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Heat Kernels and Dirac Operators
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent
How to integrate a polynomial over a simplex
It is proved that the problem is NP-hard for arbitrary polynomials via a generalization of a theorem of Motzkin and Straus, and if the polynomial depends only on a fixed number of variables, while its degree and the dimension of the simplex are allowed to vary, it is proven that integration can be done inPolynomial time.
Local Euler-Maclaurin formula for polytopes
We give a local Euler-Maclaurin formula for rational convex polytopes in a rational euclidean space . For every affine rational polyhedral cone C in a rational euclidean space W, we construct a
The Chern character of a transversally elliptic symbol and the equivariant index
Abstract. Let G be a compact Lie group acting on a compact manifold M. In this article, we associate to a G-transversally elliptic symbol on M a G-invariant generalized function on G, constructed in
Fourier Transforms of Orbits of the Coadjoint Representation
Let G be a compact Lie group with Lie algebra g. Let 0 ⊂ g* be an orbit of G under the coadjoint representation of maximal dimension 2n. For f ∈ 0, we denote by G(f) the stabilizer of f and t = ℊ(f)
Computation of the Highest Coefficients of Weighted Ehrhart Quasi-polynomials of Rational Polyhedra
An efficient algorithm for computing the highest degree coefficients of the weighted Ehrhart quasi-polynomial for a rational simple polytope in varying dimension, when the weights of the lattice points are given by a polynomial function h.