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Topics in Hyperplane Arrangements, Polytopes and Box-Splines
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Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of mathematics that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory.§The discussion is divided into five extensive parts; the first of which provides basic material on convex sets, combinatorics, polytopes, Laplace and Fourier transforms, and the language of modules over the Weyl algebra. The following four sections focus on the differentiable case, discrete case, and several applications, e.i., two independent chapters explore the computations of De Rham cohomology for the complement of a hyperplane or toric arrangement.§This book, written by two distinguished authors, engages a broad audience by providing a strong foundation in very important areas. This book may be used in a classroom setting as well as a reference for researchers.
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