M. Broué, R. Rouquier On Rickard's Equivalences

Reference: LMENS-94-1 (January 94)
Source: dvi, ps

M. Duflo, M. Vergne Familles Cohérentes sur les groupes de Lie Semi-simples et restriction aux Sous-groupes Compacts Maximaux

Reference: LMENS-94-2 (Janvier 94)
Source: dvi, ps

Abstract:Let G be a semi-simple simply connected Lie group and K be a subgroup, maximal among the subgroups compact modulo the center. Invariant eigendistributions on G can be restricted to K. It is an irritating fact that, without supplementary assumptions, this restriction does not determine the distribution. However, we prove here that this is true if, instead of a single invariant eigendistribution, one considers a family of invariant eigendistributions, coherent in the sense of W. Schmid. We also study non connected semi-simple groups: we define a notion of coherent family of invariant eigendistributions and prove a unicity theorem in this setting.

D. Harari Obstructions de Manin "transcendantes"

Reference: LMENS-94-3 (Février 94)
Source: dvi, ps

L. Desvillettes Quelques Résultats Mathématiques et Numériques pour les équations Cinétiques (thèse d'habilitation)

Reference: LMENS-94-4 (Février 94)

J. Cassaigne, V. Maillot Hauteurs des Hypersurfaces et Fonctions Zêta d'Igusa

Reference: LMENS-94-5 (Février 94)
Source: dvi, ps

Abstract: On associe à toute hypersurface Z dans PnZ deux fonctions Zêta, iS(P,s) et iE(P,s). Leur dérivée en zéro est reliée à la hauteur h__O(1)(Z) de Z. Pour certaines hypersurfaces, on donne des expressions intégrales simples de iE(P,s). On en déduit le calcul de la hauteur de certaines hypersurfaces toriques et de certaines quadriques. Comme cas particulier, on obtient la hau- teur de la grassmannienne G(2,4) vue comme hypersurface dans P5Z grâce au plongement de Plücker: c'est un nombre rationnel.

J.J Risler A Bound for the Degree of Non Holonomy

Reference: LMENS-94-6 (April 94)
Source: dvi, ps

Abstract: Let = (V1,...,Vs) be a system made with vector fields V1,...,Vs in Rn whose coordinatesPare polynomials of degree d. To such a system is associated the control system x`= uiVi. It is proven that the degree of nonholonomy of such a system is bounded by a function OE(n,d) (2nd)n2(n+1). In the case n = 2, we have OE(2,d) 6d2 - 2d + 2.

O. Catoni Energy Transforms for Metropolis and Simulated Annealing Algorithms

Reference: LMENS-94-7 (April 94)
Source: dvi, ps

Abstract: We present here a method to speed up Metropolis algorithms which can be viewed as an alternative to simulated annealing. We show that this method of energy transformation compares favourably with simulated annealing in the asymptotic of a close to one probability of convergence. It requires an estimate of the minimum value of the energy function to be known, but if only a loose estimate is available, the algorithm itself can be used to improve it. The energy transform increases the instability of local minima, thus decreasing the "difficulty" of the energy landscape.

A. Trouvé Rough Large Deviation Estimates for the Optimal Convergence Speed Exponent of Generalized Simulated Annealing Algorithms

Reference: LMENS-94-8 (April 94)
Source: dvi, ps

Abstract: We study the convergence speed of generalized simulated annealing algorithms. Large deviations estimates uniform in the cooling schedule are established for the exit from the cycles in the spirit of Catoni's sequential annealing work [2]. We compute the optimal convergence speed exponent proving a conjectured of R. Azencott [1].

A. Trouvé Cycle Decompositions and Simulated Annealing

Reference: LMENS-94-9 (October 93)
Source: dvi, ps

Abstract: The behavior of simulated annealing algorithms is tightly related to the hierarchical decomposition of their configuration spaces in cycles. In the generalized annealing framework, this decomposition which is defined recursively. In this paper, its structure is extensively studied and it is shown that the decomposition can be achieved through an implementable algorithm which allows to compute exactly the fundamental constants underlying the behavior of these algorithms.

