher convexity of coamoeba complements
Mounir Nisse, Frank Sottile
Quiver coefficients are Schubert structure constants
Anders Skovsted Buch, Frank Sottile, Alexander Yong
Some geometrical aspects of control points for toric patches
Gheorghe Craciun, Luis Garcia-Puente, Frank Sottile
The recursive nature of cominuscule Schubert calculus
Kevin Purbhoo, Frank Sottile
Irrational proofs for three theorems of Stanley
Matthias Beck, Frank Sottile
Cocommutative Hopf algebras of permutations and trees
Marcelo Aguiar, Frank Sottile
Frontiers of Reality in Schubert Calculus
Frank Sottile
Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro
Frank Sottile
Structure of the Malvenuto-Reutenauer Hopf algebra of permutations (Extended Abstract)
Marcelo Aguiar, Frank Sottile
Common transversals and tangents to two lines and two quadrics in P^3
Gábor Megyesi, Frank Sottile, Thorsten Theobald
The Secant Conjecture in the real Schubert calculus
Luis Garcia-Puente, Nickolas Hein, Christopher J. Hillar +4
Lower Bounds for Real Solutions to Sparse Polynomial Systems
Evgenia Soprunova, Frank Sottile
Complementary Algorithms For Tableaux
Tom Roby, Frank Sottile, Jeffrey Stroomer +1
Line tangents to four triangles in three-dimensional space
Hervé Brönnimann, Olivier Devillers, Sylvain Lazard +1
A congruence modulo four in real Schubert calculus with isotropic flags
Nickolas Hein, Frank Sottile, Igor Zelenko
Experimentation at the Frontiers of Reality in Schubert Calculus
Christopher Hillar, Luis Garcia-Puente, Abraham Martin del Campo +4
Orbitopes
Raman Sanyal, Frank Sottile, Bernd Sturmfels
Dense Fewnomials
Korben Rusek, Jeanette Shakalli, Frank Sottile
The Phase Limit Set of a Variety
Mounir Nisse, Frank Sottile
Toric degenerations of Bezier patches
Luis David Garcia-Puente, Frank Sottile, Chungang Zhu
Identities of Structure Constants for Schubert polynomials and Orders on S_n
Nantel Bergeron, Frank Sottile
Injectivity of 2D Toric Bézier Patches
Frank Sottile, Chungang Zhu
The number of transversals to line segments in R^3
Hervé Brönnimann, Hazel Everett, Sylvain Lazard +2
Complex static skew-symmetric output feedback control
Christopher J. Hillar, Frank Sottile
Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones
Matthias Beck, Christian Haase, Frank Sottile
Enumerative Real Algebraic Geometry
Frank Sottile
Tropical Interpolation
Frank Sottile
An excursion from enumerative goemetry to solving systems of polynomial equations with Macaulay 2
Frank Sottile
A Pieri-type formula for the K-theory of a flag manifold
Cristian Lenart, Frank Sottile
Grothendieck polynomials via permutation patterns and chains in the Bruhat order
Cristian Lenart, Shawn Robinson, Frank Sottile
Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials
Frank Sottile
Experimentation and conjectures in the real Schubert calculus for flag manifolds (extended abstract)
James Ruffo, Yuval Sivan, Evgenia Soprunova +1
Linear precision for toric surface patches
Hans-Christian Graf von Bothmer, Kristian Ranestad, Frank Sottile
Betti number bounds for fewnomial hypersurfaces via stratified Morse theory
Frederic Bihan, Frank Sottile
Elementary Transversality in the Schubert calculus in any Characteristic
Frank Sottile
Toric ideals, real toric varieties, and the algebraic moment map
Frank Sottile
Lower bounds in real algebraic geometry and orientability of real toric varieties
Evgenia Soprunova, Frank Sottile
Pieri's rule for flag manifolds and Schubert polynomials
Frank Sottile
An inequality of Kostka numbers and Galois groups of Schubert problems
