INDEX 199 Newton, Isaac, 34 Nishimura, Yasuzo, 78 node of a curve, 9 nondegenerate, 2, 49 nonnegative orthant, 83 numerical homotopy continuation, 172 order Bruhat, 97, 125 cyclic, 184 orientable, 80 Pach, Janos, 112, 113 Pandharipande, Rahul, 77 partially ordered set, see also poset Pieri formula, 144, 152 Pl¨ ucker embedding, 96 Pl¨ ucker, Julius, 165 point inflection, 164 solitary, 9, 165, 166 Pollack, Ricky, 2 polynomial Ehrhart, 31 sparse, 3, 26 univariate, 13 Wronski, 85 polynomial system generic, 2 mixed, 3, 26 unmixed, 3 Wronski, 86 polytope cross, 81 Newton, 3, 26 order, 92 poset, 91 Z2-graded, 93 linear extension, 92 sign-imbalance, 92 positive orthant, 49 preprime, 184 primitive, 5, 45 principal nilpotent, 179 problem of four lines, 6, 116, 163, 171, 181 projective space, 27 Puiseaux series, 34, 162 Puiseaux, Victor Alexandre, 34 Purbhoo, Kevin, 173, 174 quantum cohomology, 9 quantum Schubert Calculus, 118 ramification sequence, 131 Ran, Ziv, 8 rational normal curve, see also curve, rational normal real exponents, 65 regular polyhedral subdivision, 42 regular subdivision, 42 regular triangulation, 44 Rellich, Franz, 162 Richardson, Thomas, 54 Risler, Jean-Jacques, 50 Rojas, J. Maurice, 4, 54, 56 Ronga, Felice, 105 Roullier, Fabrice, 18 Roy, Marie-Fran¸ coise, 2, 54 Rusek, Korben, 54 sagbi degeneration, 98 Schechtman, Vadim, 154 scheme-theoretic limit, 40 Scherbak, Inna, 150 Schicho, Josef, 10 Schubert Calculus, 116, 118 Schubert cell, 125 Schubert condition, 117, 179 Grassmannian, 183 simple, 117, 122 special, 117 Schubert induction, 126, 152 Schubert problem, 117, 174, 179 Schubert variety, 117, 121, 126, 175, 179 simple, 117 special, 117, 144 Schubert, Hermann C¨ aser Hannibal, 5, 105, 124, 126, 128 separated subsets, 141 Sevostyanov, K., 54, 55 Shapiro Conjecture, see also Conjecture, Shapiro Shapiro, Boris, 6, 118, 161, 176 Shapiro, Michael, 6, 118, 141, 161, 170, 171, 176, 184 Shih, Justin, 54 Shub, Mike, 10 Shustin, Eugenii, 9, 77, 166 signature of a foldable triangulation, 85 Smale, Steve, 10, 172 Solomon, Jake, 10, 11, 77 Soprunova, Jenya, 11, 77 Sottile, Frank, see also author Stanley, Richard, 92 Steiner, Jacob, 105 Stewart-Gough platform, 109 Stiefel manifold, 96, 125, 134 Sturm sequence, 16–18 Sturm, Jacques Charles Fran¸ cois, 16 Sturmfels, Bernd, 5, 45, 47, 48, 50, 51, 54, 98 subgroup Borel, 179 parabolic, 179 subscheme, 63 subspace isotropic, 173

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