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Heat Kernels and Dirac Operators

- Nicole Berline, E. Getzler, M. Vergne
- Mathematics
- 1 April 1992

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… Expand

On the Segal-Shale-Weil representations and harmonic polynomials

- M. Kashiwara, M. Vergne
- Mathematics
- 1 February 1978

In this paper, we give the answer to the following two intimately related problems. (a) To decompose the tensor products of the harmonic representations into irreducible components to get a series of… Expand

Lattice points in simple polytopes

in terms of fP(h) q(x)dx where the polytope P(h) is obtained from P by independent parallel motions of all facets. This extends to simple lattice polytopes the EulerMaclaurin summation formula of… Expand

Residue formulae, vector partition functions and lattice points in rational polytopes

We obtain residue formulae for certain functions of several vari- ables. As an application, we obtain closed formulae for vector partition func- tions and for their continuous analogs. They imply an… Expand

Kostant Partitions Functions and Flow Polytopes

- Welleda Baldoni, M. Vergne
- Mathematics
- 30 August 2008

This paper discusses volumes and Ehrhart polynomials in the context of flow polytopes. The general approach that studies these functions via rational functions with poles on arrangement of… Expand

Modular forms of weight 1/2

We will construct θ-series of weight 1/2 and 3/2 for some congruence subgroups of SL(2,ℤ) by taking appropriate coefficients of the representation \( \mathop{R}\limits^{\sim } \) of SL(2;ℝ),… Expand

Residues formulae for volumes and Ehrhart polynomials of convex polytopes.

- W. Baldoni-Silva, M. Vergne
- Mathematics
- 15 March 2001

In these notes, we explain residue formulae for volumes of convex polytopes, and for Ehrahrt polynomials based on the notion of total residue. We apply this method to the computation of the volume of… Expand

How to integrate a polynomial over a simplex

- V. Baldoni, Nicole Berline, J. D. Loera, M. Köppe, M. Vergne
- Mathematics, Computer ScienceMath. Comput.
- 11 September 2008

TLDR

Toric reduction and a conjecture of Batyrev and Materov

We present a new integration formula for intersection numbers on toric quotients, extending the results of Witten, Jeffrey and Kirwan on localization. Our work was motivated by the Toric Residue… Expand

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