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