Nous espérons obtenir des resultats significatifs dans tous les domaines indiques dans la description du projet. Concretement, les résultats attendus sont indiqués en detail dans cette description (B2).
Dans le domaine de recherche en question, l'énonce de résultats que "nous comptons obtenir" relève, nous en sommes convaincus, d'une certaine malhonnéteté scientifique. Par conséquent, nous ne promettons rien, mais avons indiqué, dans le descriptif detaillé du projet, quelques uns des résultats déjà obtenus par notre équipe, et les directions ou nous comptons continuer a travailler. Nous espérons que l'évaluation du projet se fait sur la base de ces descriptifs et sur la valeur des chercheurs du associés au projet, et non sur des promesses vagues et/ou optimistes de résultats.
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I.A.Dynnikov, Three-page approach to knot theory. Universal semigroup, Funktsional'nyi Analiz I Prilozhenija, 34 (2000), no.1, 29-40 (Russian); English translation in Functional Analysis and Its Appl. 34 (2000), no.1, 24-32.
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S.N.Majumdar, S.Nechaev, Anisotropic ballistic deposition model with links to the Ulam problem and the Tracy-Widom distribution, Phys.Rev.E, 69, 011103 (2004)
O. Vasilyev, S. Nechaev, Thermodynamics and topology of disordered systems: Statistics of random knot diagrams on finite lattices, JETP, 93 (2001) 1119
O.Vasilyev, S.Nechaev, On topological correlations in trivial knots: New arguments in support of the crumpled globule concept, Theor.Math.Phys., 134 (2003) 142-159
S.Nechaev, O.Vasilyev, Topological percolation on square lattice, submitted to J.Phys.A.
S.Nechaev, R.Voituriez, On the plants leaves boundary, "jupe à godets" and conformal embeddings, J.Phys. (A): Math. Gen. 34 (2001) 11069-11082
S.Nechaev, R. Voituriez, Random walks on 3-strand braid and related hyperbolic groups, J. Phys. A: Math. Gen. 36 (2003), 43-66
G.Oshanin, R.Voituriez, Random walk generated by random permutations, preprint cond-mat/0312262
P.Zinn-Justin, The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links, Commun. Math. Phys., 238 (2003), 287-304
P.Zinn-Justin, J.-B.Zuber, Matrix Integrals and the Generation and Counting of Virtual Tangles and Links, accepté pour publication dans J. Knot Theor. Ramif.
G.Schaeffer, P.Zinn-Justin, On the Asymptotic Number of Plane Curves and Alternating Knots, accepté pour publication dans J. Exp. Math.