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The object of this week is to bring together specialists in the domains of Riemannian geometry, low-dimensional topology and geometric group theory to take stock of current interactions and encourage ...
We propose a theory of double Schubert polynomials Pw(X;Y ) for the Lie types B, C, D which naturally extends the family of Lascoux and Schutzen Ä berger in type A. These polynomials satisfy po...
Let A be an abelian variety over a number field F and A_ its dual. B. Birch and P. Swinnerton-Dyer, interested in defining the Tamagawa number  (A) of A, were led to their celebrated c...
We study conformal actions of connected nilpotent Lie groups on compact pseudo-Riemannian manifolds. We prove that if a type-(p,q) compact manifold M supports a conformal action of a connected nilpo...
The main motivation of this paper arises from classical questions about actions of Lie groups preserving a geometric structure: which Lie groups can act on a manifold preserving a given structure, a...
In his doctoral thesis [3] and subsequent papers [4, 5], Todd Drumm developed a theory of fundamental domains for discrete groups of isometries of Minkowski (2 + 1)-space E, using polyhedra called c...
A symplectic structure on a manifold is a closed nondegenerate exterior 2- form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metr...
Bartholdi, Neuhauser and Woess proved that a family of metabelian groups including lamplighters have a striking geometric manifestation as 1-skeleta of horocyclic products of trees. The purpose of thi...
We examine the geometry of the word problem of two different types groups: those satisfying weak almost-convexity conditions and those admitting geodesic combings whose width satisfy minimally restric...
We establish the lower bound p2t (e, e)  exp(−t1/3), for the large times asymptotic behaviours of the probabilities p2t (e, e) of return to the origin at even times 2t, for random walks assoc...
G is the real points of a linear connected reductive group. - g0 := Lie(G),  Cartan involution, g0 = k0 + s0, g := (g0)C, K maximal compact subgroup, g = k + s, - P = MAN minimal parabolic subgrou...
The full unitary dual for the complex classical groups viewed as real Lie groups is computed in [B1]. This was close to 20 years ago. Since then there have been many advances, but the general proble...
1.1. Positive de nite functions. We start with the classical notion of positive de nite functions. De nition. A continuous function f : R 􀀀! C is called positive de nite if it satis es (1...
We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results are closely related to the fact that uniform block permutations form a fact...
A 2-step nilpotent Lie algebra n is said to be of type (p,q)if dim(n)=p+q and dim([n,n])=p. By considering a class of 2-step nilpotent Lie algebras naturally attached to graphs, we prove that there ex...

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