Schubert calculus

English Alternative forms en Schubert enumerative calculus Etymology Named after German mathematician Hermann Schubert (1848–1911), who introduced the theory in the nineteenth century. Noun - en mathematics 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. en by generalization The enumerative geometry of linear subspaces; the study of analogous questions in generalised cohomology theories. en 1986 Christopher I. Byrnes; Anders Lindquist Frequency Domain and State Space methods for Linear Systems North-Holland https://books.google.com.au/books?id=PRyoAAAAIAAJ&q=%22Schubert+calculus%22%7C%22Schubert+calculus%22&dq=%22Schubert+calculus%22%7C%22Schubert+calculus%22&hl=en&sa=X&ved=0ahUKEwij7uH26-viAhULw1QKHUqHAtQQ6AEIsgEwGg 77 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 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, Instituto Nacional de Matemática Pura e Aplicada 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. Translations branch of algebraic geometry; calculus used to solve certain counting problems See also en Schubert cell en Schubert variety Further reading Enumerative geometry Hilbert's fifteenth problem Intersection theory Schubert calculus on Encyclopedia of Mathematics en eponyms