B. Helffer, P. Kerdelhué On the Total Bandwidth for the Rational Harper's Equation

Reference: LMENS-94-10 (May 94)

P. Colmez Fonctions Zeta p-adiques en s=0

Reference: LMENS-94-11 (Mai 94)
Source: dvi, ps

M. Vergne A Note on Jeffrey-Kirwan-Witten's Localisation Formula

Reference: LMENS-94-12 (June 94)
Source: dvi, ps

V. Maillot Un Calcul de Schubert Arithmétique

Reference: LMENS-94-13 (Juin 94)
Source: dvi, ps

Abstract: On développe un analogue arithmétique du calcul de Schubert sur les Grassmaniennes. Les résultats obtenus permettent de donner une_description combinatoire de la structure de l'anneau de Chow-Arakelov CH*(G (p,n)) en terme_de générateurs et relations. On en déduit la table de multiplication de CH*(G (p,n)) dans une "base" explicite. On donne alors une formule pour la hauteur de l'image d'une Grassmanienne par le plongement de Plücker, on montre en particulier qu'une telle hauteur est toujours un nombre rationnel.

M. Martin-Deschamps, D. Perrin Le Schéma de Hilbert des Courbes localement Cohen-Macaulay n'est (presque) jamais connexé ni réduit

Reference: LMENS-94-14 (Juillet 94)
Source: dvi, ps

S. Dozias Spectral Properties and Semiclassical Asymptotics for h-pseudodifferential Operators with periodic Flow

Reference: LMENS-94-15 (July 94) Source: dvi, ps

Abstract: We study the repartition of the eigenvalues of an h-pseudodifferen-tial operator in a small neighbourhood of an energy where the Hamiltonian flow associated with the principal symbol of the operator is periodic. The main tools we use are the composition of Fourier in- tegral operators and the computation of the principal symbol of the composed operator. These rules of composition are developed for the Gutzwiller's trace formula in Meinrenken's article [21].

N. Berline, M. Vergne L'Indice Equivariant des Opérateurs Transversalement Elliptiques

Reference: LMENS-94-16 (Septembre 94)
Source: dvi, ps

Abstract: Dans cet article, nous montrons que l'indice cohomologique (construit dans [11]) d'un symbole transversalement elliptique satisfait certaines propriétés fonctorielles. Nous calculons d'autre part l'indice cohomologique pour certains symboles transversalement elliptiques particuliers. En reprenant les arguments donnés par Atiyah dans [1] on en déduit que l'indice cohomologique du symbole d'un opérateur transversalement elliptique P est égal à l'indice analytique de P .

H. Berestycki, A. Bonnet, S.J. Chapman A Semi-elliptic System Arising in the Theory of Type-II Superconductivity

Reference: LMENS-94-17 (September 94)

D. Harari Arithmétique des Variétes Fibrées au-dessus de l'Espace Affine

Reference: LMENS-94-18 (Septembre 94)
Source: dvi, ps

Abstract: Le but de cette note est de généraliser le théorème 4.2.1 de [5], qui portait sur le principe de Hasse pour les fibrés au-dessus de la droite affine, aux variétés fibrées au-dessus de l'espace affine Ank. Un autre relâchement dans les hypothèses (qui nous est d'ailleurs nécessaire pour faire fonctionner la démonstration, qui se fait par récurrence sur n) est que l'on autorise maintenant que le groupe de Brauer géométrique de la fibre générique soit fini (et non plus forcément nul), ce qui est par exemple le cas si cette fibre générique est géométriquement unirationnelle.

