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Showing papers in "Advances in Mathematics in 2006"


Journal ArticleDOI
TL;DR: In this article, a new category C, called the cluster category, is introduced, which is obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field.

972 citations


Journal ArticleDOI
TL;DR: In this article, Ricca et al. proved the global in time regularity for the 2D Boussinesq system with either the zero diffusivity or the zero viscosity.

458 citations


Journal ArticleDOI
TL;DR: In this paper, the authors introduced invariants for closed, oriented three-manifolds, defined using a variant of Lagrangian Floer homology in the symmetric products of Riemann surfaces.

318 citations


Journal ArticleDOI
TL;DR: In this article, the L p -Minkowski problem was solved for p ⩾ n + 1 in the smooth category and the relevant Monge-Ampere equation (0.1) is solved for all p > 1.

313 citations


Journal ArticleDOI
TL;DR: In this paper, a new construction of the algebraic K-theory of small permutative categories is given, which preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and output.

186 citations


Journal ArticleDOI
TL;DR: In this article, the authors apply ideas from commutative algebra and Morita theory to algebraic topology using ring spectra and prove new duality results in algebra and topology.

182 citations


Journal ArticleDOI
TL;DR: In this paper, the authors further develop the theory for braided tensor categories and establish a correspondence of ribbon categories that can be applied to, and is in fact motivated by, the coset construction in conformal quantum field theory.

166 citations


Journal ArticleDOI
TL;DR: In this paper, the authors give a presentation for the finite W-algebra associated to a nilpotent matrix in the general linear Lie algebra over C. In particular, the presentation is that of the Yangian of level l associated to gln, as was first observed by Ragoucy and Sorba.

154 citations


Journal ArticleDOI
TL;DR: In this paper, the Calderon-Zygmund singular integral operator theory and the Hardy-Littlewood maximal function were used to prove that the existence of solutions u∈W01,p(Ω) of divu=f for f∈Lp(∩) with vanishing mean value and 1

146 citations


Journal ArticleDOI
TL;DR: Chari and Pressley as discussed by the authors constructed a Poincare?Birkhoff?Witt type basis for the Weyl modules and proved the conjecture made in [V.QA/0004174] of the current algebra of.

142 citations


Journal ArticleDOI
Wenxiong Chen1
TL;DR: The L p Minkowski problem in the plane has been the object of a number of recent investigations as discussed by the authors, and various existence results for 0 ⊾ p ⩾ - 2.

Journal ArticleDOI
TL;DR: In this article, the authors generalize the local index formula of Connes and Moscovici to the case of spectral triples for a * -subalgebra A of a general semi-neumann algebra.

Journal ArticleDOI
TL;DR: In this paper, the coarse geometric Novikov conjecture for spaces which admit a uniform embedding into a uniformly convex Banach space was proved for the case of uniform embeddings.

Journal ArticleDOI
TL;DR: The multiplicative preprojective algebras as mentioned in this paper provide a natural setting for the middle convolution operation introduced by N.M. Katz in his book "Rigid Local Systems" and put in an algebraic setting by M.P. Holland and the first author.

Journal ArticleDOI
TL;DR: In this article, the relationship between the colored Jones polynomial and the A-polynomial of a knot was studied and the AJ conjecture was established for a large class of two-bridge knots.

Journal ArticleDOI
TL;DR: In this paper, a generalization of lattice points in rational polytopes and the enumeration of proper graph colorings is presented, with applications to graph and signed-graph coloring, compositions of an integer, and antimagic labelling.

Journal ArticleDOI
TL;DR: In this article, a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems is presented, and a new elliptic beta integral for the root system of type A is obtained.

Journal ArticleDOI
TL;DR: In this article, an extrapolation theory that allows us to obtain, from weighted L p inequalities on pairs of functions for p fixed and all A ∞ weights, estimates for the same pairs on very general rearrangement invariant quasi-Banach function spaces with A ∆ weights.

Journal ArticleDOI
TL;DR: In this paper, it was shown that there exist at least two geometrically distinct brake orbits in every bounded convex symmetric domain in R n for n ⩾ 2.

Journal ArticleDOI
TL;DR: In this paper, it was shown that linear embeddings of subsets of Euclidean space in low-dimensional normed spaces can be obtained in order to improve the dependence on ǫ in Dvoretzky's theorem.

Journal ArticleDOI
TL;DR: In this paper, the even local index formula of Connes and Moscovici was generalized to the case of spectral triples for a * -subalgebra A of a general semi-neumann algebra.

Journal ArticleDOI
TL;DR: In this paper, the authors define the notion of Connes-von Neumann spectral triple and consider the associated index problem, and compute the analytic Chern-Connes character of such a generalized spectral triple, and prove the corresponding local formula for its Hochschild class.

Journal ArticleDOI
TL;DR: In this article, the p-relative version of the Berhuy-Reichstein canonical dimension for an algebraic group over an arbitrary field of an arbitrary characteristic (p is any prime integer) is presented.

Journal ArticleDOI
TL;DR: In this article, the authors consider a general class of badly approximable subsets of a metric space and show that these subsets have full Hausdorff dimension.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated a group B? that includes Artin's braid group B8 and Thompson's group F. The elements of B? are represented by braids diagrams in which the distances between the strands are not uniform and, besides the usual crossing generators, new rescaling operators shrink or stretch the distances.

Journal ArticleDOI
TL;DR: In this article, the authors introduce a notion of a smooth valuation on an arbitrary smooth manifold and establish some of the basic properties of it, which is a generalization of the notion of valuation on a smooth manifold.

Journal ArticleDOI
TL;DR: In this article, the standard Poisson structure on the rectangular matrix variety M m, n (C ) is investigated via the orbits of leaves under the action of the maximal torus T ⊂ GL m + n ( C ).

Journal ArticleDOI
TL;DR: In this article, a generalized Littlewood-Paley theory for semigroups acting on L p -spaces of functions with values in uniformly convex or smooth Banach spaces was developed.

Journal ArticleDOI
TL;DR: In this article, a quasilocal subsets of homomorphic vertex operators is introduced and studied, and it is proved that on any maximal quasILocal subspace there exists a natural vertex algebra structure and that any quasilyocal subset of Hom ( W, W ( ( ( x ) ) ) generates a vertex algebra.

Journal ArticleDOI
TL;DR: In particular, this article gave a local conformal net corresponding to the moonshine vertex operator algebras of Frenkel-Lepowsky-Meurman and Meurman.