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	General isotropic flags are general (for Grassmannian Schubert calculus), 3 pages. arXiV:math.AG/0801.2611
2	Galois groups of Schubert problems via homotopy computation, with Anton Leykin, 17 pages. ArXiV:0710.4607.
3	A Littlewood-Richardson rule for Grassmannian permutations with Kevin Purbhoo. Proc. Amer. Math. Soc., to appear. ArXiv.org/0708.1582. 9 pages.
4	The recursive nature of cominuscule Schubert calculus with Kevin Purbhoo Advances in Mathematics, 215 (2008), pp. 1935--1961.
5	The equivariant cohomology rings of quot schemes, with Tom Braden, and Linda Chen. Pacific Journal of Mathematics, to appear. math.AG/0602161. 26 pp. July 2008.
6	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.
7	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.
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	Quiver Coefficients are Schubert Structure Constants, with Anders Buch and Alex Yong, Mathematics Research Letters, Volume 12, Issue 4, (2005) 567-574.
10	Elementary transversality in the Schubert calculus in any characteristic. Michigan Math Journal, 51 (2003), 651-666.
11	Skew Schubert polynomials, with Cristian Lenart, Proc. Amer. Math. Soc., 131 (2003), 3319-3328.
12	A Pieri-type formula for isotropic flag manifolds, with Nantel Bergeron, Trans. Amer. Math. Soc., 354 No. 7, (2002), 2659-2705.
13	Skew Schubert functions and the Pieri formula for flag manifolds, with Nantel Bergeron. Trans. Amer. Math. Soc., 354 No. 2, (2002), 651-673.
14	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.
15	A sagbi basis for the quantum Grassmannian, with Bernd Sturmfels. J. Pure and Appl. Algebra, 158, 24 April 2001 pp. 347-366.
16	Some real and unreal enumerative geometry for flag manifolds, Michigan Math Journal, 48 (2000) pp. 573-592.
17	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.
18	Real rational curves in Grassmannians, J. Amer. Math. Soc. 13 (2000), 333-341.
19	Pieri-type formulas for maximal isotropic Grassmannians via triple intersections, Colloquium Mathematicum, 82 (1999), pp. 49--63.
20	A monoid for the Grassmannian Bruhat order, with Nantel Bergeron, European Journal of Combinatorics, 20, (1999), pp. 197-211.
21	The special Schubert calculus is real, Electronic Research Announcements of the AMS, 5, 1999, pp. 35-39.
22	Numerical Schubert calculus, with Birkett Huber and Bernd Sturmfels, Journal of Symbolic Computation, 26, (1998) pp. 767-788.
23	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.
24	Pieri's formula via explicit rational equivalence, Canad. J. Math., 46 (1997), pp. 1281-1298. A 5 page supplement.
25	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.
26	Pieri's formula for flag manifolds and Schubert polynomials, Annales de l'Institut Fourier, 46 (1996), pp. 89-110.