A(2)((2)) parafermions: a new conformal field theory

A new parafermionic algebra associated with the homogeneous space A(2)((2))/U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A(2)((2)) parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy-momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W-algebra type primary field with spin two. (C) 2002 Published by Elsevier Science B.V.

Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds

2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07.

Pure motives, mixed motives and extensions of motives associated to singular surfaces

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface X and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor D in a non-singular blow-up of X. If all geometric irreducible components of D are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical subquotients of the motive with compact support of the smooth part of X. Specializing to Hilbert-Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

Homotopy exponents for large H-Spaces

We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.

Formal deformations of Poisson structures in low dimensions

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal eformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.

The trematodes and cestodes of Sorex araneus L. in Valaam Island (Ladoga Lake, USSR). 1

The trematode and the cestode fauna was examined in 50 specimens of common shrews Sorex araneus L. (Insectivora: Soricidae) cillected in Valaam Island, URSS during 1988 and 1989. Two species of Trematoda and seven species of Cestoda were identified; prevalence of infection was as follows: Brachulaemus fulvus (86% ), Rubenstrema exasperatum (4% ), Hymenolepis scutigera (54% ), Neoskrjabinolepis schaldybini (26% ), Vigisolepis spinulosa (4% ), Choanotaenia crassiscolex (86% ), Choanotaenia hepatica (6% ), Dilepis undula (2% ) and Polycercus sp. (2% ).

Association of hemolytic activity of Pseudomonas entomophila, a versatile soil bacterium, with cyclic lipopeptide production.

Pseudomonas entomophila is an entomopathogenic bacterium that is able to infect and kill Drosophila melanogaster upon ingestion. Its genome sequence suggests that it is a versatile soil bacterium closely related to Pseudomonas putida. The GacS/GacA two-component system plays a key role in P. entomophila pathogenicity, controlling many putative virulence factors and AprA, a secreted protease important to escape the fly immune response. P. entomophila secretes a strong diffusible hemolytic activity. Here, we showed that this activity is linked to the production of a new cyclic lipopeptide containing 14 amino acids and a 3-C(10)OH fatty acid that we called entolysin. Three nonribosomal peptide synthetases (EtlA, EtlB, EtlC) were identified as responsible for entolysin biosynthesis. Two additional components (EtlR, MacAB) are necessary for its production and secretion. The P. entomophila GacS/GacA two-component system regulates entolysin production, and we demonstrated that its functioning requires two small RNAs and two RsmA-like proteins. Finally, entolysin is required for swarming motility, as described for other lipopeptides, but it does not participate in the virulence of P. entomophila for Drosophila. While investigating the physiological role of entolysin, we also uncovered new phenotypes associated with P. entomophila, including strong biocontrol abilities.

Muscle recovery after repair of short and long peripheral nerve gaps using fibrin conduits.

Peripheral nerve injuries with loss of nervous tissue are a significant clinical problem and are currently treated using autologous nerve transplants. To avoid the need for donor nerve, which results in additional morbidity such as loss of sensation and scarring, alternative bridging methods have been sought. Recently we showed that an artificial nerve conduit moulded from fibrin glue is biocompatible to nerve regeneration. In this present study, we have used the fibrin conduit or a nerve graft to bridge either a 10 mm or 20 mm sciatic nerve gap and analyzed the muscle recovery in adult rats after 16 weeks. The gastrocnemius muscle weights of the operated side were similar for both gap sizes when treated with nerve graft. In contrast, muscle weight was 48.32 ± 4.96% of the contra-lateral side for the 10 mm gap repaired with fibrin conduit but only 25.20 ± 2.50% for the 20 mm gap repaired with fibrin conduit. The morphology of the muscles in the nerve graft groups showed an intact, ordered structure, with the muscle fibers grouped in fascicles whereas the 20 mm nerve gap fibrin group had a more chaotic appearance. The mean area and diameter of fast type fibers in the 20 mm gap repaired with fibrin conduits were significantly (P<0.01) worse than those of the corresponding 10 mm gap group. In contrast, both gap sizes treated with nerve graft showed similar fiber size. Furthermore, the 10 mm gaps repaired with either nerve graft or fibrin conduit showed similar muscle fiber size. These results indicate that the fibrin conduit can effectively treat short nerve gaps but further modification such as the inclusion of regenerative cells may be required to attain the outcomes of nerve graft for long gaps.

Homologia de Lawson i descens

La meva recerca en els tres anys de gaudiment de beca s'ha centrat en l'estudi de teories semitopològiques definides a través d'espais de cicles algebraics, introduïts per Friedlander i Lawson. Hem estudiat propietats de descens d'aquestes teories i hem construït una successió espectral que calcula explícitament la cohomologia mòrfica d'una varietat tòrica. D'altra banda, estem treballant en l'estudi de propietats d'invariància homotòpica per la cohomologia mòrfica, així com en l'estructura algebraica dels grups d'homologia de Lawson.

Derivation of the gauge-invariant action for open and closed free bosonic string field theories

The gauge-invariant actions for open and closed free bosonic string field theories are obtained from the string field equations in the conformal gauge using the cohomology operations of Banks and Peskin. For the closed-string theory no restrictions are imposed on the gauge parameters.

Some aspects of N=2 superstring

The string model with N=2 world-sheet supersymmetry is approached via ghosts, Becchi-Rouet-Stora-Tyutin cohomology, and bosonization. Some amplitudes involving massless scalars and vectors are computed at the tree level. The constraints of locality on the spectrum are analyzed. An attempt is made to "decompactify" the model into a four-dimensional theory.

Perturbation theory and locality in the Field-Antifield formalism

The BatalinVilkovisky formalism is studied in the framework of perturbation theory by analyzing the antibracket BecchiRouetStoraTyutin (BRST) cohomology of the proper solution S0. It is concluded that the recursive equations for the complete proper solution S can be solved at any order of perturbation theory. If certain conditions on the classical action and on the gauge generators are imposed the solution can be taken local.

Monoidal functors, acyclic models and chain operads

We prove that for a topological operad $P$ the operad of oriented cubical singular chains, $C^{\ord}_\ast(P)$, and the operad of simplicial singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{\ord}_\ast(P\nsemi\mathbb{Q})$ is formal if and only if $S_\ast(P\nsemi\mathbb{Q})$ is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras.

Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

Variétés de drapeaux et opérateurs différentiels

Soit G un groupe algébrique semi-simple sur un corps de caractéristique 0. Ce mémoire discute d'un théorème d'annulation de la cohomologie supérieure du faisceau D des opérateurs différentiels sur une variété de drapeaux de G. On démontre que si P est un sous-groupe parabolique de G, alors H^i(G/P,D)=0 pour tout i>0. On donne en fait trois preuves indépendantes de ce théorème. La première preuve est de Hesselink et n'est valide que dans le cas où le sous-groupe parabolique est un sous-groupe de Borel. Elle utilise un argument de suites spectrales et le théorème de Borel-Weil-Bott. La seconde preuve est de Kempf et n'est valide que dans le cas où le radical unipotent de P agit trivialement sur son algèbre de Lie. Elle n'utilise que le théorème de Borel-Weil-Bott. Enfin, la troisième preuve est attribuée à Elkik. Elle est valide pour tout sous-groupe parabolique mais utilise le théorème de Grauert-Riemenschneider. On présente aussi une construction détaillée du faisceau des opérateurs différentiels sur une variété.