Annals of Mathematics

最新文章

• Classification of irreducible holonomies of torsion-free affine connections AI翻译
  作者：Merkulov, S; Schwachhöfer, L
• Menger curvature and rectifiability AI翻译
  作者：Léger, JC
• The spectrum of coupled random matrices AI翻译
  作者：Adler, M; Van Moerbeke, P
• Doubles of groups and hyperbolic LERF 3-manifolds AI翻译
  作者：Gitik, R
  摘要：We show that the quasiconvex subgroups in doubles of certain negatively curved groups are closed in the profinite topology. This allows us to construct the first known large family of hyperbolic 3-manifolds such that any finitely generated subgroup of the fundamental group of any member of the family is closed in the profinite topology.
• Permanents, Pfaffian orientations, and even directed circuits AI翻译
  作者：Robertson, N; Seymour, PD; Thomas, R
  摘要：Given a 0-1 square matrix A, when can some of the 1's be changed to -1's in such a way that the permanent of A equals the determinant of the modified matrix? When does a real square matrix have the property that every real matrix with the same sign pattern (that is, the corresponding entries either have the same sign or are both zero) is nonsingular? When is a hypergraph with n vertices and n hyperedges minimally nonbipartite? When does a bipartite graph have a Pfaffian orientation? Given a di...
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model AI翻译
  作者：Bleher, P; Its, A
  摘要：We derive semiclassical asymptotics for the orthogonal polynomials P-n(z) on the line with respect to the exponential weight exp(-NV(z)), where V(z) is a double-well quartic polynomial, in the limit when n, iV --> infinity. We assume that epsilon less than or equal to (n/N) less than or equal to lambda(cr) - epsilon for some epsilon > 0, where lambda(cr) is the critical value which separates orthogonal polynomials With two cuts from the ones with one cut. Simultaneously we derive semiclassical...
• Gromov's measure equivalence and rigidity of higher rank lattices AI翻译
  作者：Furman, A
  摘要：In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the motivations for this notion. The main result of this paper is ME rigidity of higher rank lattices: any countable group which is ME to a lattice in a simple Lie group G of higher rank, is commensurable to a lattice in G.
• Companion forms and weight one forms AI翻译
  作者：Buzzard, K; Taylor, R
• The Cassels-Tate pairing on polarized abelian varieties AI翻译
  作者：Poonen, B; Stoll, M
  摘要：Let (A, lambda) be a principally polarized abelian variety defined over a global field k, and let TCC(A) be its Shafarevich-Tate group. Let III(A)(nd) denote the quotient of III(A) by its maximal divisible subgroup. Cassels and Tate constructed a nondegenerate pairing III(A)(nd) x III(A)(nd) --> Q/Z. If A is an elliptic curve, then by a result of Cassels the pairing is alternating. But in general it is only antisymmetric. Using some new but equivalent definitions of the pairing, we derive gene...
• Metal-insulator transition for the almost Mathieu operator AI翻译
  作者：Jitomirskaya, SY
  摘要：We prove that for Diophantine omega and almost every theta, the almost Mathieu operator, (H(omega,lambda,theta)Psi)(n) = Psi(n + 1) + Psi(n - 1) + lambda cos 2 pi(wn + theta)Psi(n), exhibits localization for lambda > 2 and purely absolutely continuous spectrum for lambda < 2. This completes the proof of (a correct version of) the Aubry-Andre conjecture.