M. Vergne Multiplicities Formulas for Geometric Quantization. Part I

Reference: LMENS-94-19 (October 94)

M. Vergne Multiplicities Formulas for Geometric Quantization. Part II

Reference: LMENS-94-20 (October 94)

M. Vergne Equivariant Index Formulas for Orbifolds

Reference: LMENS-94-21 (October 94)

O. Catoni The Energy Transformation Method for the Metropolis Algorithm Compared with Simulated Annealing

Reference: LMENS-94-22 (November 94)
Source: dvi, ps

Abstract: We present and analyze a new speed-up technique for Monte Carlo optimization: the energy transformation method, where the Metropolis algo- rithm is used repeatedly with more and more favourable energy functions derived from the original one by increasing transformations. We compare our method with simulated annealing in the limit of a large number of iterations in the general case. Then we study an example of large state space and show on this example that the limit of a large problem and the limit of a large number of iterations give different comparison results. Our method is always the most suc-cessful in the limit of a large number of iterations, whereas in the limit of a large state space, it is more efficient than simulated annealing only if a block-wise optimization scheme is used. Block-wise optimization schemes will be discussed further in a forthcoming paper.

AMS Classification (1991): 60J10, 90C42

A. Chambert-Loir Extension Universelle d'une Variété Abélienne et Hauteurs des Points de Torsion

Reference: LMENS-94-23 (Novembre 94)
Source: dvi, ps

Abstract: Nous évaluons la hauteur des points de torsion de l'extension universelle d'une variété abélienne définie sur un corps de nombres. Nous montrons en particulier que la moyenne des hauteurs des points d'ordre premier p croît comme log p quand p tend vers l'infini. Ceci généralise des résultats obtenus par Paula Cohen pour les courbes elliptiques.
Pour cela, on utilise la théorie des hauteurs < à la Arakelov > qui permet de comprendre cette hauteur comme la somme d'une intersection sur un modèle entier convenable de l'extension universelle et d'un terme à l'infini. La p-partie, calculée grâce à la classification de Raynaud de certains schémas en groupes finis, fournit la principale contribution.
Nous donnons en appendice une application aux périodes p-adiques.

A.-M. Aubert Dualité dans le Groupe de Grothendick de la Catégorie des Représentations Lisses de Longueur Finie d'un Groupe Réductifs p-adique

Reference: LMENS-94-24 (Novembre 94)
Source: dvi, ps

Abstract: We define an involution on the Grothendieck ring of the category of finite length smooth representations of a p-adic algebraic group, which is a direct analogue Curtis-Alvis duality for finite groups of Lie type. This involution commutes with taking the contragredient, with parabolic induction and, up a few twists, with truncation. It also preserves the irreducible representations up to sign.

A. Trouvé Asymptotical Behavior of Several Interacting Annealing Processes

Reference: LMENS-94-25 (December 94)
Source: dvi, ps

Abstract: We prove that the optimal convergence speed exponent for parallel annealing based on periodically interacting multiple searches with time period ris always worse than for independent multiple searches whenever the cost function has only one global minimum. Our proofs will be based on large deviation estimates coming from the theory of generalized simulated annealing (G.S.A).

AMS Classification (1991): Primary 60F10; secondary 60J10,

A.-M. Aubert Formule des Traces sur les Corps Finis

Reference: LMENS-94-26 (Decembre 94)
Source: dvi, ps

A. Beauville Conformal blocks, Fusion rings and the Verlinde formula

Reference: LMENS-DIVERS-94-1 (Avril 94)
Source: dvi

Abstract: A Rational Conformal Field Theory (RCFT) is a functor which associates to any Riemann surface with marked points a finite-dimensional vector space, so that certain axioms are satisfied; the Verlinde formula computes the dimension of these vector spaces. For some particular RCFTs associated to a compact Lie group G (the WZW models), these spaces have a beautiful algebro-geometric interpretation as spaces of "generalized theta functions", that is, sections of a determinant bundle (or its powers) over the moduli space of G-bundles on a Riemann surface. In this paper we explain the formalism of the Verlinde formula: the dimension of the spaces are encoded in a finite-dimensional Z-algebra, the "fusion.netscape-preferences ring" of the theory; everything can be expressed in terms of the characters of this ring. We show how to compute these characters in the case of the WZW model and thus obtain an explicit formula for the dimension of the space of generalized theta functions.

AMS Classification: Primary 17B81, 81T40; Secondary 17B67, 81R10
Keywords: Conformal blocks, Factorization rules, fusion rings, fusion rules, Rational Conformal Field Theory, Verlinde formula, WZW-model

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