Showing papers in "Advances in Mathematics in 2003"

TL;DR: In this article, Ozsvath and Szabo introduced absolute gradings on the three-manifold invariants developed in Ozvath and Zabo (Holomorphic disks and topological invariants for closed threemanifolds, math.SG/0101206, Ann. of Math.

TL;DR: In this paper, the authors construct moduli spaces for weighted pointed curves using methods of the log minimal model program, and describe the induced birational morphisms between moduli space as the weights are varied.

TL;DR: In this article, the authors studied the structure of racks, their cohomology groups and the corresponding Nichols algebras of braided vector spaces arising from groups, and showed advances in these three directions.

TL;DR: In this paper, it was shown that the Kortewegde Vries equation, the Camassa-Holm equation, and the Hunter-Saxton equation have the same symmetry group and similar bihamiltonian structures.

TL;DR: In this paper, the uniqueness of planar convex polygons of given outer orientations to the sides and prescribed areas of the triangles formed by the origin with any two consecutive vertices was shown.

TL;DR: In this paper, the authors develop the cocycle bicrossed product construction, starting from a matched pair of locally compact quantum groups, and define exact sequences and establish a one-to-one correspondence between cocyclic products and cleft extensions.

TL;DR: In this article, a general notion of depth two for ring homomorphism N → M is introduced and the step two centralizers A =End N M N and B=(M⊗ N M) N are shown in a natural way via H-equivalence to be dual bimodules for Morita equivalent endomorphism rings.

TL;DR: In this paper, a notion of an n-fold monoidal category was developed, which corresponds in a precise way to the notion of a nfold loop space, and a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an NCL.

TL;DR: For the group O(p,q) of conformal transformations on R p−1,q−1, the authors of as mentioned in this paper gave a new construction of its minimal unitary representation via Euclidean Fourier analysis.

TL;DR: In this article, the distribution function F n ( q, t ) of a pair of statistics on Catalan words is defined as the sum of these statistics restricted to Catalan words ending in s ones.

TL;DR: In this article, the irreducible components of Springer fibers for hook and two-row nilpotent elements of gl n (C ) were described as iterated bundles of flag manifolds and Grassmannians.

TL;DR: In this article, the authors apply methods from conformal geometry of pseudo-Riemannian manifolds to a general construction of an infinite-dimensional representation of the conformal group on the solution space of the Yamabe equation.

TL;DR: In this paper, the Tits-Freudenthal construction of the magic square was extended to include exceptional simple Lie algebras as octonionic analogues of the classical matrix Lie algesbras.

TL;DR: In this article, a formula for the Chern character of an odd L (1, ∞) -summable Breuer-Fredholm module in terms of a Hochschild 1-cycle is given.

TL;DR: The notion of a convex geometry as mentioned in this paper extends the notion of finite closure systems with the anti-exchange property known in combinatorics, which is essential for the different embedding results in the class of join-semidistributive lattices.

TL;DR: In this article, the Kontsevich formality L ∞ -morphism U : T poly • (R d )→ D poly• ( R d ), A = C ∞ (Rd), A =C ∞(R d ).

TL;DR: In this article, the notions of labelled set and numerosity are introduced to generalize the counting process of finite sets and the resulting numbers, called numerosities, are then used to develop nonstandard analysis.

TL;DR: In this paper, the branching law corresponding to restricting the minimal unitary representation to natural symmetric subgroups is studied. But the branching laws are not restricted to Riemannian manifolds.

TL;DR: In this paper, a theory of real blow-ups of projective hyperplane arrangements is proposed, where the hyperplane arrangement is associated to a finite reflection group W and if the blow-up locus is W -invariant, the resulting manifold will admit a cell decomposition whose maximal cells are all combinatorially isomorphic to a given convex polytope P.

TL;DR: In this paper, the behavior of Legendrian and transverse knots under the operation of connected sums was studied and it was shown that there exist Legendrian knots that are not distinguished by any known invariant.

TL;DR: In this paper, the authors studied several aspects of asymptotically hyperbolic (AH) Einstein metrics, mostly on 4-manifolds, and proved boundary regularity (at infinity) for such metrics and established uniqueness under natural conditions on the boundary data.

TL;DR: In this paper, a relation between the categories of representations of Ul and Ul-modules is established, and it is shown that the category of ul-modules has a Hecke eigen-property with respect to representations lifted by means of the quantum Frobenius map U l →U( g ), where g is the Langlands dual Lie algebra.

TL;DR: In this paper, an improved approach to the theory of harmonic measures for foliated spaces introduced by Garnett is presented, based on a method for solving elliptic equations on foliated space and on the Hille-Yosida theory.

TL;DR: In this article, a reduced, arithmetically Gorenstein configuration G of linear varieties of arbitrary dimension whose Artinian reduction has the given SI-sequence as Hilbert function and has the weak Lefschetz property was constructed.

TL;DR: In this article, it was shown that peak quasisymmetric functions and enumeration of chains in Eulerian posets can be seen as the dual basis of peak sets for the algebra of peak functions.

TL;DR: In this article, the existence of a positive periodic solution y ∈ C2(R) of two-dimensional Lp-Minkowski problem y 1−p(x)(y″(x)+y(x))=g(x), where p∉{0,2}.

TL;DR: In this paper, it was shown that any object in a braided monoidal 2-category with duals determines an invariant of 2-tangles in 4-dimensions.

TL;DR: The exponent of a variety of algebras over a field of characteristic zero has been recently proved to be an integer as mentioned in this paper, and it has been shown that the number of these minimal varieties is finite for any given exponent.

TL;DR: In this paper, a model of the Shimura variety at a prime p, with parahoric level structure at p, was investigated and it was shown that this model is flat, as conjectured by Rapoport and Zink.

TL;DR: In this paper, the authors propose a construction of string cohomology spaces for Calabi-Yau hypersurfaces that arise in Batyrev's mirror symmetry construction, defined explicitly in terms of the corresponding reflexive polyhedra in a mirror-symmetric manner.