Showing papers in "Advances in Mathematics in 2007"

TL;DR: In this paper, a graph-theoretic analogue of the Riemann-Roch theorem is presented, and the existence or non-existence of a winning strategy for a certain chip-firing game played on the vertices of a graph is characterized.

TL;DR: In this paper, the concept of maximal (n − 1 ) -orthogonal subcategories over Artin algebras and orders was introduced, and the Auslander-Reiten theory on them was developed.

TL;DR: In this paper, the fundamental elements and results of a new theory of regular functions of one quaternionic variable were developed, following a classical idea of Cullen, but using a more geometric formulation to show that it is possible to build a rather complete theory.

TL;DR: Geis et al. as discussed by the authors showed that the stable category of Cohen-Macaulay modules is 3-Calabi-Yau, and generalized the results to d-calabi-yau.

TL;DR: In this paper, a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized Kahler structures interpolates between holomorphic reduction of complex manifolds and symplectic reduction.

TL;DR: In this article, the authors construct a purely algebraic version of Gromov-Witten invariants at all genera, which depend on a Calabi-Yau A ∞ category.

TL;DR: In this paper, a relative version of Kontsevich's formality theorem for supermanifolds is shown to be L∞-quasiisomorphic to the DGLA of multidifferential operators acting on sections of the exterior algebra of the conormal bundle.

TL;DR: In this article, it was shown that Kirillov?Reshetikhin modules and Weyl modules are in fact all Demazure modules and that the crystals of the Weyl module are the same up to some additional label zero arrows.

TL;DR: In this article it was shown that the category of inverse quantal frames is equivalent to complete and infinitely distributive inverse monoids, and as a consequence they obtain a (non-functorial) correspondence between these and localic etale groupoids that generalizes more classical results concerning inverse semigroups and topological groupoids.

TL;DR: In this paper, a good-? inequality with two parameters and Calderon?Zygmund decomposition are used to obtain weighted norm estimates for singular non-integral operators with bounded mean oscillation functions.

TL;DR: In this article, a new approach to the invertibility of the layer potentials associated with elliptic equations and systems in a bounded Lipschitz domain in R n was developed.

TL;DR: In this article, the relation between random matrices and free probability theory was extended from the level of expectations to a level of fluctuations, and the concept of second order freeness was introduced to understand global fluctuations of Haar distributed unitary random matrix.

TL;DR: For a simple graph, the vertex cover algebra is generated by elements of degree 2, and it is standard graded if and only if the graph is bipartite as discussed by the authors, and the maximal degree of the generators of vertex cover algebras is given.

TL;DR: In this paper, a triangulated category of graded matrix factorizations for a polynomial of type ADE is studied and it is shown that it is equivalent to the derived category of finitely generated modules over the path algebra of the corresponding Dynkin quiver.

TL;DR: The notion of moment map and of Hamiltonian reduction in non-commutative differential geometry was introduced in this paper, which is a generalization of the notion of double derivation.

TL;DR: In this article, the authors describe intrinsically regular submanifolds in Heisenberg groups H and prove that they are graphs in a natural group way, as well as that an area formula holds for the intrinsic Hausdorff measure.

TL;DR: In this article, the blocks of the cyclotomic Hecke algebras of type G ( r, 1, n ) over an arbitrary field are classified. But the classification of the blocks is incomplete, since Cox has discovered that this previous proof is incomplete.

TL;DR: In this article, the authors show that the FS exponent of a pivotal category is a multiple of its exponent, in the sense of Etingof, by a factor not greater than 2.

TL;DR: In this paper, a sub-Riemannian calculus for hypersurfaces in graded nilpotent Lie groups is developed, based on a geometric framework such as horizontal Levi-Civita connection, second fundamental form, and horizontal Laplace-Beltrami operator.

TL;DR: In this paper, the Hardy-Rellich inequalities are improved by decomposition into spherical harmonics, where in addition various new inequalities are obtained (e.g. Rellich-Sobolev inequalities).

TL;DR: A polynomial f has the halfplane property if there is an open half-plane H subset of C, whose boundary contains the origin, such that f is non-zero whenever all the variables are in H.

TL;DR: The central limit theorem for convex sets was shown to hold for the Lp-centroid bodies in this paper, and the reverse Holder inequality for their mean width was proved.

TL;DR: In this paper, the second part of a series on configurations in an abelian category A is presented, where the authors define an associative multiplication ∗ on CF (Obj A ) using pushforwards and pullbacks along 1-morphisms between configuration moduli stacks, so that CF ( Obj A ) is a Q -algebra.

TL;DR: In this article, the Hausdorff and box dimension of the limit sets for a class of planar non-Moran-like geometric constructions generalizing the Bedford-McMullen general Sierpinski carpets was determined.

TL;DR: In this paper, a universal enveloping algebra for Sabinin algebras is presented, and the corresponding Poincare-Birkhoff-Witt Theorem is proved.

TL;DR: In this paper, the authors studied moduli spaces of configurations in an abelian category and showed that the moduli space of t-semistable, indecomposable and t-stable objects in class a are constructible sets.

TL;DR: In this article, the supercritical 2D dissipative quasi-geostrophic equation is studied and a global well-posedness result for small initial data lying in critical Besov spaces constructed over Lebesgue spaces with p ∈ [ 1, ∞ ] is given.

TL;DR: In this paper, the homotopy theory of n-fold loop spaces is shown to be equivalent to the theory of reduced Tn-spaces, where Tn is an iterated wreath product of the simplex category.

TL;DR: Geck and Kim as discussed by the authors studied the minimal length elements in some double cosets of Coxeter groups and used them to study Lusztig's G-stable pieces and the generalization of Gstable pieces introduced by Lu and Yakimov.

TL;DR: In this article, it was shown that for a uniform random sorting network, as n → ∞ the space-time process of swaps converges to the product of semicircle law and Lebesgue measure.