Frank Sottile: Papers in Applicable Algebraic Algebraic Geometry

Papers in Combinatorics,   Geometry,   Schubert calculus,   Combinatorial Hopf Algebras,   Real Algebraic Geometry,   Computational Algebraic Geometry,   and Computational Geometry.

1	Khovanskii-Rolle continuation for real solutions, with Daniel J. Bates, Foundations of Computational Mathematics. DOI: 10.1007/s10208-011-9097-1. 25 pages.
2	Fewnomial bounds for completely mixed polynomial systems, with Frédéric Bihan, Advances in Geometry, (2011), DOI:10.1515/ADVGEOM.2011.019.
3	Some geometrical aspects of control points for toric patches with Gheorghe Craciun and Luis Garcia, in Mathematical Methods for Curves and Surfaces, Lecture Notes in Computer Science 5862, Springer 2010, 111–135.
4	Linear precision for toric surface patches, with Kristian Ranestad and Hans-Christian Graf von Bothmer. 25 pages. ArXiv.org/0806.3230. Foundations of Computational Mathematics, 10, Issue 1 (2010), 37--66, DOI: 10.1007/s10208-009-9052-6.
5	Linear precision for parametric patches with Luis Garcia Advances in Computational Mathematics. 33 (2010), Page 191--214. DOI: 10.1007/s10444-009-9126-7
6	Gale duality for complete intersections, with Frédéric Bihan, Annales de l'Institut Fourier, Tome 58 (2008) fasicule 3, 877--891. A Singular script which computes examples of the Kouchnirenko Theorem for systems of Master functions.
7	Bounds on the number of real solutions to polynomial equations, with Daniel J. Bates, Frédéric Bihan, IMRN, 2007, 2007:rnm114-7.
8 9	Sharpness of fewnomial bound and the number of components of a fewnomial hypersurface, with Frédéric Bihan and J. Maurice Rojas. IMA Volume 146: Algorithms in Algebraic Geometry edited by Alicia Dickenstein, Frank-Olaf Schreyer, and Andrew J. Sommese. 15--20, Springer, New York, 2007.
8 9	Sharpness of fewnomial bound and the number of components of a fewnomial hypersurface, with Frédéric Bihan and J. Maurice Rojas. IMA Volume 146: Algorithms in Algebraic Geometry edited by Alicia Dickenstein, Frank-Olaf Schreyer, and Andrew J. Sommese. 15--20, Springer, New York, 2007.
10	New fewnomial upper bounds from Gale dual polynomial systems, with Frédéric Bihan, Moscow Mathematics Journal, 7 (2007), Number 3, 387--407.
11	Polynomial systems with few real zeroes, with Benoît Bertrand and Frédéric Bihan, Mathematisches Zeitschrift, 253 (2006), no. 2, 361--385.
12	Lower Bounds for Real Solutions to Sparse Polynomial Systems, with Evgenia Soprunova, Advances in Mathematics, Volume 204, Issue 1, 1 August 2006, 116--151.
13	Toric ideals, real toric varieties, and the moment map, in Topics in Algebraic Geometry and Geometric Modeling, ed. by R. Goldman and R. Krasuaskas, Contemp. Math. 334, 2003. pp. 225--240. (Proceedings of AGGM, Vilnius, Lithuania.)
14	Enumerative Real Algebraic Geometry, in Algorithmic and Quantitative Aspects of Real Algbraic Geometry, S. Basu and L. Gonzalez-Vega, eds., DIMACS series 60, AMS, 2003. pp. 139--180.       Expanded on-line version.
15	From enumerative geometry to solving systems of polynomial equations with Macaulay 2, in Computations in Algebraic Geometry with Macaulay 2, edited by D. Eisenbud, D. Grayson, M. Stillman, and B. Sturmfels. Algorithms and Computation in Mathematics 8, Springer-Verlag, 2001. pp. 101-129. Macaulay 2 source code for computations in the paper. (This requires the Macaulay 2 package realroots.m2.)
16	Rational curves on Grassmannians: systems theory, reality, and transversality, In "Advances in Algebraic Geometry Motivated by Physics", ed. by Emma Previato, Contemporary Mathematics, 276, 2001, pp. 9--42.
17	Numerical Schubert calculus, with Birkett Huber and Bernd Sturmfels, Journal of Symbolic Computation, 26, (1998) pp. 767-788.
18	Some remarks on real and complex output feedback, with Joachim Rosenthal, Sys. & Control Lett., 33 (1998), pp. 73-80. A non-trivial real system that cannot be controlled by real output feedback.