Christopher J. Brooks, Abraham Martin del Campo, Frank Sottile
Real solutions to equations from geometry
Frank Sottile
Rational curves on Grassmannians: systems theory, reality, and transversality
Frank Sottile
A combinatorial proof that Schubert vs. Schur coefficients are nonnegative
Sami Assaf, Nantel Bergeron, Frank Sottile
New Hopf Structures on Binary Trees (Extended Abstract)
Stefan Forcey, Aaron Lauve, Frank Sottile
Convex Hulls of Orbits and Orientations of a Moving Protein Domain
Marco Longinetti, Luca Sgheri, Frank Sottile
Lines Tangent to 2n-2 spheres in R^n
Frank Sottile, Thorsten Theobald
Non-Archimedean coamoebae
Mounir Nisse, Frank Sottile
Linear precision for parametric patches
Luis Garcia-Puente, Frank Sottile
A Littlewood-Richardson rule for Grassmannian Permutations
Kevin Purbhoo, Frank Sottile
Cohomological consequences of the pattern map
Praise Adeyemo, Frank Sottile
Cofree compositions of coalgebras (extended abstract)
Stefan Forcey, Aaron Lauve, Frank Sottile
Experimentation in the Schubert Calculus
Abraham Martin del Campo, Frank Sottile
Real enumerative geometry and effective algebraic equivalence
Frank Sottile
Structure of the Malvenuto-Reutenauer Hopf algebra of permutations
Marcelo Aguiar, Frank Sottile
Experimentation and conjectures in the real Schubert calculus for flag manifolds
James Ruffo, Yuval Sivan, Evgenia Soprunova +1
Lower Bounds in Real Schubert Calculus
Nickolas Hein, Christopher J. Hillar, Frank Sottile
On the Sharpness of fewnomial bound and the number of components of a fewnomial hypersurface
Frederic Bihan, J. Maurice Rojas, Frank Sottile
A sagbi basis for the quantum Grassmannian
Frank Sottile, Bernd Sturmfels
The special Schubert calculus is real
Frank Sottile
Maximally inflected real rational curves
Viatcheslav Kharlamov, Frank Sottile
Fewnomial bounds for completely mixed polynomial systems
Frederic Bihan, Frank Sottile
Enumerative geometry for real varieties
Frank Sottile
Cofree compositions of coalgebras
Stefan Forcey, Aaron Lauve, Frank Sottile
Real Rational Curves in Grassmannians
Frank Sottile
Pieri's Formula Via Explicit Rational Equivalence
Frank Sottile
Discriminant coamoebas through homology
Mikael Passare, Frank Sottile
Cremona Convexity, Frame Convexity, and a Theorem of Santaló
Jacob E. Goodman, Andreas Holmsen, Ricky Pollack +2
Line problems in nonlinear computational geometry
Frank Sottile, Thorsten Theobald
Double transitivity of Galois Groups in Schubert Calculus of Grassmannians
Frank Sottile, Jacob White
Galois groups of Schubert problems of lines are at least alternating
Christopher J. Brooks, Abraham Martin del Campo, Frank Sottile
A New Proof of Hilbert's Theorem on Ternary Quartics
Victoria Powers, Bruce Reznick, Claus Scheiderer +1
Pieri-type formulas for maximal isotropic Grassmannians via triple intersections
Frank Sottile
Bounds on the number of real solutions to polynomial equations
Daniel J. Bates, Frédéric Bihan, Frank Sottile
Structure of the Loday-Ronco Hopf algebra of trees
Marcelo Aguiar, Frank Sottile
Real k-flats tangent to quadrics in R^n
Frank Sottile, Thorsten Theobald
Polynomial systems with few real zeroes
Benoit Bertrand, Frederic Bihan, Frank Sottile
A congruence modulo four in real Schubert calculus
Nickolas Hein, Frank Sottile, Igor Zelenko
The envelope of lines meeting a fixed line that are tangent to two spheres
Gábor Megyesi, Frank Sottile
The Equivariant Chow rings of quot schemes
Tom Braden, Linda Chen, Frank Sottile
Skew Littlewood-Richardson rules from Hopf algebras
Thomas Lam, Aaron Lauve, Frank Sottile