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Books > Science & Mathematics > Mathematics > Topology > Algebraic topology
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k-Schur Functions and Affine Schubert Calculus (Paperback, Softcover reprint of the original 1st ed. 2014)
Loot Price: R3,862
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k-Schur Functions and Affine Schubert Calculus (Paperback, Softcover reprint of the original 1st ed. 2014)
Series: Fields Institute Monographs, 33
Expected to ship within 10 - 15 working days
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This book gives an introduction to the very active field of
combinatorics of affine Schubert calculus, explains the current
state of the art, and states the current open problems. Affine
Schubert calculus lies at the crossroads of combinatorics,
geometry, and representation theory. Its modern development is
motivated by two seemingly unrelated directions. One is the
introduction of k-Schur functions in the study of Macdonald
polynomial positivity, a mostly combinatorial branch of symmetric
function theory. The other direction is the study of the Schubert
bases of the (co)homology of the affine Grassmannian, an
algebro-topological formulation of a problem in enumerative
geometry. This is the first introductory text on this subject. It
contains many examples in Sage, a free open source general purpose
mathematical software system, to entice the reader to investigate
the open problems. This book is written for advanced undergraduate
and graduate students, as well as researchers, who want to become
familiar with this fascinating new field.
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