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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 recentExpand
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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 aExpand
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How to integrate a polynomial over a simplex
TLDR
We prove that the problem is NP-hard for arbitrary polynomials via a generalization of a theorem of Motzkin and Straus. Expand
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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 inExpand
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A proof of Bismut local index theorem for a family of Dirac operators
On donne une demonstration du theoreme de Bismut basee sur le developpement classique des noyaux de la chaleur. On exprime le noyau de la chaleur du laplacien d'un fibre vectoriel comme une moyenneExpand
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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)Expand
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Computation of the Highest Coefficients of Weighted Ehrhart Quasi-polynomials of Rational Polyhedra
TLDR
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. Expand
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A computation of the equivariant index of the Dirac operator
On donne une demonstration des formules de points fixes d'Atiyah-Singer pour l'operateur de Dirac tordu sur une variete de Riemann M, en utilisant l'equation de la chaleur sur sa variete des reperesExpand
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