Frank Sottile: Papers on Schubert Calculus

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

1	A Skew Littlewood-Richardson rule from Hopf algebras with Thomas Lam and Aaron Lauve. IMRN, doi:10.1093/imrn/rnq104, Published June 2, 2010.
2	Experimentation at the Frontiers of Reality in Schubert Calculus with Chris Hillar, Luis García-Puente, Abraham Martín del Campo-Sanchez, James Ruffo, Zach Teitler, and Stephen L. Johnson. Contemporary Mathmematics, 317, Amer. Math. Soc., Providence, RI, 2010, pp. 365-380.
3	Frontiers of Reality in Schubert Calculus Bulletin of the AMS, 47, No 1. (2010), 31-71.
4	General isotropic flags are general (for Grassmannian Schubert calculus), Journal of Algebraic Geometry, 19 (2010), 367-370.
5	Galois groups of Schubert problems via homotopy computation, with Anton Leykin, Mathematics of Computation, 78 (2009) 1749--1765.
6	A Littlewood-Richardson rule for Grassmannian permutations with Kevin Purbhoo. Proc. Amer. Math. Soc., 137 (2009) 1875--1882.
7	The equivariant cohomology rings of quot schemes, with Tom Braden, and Linda Chen. Pacific Journal of Mathematics, 238, No. 2 (2008) 201--232.
8	The recursive nature of cominuscule Schubert calculus with Kevin Purbhoo Advances in Mathematics, 217 (2008), pp. 1962--2004.
9	A Pieri-type formula for the K-theory of a flag manifold, with Cristian Lenart, Trans. Amer. Math. Soc., Trans. Amer. Math. Soc. 359 (2007), 2317--2342.
10	Grothendieck Polynomials via Permutation Patterns and chains in the Bruhat Order, with Cristian Lenart and Shawn Robinson. American Journal of Mathematics, 128, No. 4, (2006), 805--848.
11	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.
12	Quiver Coefficients are Schubert Structure Constants, with Anders Buch and Alex Yong, Mathematics Research Letters, Volume 12, Issue 4, (2005) 567--574.
13	Elementary transversality in the Schubert calculus in any characteristic. Michigan Math Journal, 51 (2003), 651--666.
14	Skew Schubert polynomials, with Cristian Lenart, Proc. Amer. Math. Soc., 131 (2003), 3319-3328.
15	A Pieri-type formula for isotropic flag manifolds, with Nantel Bergeron, Trans. Amer. Math. Soc., 354 No. 7, (2002), 2659--2705.
16	Skew Schubert functions and the Pieri formula for flag manifolds, with Nantel Bergeron. Trans. Amer. Math. Soc., 354 No. 2, (2002), 651--673.
17	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.
18	A sagbi basis for the quantum Grassmannian, with Bernd Sturmfels. J. Pure and Appl. Algebra, 158, 24 April 2001 pp. 347-366.
19	Some real and unreal enumerative geometry for flag manifolds, Michigan Math Journal, 48 (2000) pp. 573-592.
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	Real rational curves in Grassmannians, J. Amer. Math. Soc. 13 (2000), 333-341.
22	Pieri-type formulas for maximal isotropic Grassmannians via triple intersections, Colloquium Mathematicum, 82 (1999), pp. 49--63.
23	A monoid for the Grassmannian Bruhat order, with Nantel Bergeron, European Journal of Combinatorics, 20, (1999), pp. 197-211.
24	The special Schubert calculus is real, Electronic Research Announcements of the AMS, 5, 1999, pp. 35-39.
25	Numerical Schubert calculus, with Birkett Huber and Bernd Sturmfels, Journal of Symbolic Computation, 26, (1998) pp. 767-788.
26	Schubert polynomials, the Bruhat order, and the geometry of flag manifolds, with Nantel Bergeron, Duke Math. J., 95, (1998), pp. 373-423. A 16 page supplement. A description of how Table 1 was generated.
27	Pieri's formula via explicit rational equivalence, Canad. J. Math., 46 (1997), pp. 1281-1298. A 5 page supplement.
28	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.
29	Pieri's formula for flag manifolds and Schubert polynomials, Annales de l'Institut Fourier, 46 (1996), pp. 89--110.