Meaning of Schubert calculus | Babel Free

Definitions

1. A branch of algebraic geometry concerned with solving certain types of counting problem in projective geometry; a symbolic calculus used to represent and solve such problems;
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2. A branch of algebraic geometry concerned with solving certain types of counting problem in projective geometry; a symbolic calculus used to represent and solve such problems; (by generalisation) the enumerative geometry of linear subspaces; the study of analogous questions in generalised cohomology theories.
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3. the enumerative geometry of linear subspaces; the study of analogous questions in generalised cohomology theories.
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Examples

“Hall appears to have⟳ been first with this observation, too, for in a lecture⟳ he gave at a 1959 Canadian Mathematical Congress conference in Banff on the algebra of symmetric polynomials he noted that the Schubert calculus has combinatorics similar to that of the symmetric polynomials [9].”

“2014, Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark⟳ Shimozono, Mike Zabrocki, k-Schur Functions and Affine Schubert Calculus, Springer, Fields Institute for Research⟳ in the Mathematical Sciences, page 2, The rich combinatorial backbone of the theory of Schur functions, including the Robinson–Schensted algorithm, jeu-de-taquin, the plactic monoid (see⟳ for example [139]), crystal bases [127], and puzzles [74], now underlies Schubert calculus and in particular produces a direct⟳ formula for the Littlewood-Richardson coefficients.”

“2016, Letterio Gatto, Parham Salehyan, Hasse-Schmidt Derivations on Grassmann Algebras, IMPA, Springer, page 117, This point⟳ of view⟳ was extensively developed by Laksov–Thorup [96–98] and Laksov [93, 94] in the case of equivariant Schubert calculus.”

CEFR level