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D-Index & Metrics

Mathematics

D-Index
30
Citations
3363
World Ranking
3548
National Ranking
1370

Overview

Frank Sottile is affiliated with Texas A&M University in the United States. Their work spans the fields of Mathematics and Computer Science, contributing significantly to both domains through numerous publications. Their main areas of study include Computational Theory and Mathematics, Geometry and Topology, Computational Mechanics, Algebra and Number Theory, and Discrete Mathematics and Combinatorics.

The research topics covered by Frank Sottile emphasize Polynomial and Algebraic Computation, Advanced Numerical Analysis Techniques, Algebraic Geometry and Number Theory, Commutative Algebra and Its Applications, Advanced Combinatorial Mathematics, Computational Geometry and Mesh Generation, and Geometric and Algebraic Topology.

Some recent publications by Sottile include:

  • Generic properties of dispersion relations for discrete periodic operators, 2020, Journal of Mathematical Physics
  • Numerical homotopies from Khovanskii bases, 2021, Mathematics of Computation
  • A numerical toolkit for multiprojective varieties, 2020, Mathematics of Computation
  • Numerical Nonlinear Algebra, 2023, arXiv (Cornell University)
  • Critical points of discrete periodic operators, 2024, Journal of Spectral Theory

Frank Sottile regularly collaborates with several researchers, including Thomas Yahl, Anton Leykin, Jose Israel Rodriguez, Abraham Martín del Campo, and Michael Burr. This collaboration has resulted in multiple joint publications.

Frequent publication venues for Sottile's work include:

  • arXiv (Cornell University)
  • Mathematics of Computation
  • Journal of Software for Algebra and Geometry
  • Journal of Mathematical Physics
  • Journal of Spectral Theory

Best Publications

  • Combinatorial Hopf algebras and generalized Dehn–Sommerville relations

    Marcelo Aguiar;Nantel Bergeron;Frank Sottile

  • Structure of the Malvenuto–Reutenauer Hopf algebra of permutations

    Marcelo Aguiar;Frank Sottile

  • Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems

    Jonathan D. Hauenstein;Frank Sottile

  • Real Solutions to Equations from Geometry

    Frank Sottile

  • Schubert polynomials, the Bruhat order, and the geometry of flag manifolds

    Nantel Bergeron;Frank Sottile

  • Pieri's formula for flag manifolds and Schubert polynomials

    Frank Sottile

  • Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro

    Frank Sottile

  • Structure of the Loday–Ronco Hopf algebra of trees

    Marcelo Aguiar;Frank Sottile

  • Noncommutative Pieri operators on posets

    Nantel Bergeron;Stefan Mykytiuk;Frank Sottile;Stephanie van Willigenburg

  • Numerical Schubert Calculus

    B. Huber;F. Sottile;B. Sturmfels

  • NEW FEWNOMIAL UPPER BOUNDS FROM GALE DUAL POLYNOMIAL SYSTEMS

    Frederic Bihan;Frank Sottile

  • Tableau Switching

    Georgia Benkart;Frank Sottile;Jeffrey Stroomer

  • Enumerative geometry for the real Grassmannian of lines in projective space

    Frank Sottile

  • ORBITOPES

    Unknown

  • Irrational proofs for three theorems of Stanley

    Matthias Beck;Frank Sottile

  • Frontiers of reality in Schubert calculus

    Frank Sottile

  • The special Schubert calculus is real

    Frank Sottile;Frank Sottile

  • GALOIS GROUPS OF SCHUBERT PROBLEMS VIA HOMOTOPY COMPUTATION

    Anton Leykin;Frank Sottile

  • Some remarks on real and complex output feedback

    Joachim Rosenthal;Frank Sottile

  • (Formulas of Brion, Lawrence, and Varchenko on rational generating functions for cones)

    Matthias Beck;Christian Haase;Frank Sottile

  • Lower bounds for real solutions to sparse polynomial systems

    Evgenia Soprunova;Frank Sottile

  • Cocommutative Hopf Algebras of Permutations and Trees

    Marcelo Aguiar;Frank Sottile

Frequent Co-Authors

Bernd Sturmfels
Bernd Sturmfels Max Planck Institute for Mathematics in the Sciences
Thomas Lam
Thomas Lam University of Michigan–Ann Arbor
Sue Whitesides
Sue Whitesides University of Victoria
Olivier Devillers
Olivier Devillers University of Lorraine
Ioannis Z. Emiris
Ioannis Z. Emiris National and Kapodistrian University of Athens
Joachim Rosenthal
Joachim Rosenthal University of Zurich
Peter Kuchment
Peter Kuchment Texas A&M University

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