Schubert calculus

Noun

Schubert calculus (uncountable)

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;
   • 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].1986, Christopher I. Byrnes, Anders Lindquist, Frequency Domain and State Space methods for Linear Systems, North-Holland, page 77
   • 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...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...
2. the enumerative geometry of linear subspaces; the study of analogous questions in generalised cohomology theories.