Frank Sottile: Papers in Effective and Computational Algebraic Geometry

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

1	Betti number bounds for fewnomial hypersurfaces via stratified Morse theory, with Frédéric Bihan, 7 pages. arXiv:0801.2554.
2	Galois groups of Schubert problems via homotopy computation, with Anton Leykin, 17 pages. ArXiV:0710.4607. Mathematics of Computation, to appear.
3	Bounds on the number of real solutions to polynomial equations, with Daniel J. Bates, Frédéric Bihan, IMRN, 2007, 2007:rnm114-7.
4	Gale duality for complete intersections, with Frédéric Bihan, Annales de l'Institut Fourier, Tome 58 (2008) fasicule 3, pp.~877-891. A Singular script which computes examples of the Kouchnirenko Theorem for systems of Master functions.
5	The equivariant cohomology rings of quot schemes, with Tom Braden, and Linda Chen. Pacific Journal of Mathematics, 238, No. 2 (2008) 201--232.
6	New fewnomial upper bounds from Gale dual polynomial systems, with Frédéric Bihan, Moscow Mathematics Journal, 7 (2007), Number 3, 387--407.
7	Real Hessian Curves with Adriana Ortiz-Rodríguez. Boletín de la Sociedad Mathemática Mexicana, Volume 13 Number 3 (2007), 157--166. Companion web page.
8	Experimentation and conjectures in the real Schubert calculus for flag manifolds, with James Ruffo, Yuval Sivan, Evgenia Soprunova, Experimental Mathematics, 15, No. 2 (2006), 199-221.
9	Polynomial systems with few real zeroes, with Benoît Bertrand and Frédéric Bihan, Mathematisches Zeitschrift, 253 (2006), no. 2, 361--385.
10	Lower Bounds for Real Solutions to Sparse Polynomial Systems, with Evgenia Soprunova, Advances in Mathematics, Volume 204, Issue 1, 1 August 2006, Pages 116-151.
11	Real k-flats tangent to quadrics in Rn, with Thorsten Theobald. Proc. Amer. Math. Soc., 133 (2005), 2835-2844.
12	The envelope of lines meeting a fixed line and tangent to two spheres, with Gábor Megyesi, Discrete and Computational Geometry, 33, Number 4, (2005) 617--644.     Companion web page.
13	Maximally inflected real rational curves, with Viatcheslav Kharlamov. Moscow Mathematics Journal 3 (2003), no. 3, 947--987, 1199--1200.     Companion Web Page.
14	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.)
15	Common transversals and tangents to two lines and two quadrics in P3, with Gábor Megyesi and Thorsten Theobald. Discrete and Computational Geometry, 30, (2003), pp. 543-571.     Companion Web Page.
16	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.
17	Lines tangent to 2n-2 spheres in Rn, with Thorsten Theobald, Trans. Amer. Math. Soc., 354 (2002), 4815-4829.   Some pictures and computer code.
18	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.)
19	A sagbi basis for the quantum Grassmannian, with Bernd Sturmfels. J. Pure and Appl. Algebra, 158, 24 April 2001 pp. 347-366.
20	Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro, Experimental Mathematics, 9, Number 2, (2000), pp. 161-182. An archive of the computations and Maple scripts for some proofs.
21	Numerical Schubert calculus, with Birkett Huber and Bernd Sturmfels, Journal of Symbolic Computation, 26, (1998) pp. 767-788.
22	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.
23	Pieri's formula via explicit rational equivalence, Canad. J. Math., 46 (1997), pp. 1281-1298. A 5 page supplement.
24	Enumerative geometry for the real Grassmannian of lines in projective space, Duke Math. J., 87, (1997), 59-85. Published version of Ph.D. Thesis. The 8 page supplement.