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This book introduces the important ideas of algebraic topology by emphasizing the relation of these ideas with other areas of mathematics. Rather than choosing one point of view of modern topology (ho

Intersection theory has played a central role in mathematics, from the ancient origins of algebraic geometry in the solutions of polynomial equations to the triumphs of algebraic geometry during the l

The aim of this book is to develop the combinatorics of Young tableaux and to show them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties. The first part of the book is a self-contained presentation of the basic combinatorics of Young tableaux, including the remarkable constructions of 'bumping' and 'sliding', and several interesting correspondences. In Part II these results are used to study representations with geometry on Grassmannians and flag manifolds, including their Schubert subvarieties, and the related Schubert polynomials. Much of this material has never appeared in book form.There are numerous exercises throughout, with hints or answers provided. Researchers in representation theory and algebraic geometry as well as in combinatorics will find Young Tableaux interesting and useful; students will find the intuitive presentation easy to follow.

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic g

In various contexts of topology, algebraic geometry, and algebra (e.g. group representations), one meets the following situation. One has two contravariant functors K and A from a certain category to

In twelve engaging essays, William Fulton chronicles the history of urban planning in the Los Angeles metropolitan area, tracing the legacy of short-sighted political and financial gains that has resu

This heavily-illustrated book is an ideal introduction for beginners to the finite-dimensional representations of Lie groups and Lie algebras. Packed with examples, the book begins with a brief tour

Most Americans today do not live in discrete cities and towns, but rather in an aggregation of cities and suburbs that forms one basic economic, multi-cultural, environmental and civic entity. These “

Two emcees from the Bronx, NY entered the American hip-hop landscape of the mid-1990s with comprehensive insider slang that bewildered as they radiated the look of a bygone era of black culture. Geech