14876309
The bipartite Brill-Gordan locus and angular momentum
AbstractGiven integers n,d,e with $1 \leqslant e < \frac{d}{2},$ let $X \subseteq {\Bbb P}^{\binom{d+n}{d}-1}$ denote the locus of degree d hypersurfaces in ${\Bbb P}^n$ which are supported on two hyperplanes with multiplicities d-e and e. Thus X is the Brill-Gordan locus associated to the partition (d-e,e). The main result of this paper is an exact determination of the Castelnuovo regularity of the ideal of X. Moreover, we show that X is r-normal for $r \geqslant 3.$ In the case of binary forms (i.e., for n = 1) we give an invariant-theoretic description of the ideal generators and, furthermore, exhibit a set of two covariants which define this locus set-theoretically. In addition to the standard cohomological tools in algebraic geometry, the proof crucially relies on the nonvanishing of certain 3j-symbols from the quantum theory of
angular momentum.
13943019
The Jacobian Conjecture as a Problem of Perturbative Quantum Field Theory
Abstract. The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so-called formal inverse approach, that of perturbative quantum field theory.

119589214
A massless quantum field theory over the p-adics
This is an extended abstract for a talk given at the Oberwolfach workshop "The Renormalization Group", March 13th - March 19th, 2011.
119161955
The Ground State Energy of the Massless Spin-Boson Model
We provide an explicit combinatorial expansion for the ground state energy of the massless spin-Boson model as a power series in the coupling parameter. Our method uses the technique of cluster expansion in constructive quantum field theory and takes as a starting point the functional integral representation and its reduction to an Ising model on the real line with long range interactions. We prove the analyticity of our expansion and provide an explicit lower bound on the radius of convergence. We do not need multiscale nor renormalization group analysis. A connection to the loop-erased random walk is indicated.
118707104
Explicit Fermionic Tree Expansions
We express connected Fermionic Green's functions in terms of two totally explicit tree formulas. The simplest and most symmetric formula, the Brydges–Kennedy formula is compatible with Gram's inequality. The second one, the rooted formula of Abdesselam and Rivasseau, respects even better the antisymmetric structure of determinants, and allows the direct comparison of rows and columns which correspond to the mathematical implementation in Grassmann integrals of the Pauli principle. To illustrate the power of these formulas, we give a ‘three lines proof’ that the radius of convergence of the Gross–Neveu theory with cutoff is independent of the number of colors, using either one or the other of these formulas.
17794922
Trees, forests and jungles: a botanical garden for cluster expansions
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and test them on a series of pedagogical examples.
170390949
Recherche de production resonante de sleptons au run I de D0 & identification et mesure des electrons au run II
Une recherche de production resonante de particules supersymetrique (smuon et sneutrino du muon) est presentee. Le cadre theorique de cette etude est le modele msugra, ou on considere cinq parametres libres : m 0, m 1 / 2, tan, a 0, sign(), avec r-parite violee (un parametre). Deux methodes d'analyse ont ete appliquees : l'analyse sequentielle consideree comme une methode traditionnelle et l'analyse par reseau de neurones qui est de plus en plus utilisee comme outil en physique des particules. Notre etude est basee sur les donnees du run i de l'experience d aupres du tevatron a fermilab (usa). La luminosite consideree est de 94pb 1. Aucun exces par rapport aux predictions du modele standard n'a ete observe, on interprete par consequent ce resultat en termes de limites sur les parametres du modele utilise. Des contours d'exclusion a 95% de niveau de confiance dans le plan (m 0, m 1 / 2) sont donnes. Des valeurs de m 0 et m 1 / 2 jusqu'a 230 gev et 260 gev sont exclues pour une constante de couplage 2 1 1 = 0. 09, tan = 2, sign () = 1 et a 0 = 0. On peut aussi interpreter ce resultat par des contours d'exclusion dans les plans des masses, (m , m x 10) par exemple, ou est le sneutrino du muon et x 0 1 est le neutralino le plus leger. Des masses (relatives) du et x 0 1 de 280 gev et 112gev sont exclues a 95% de niveau de confiance. Cette meme analyse peut etre refaite sur les donnees du run ii qui beneficie d'une plus grande luminosite instantanee (5. 2 10 3 2 cm 2s 1 au run ii contre 0. 86 10 3 2 cm 2s 1 au run i) et une plus grande energie dans le centre de masse (2tev contre un 1. 8tev au run i). Cela permettra de restreindre d'avantage les parametres de msugra et comme consequence les masses des particules supersymetriques. Une autre partie de ce travail traite de l'identification de l'electron au run ii qui est tres importante pour la recherche d'une nouvelle physique. Plusieurs outils sont utilises pour une telle fin. Particulierement nous avons etudie les performances de la matrice de covariance (matrice h).
110275378
The control and monitoring system for the ATLAS semi-conductor tracker
Abstract The ATLAS Semi-Conductor Tracker (SCT) will be made of 4088 silicon modules mounted on four barrel supports and eighteen end cap disks. At present module production has started in different sites all around the world. The assembly of the modules into the support structures is taking place at three different macro-assembly sites. To allow for the safety operation of the detector a Detector Control System (DCS) is being developed at CERN that will be close to the final ATLAS configuration. The DCS will control and monitor the power supply provided to the modules, the cooling system and the environmental variables. This paper will give an overview of the system required to operate and readout large-scale silicon detectors.