2006

最新文章

• Unstable products of smooth curves AI翻译
  作者：Ross, J.
  作者单位：Columbia University
  摘要：We give examples of smooth manifolds with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kahler classes that do not admit any constant scalar curvature Kahler metrics. These manifolds also have unstable Hilbert and Chow points. We compare this to the work of Song-Weinkove on the J-flow.
• The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points. II AI翻译
  作者：Harcos, G; Michel, P
  作者单位：University of Texas System; University of Texas Austin; Universite de Montpellier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：We prove a general subconvex bound in the level aspect for Rankin-Selberg L-functions associated with two primitive holomorphic or Maass cusp forms over Q. We use this bound to establish the equidistribution of incomplete Galois orbits of Heegner points on Shimura curves associated with indefinite quaternion algebras over Q.
• Evolution of minimal torus in Riemannian manifolds AI翻译
  作者：Ding, Weiyue; Li, Jiayu; Liu, Qingyue
  作者单位：Peking University; Chinese Academy of Sciences; Abdus Salam International Centre for Theoretical Physics (ICTP); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szego asymptotics AI翻译
  作者：Damanik, David; Simon, Barry
  作者单位：California Institute of Technology
  摘要：We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szego asymptotics off the real axis. A key idea is to prove the equivalence of Szego asymptotics and of Jost asymptotics for the Weyl solution. We also prove L-2 convergence of Szego asymptotics on the spectrum.
• CM-values of Hilbert modular functions AI翻译
  作者：Bruinier, JH; Yang, TH
  作者单位：University of Cologne; University of Wisconsin System; University of Wisconsin Madison
• Hyperbolic manifolds with convex boundary AI翻译
  作者：Schlenker, JM
  作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS)
  摘要：Let (M, partial derivative M) be a 3-manifold, which carries a hyperbolic metric with convex boundary. We consider the hyperbolic metrics on M such that the boundary is smooth and strictly convex. We show that the induced metrics on the boundary are exactly the metrics with curvature K >-1, and that the third fundamental forms of partial derivative M are exactly the metrics with curvature K < 1, for which the closed geodesics which are contractible in M have length L > 2 pi. Each is obtained e...
• Finite covers of random 3-manifolds AI翻译
  作者：Dunfield, Nathan M.; Thurston, William P.
  作者单位：California Institute of Technology; Cornell University
  摘要：A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this mode...
• Cohomology of tilting modules over quantum groups and t-structures on derived categories of coherent sheaves AI翻译
  作者：Bezrukavnikov, Roman
  作者单位：Massachusetts Institute of Technology (MIT)
  摘要：The paper is concerned with cohomology of the small quantum group at a root of unity, and of its upper triangular subalgebra, with coefficients in a tilting module. It turns out to be related to irreducible objects in the heart of a certain t-structure on the derived category of equivariant coherent sheaves on the Springer resolution, and to equivariant coherent IC sheaves on the nil-cone. The support of the cohomology is described in terms of cells in affine Weyl groups. The basis in the Grot...
• The f(q) mock theta function conjecture and partition ranks AI翻译
  作者：Bringmann, Kathrin; Ono, Ken
  作者单位：University of Wisconsin System; University of Wisconsin Madison
  摘要：In 1944, Freeman Dyson initiated the study of ranks of integer partitions. Here we solve the classical problem of obtaining formulas for N-e(n) (resp. N-o(n)), the number of partitions of n with even (resp. odd) rank. Thanks to Rademacher's celebrated formula for the partition function, this problem is equivalent to that of obtaining a formula for the coefficients of the mock theta function f(q), a problem with its own long history dating to Ramanujan's last letter to Hardy. Little was known a...
• On the Kashiwara-Vergne conjecture AI翻译
  作者：Alekseev, A; Meinrenken, E
  作者单位：University of Geneva; University of Toronto
  摘要：Let G be a connected Lie group, with Lie algebra g. In 1977, Duflo constructed a homomorphism of g-modules Duf : S( g). U( g), which restricts to an algebra isomorphism on invariants. Kashiwara and Vergne ( 1978) proposed a conjecture on the Campbell-Hausdorff series, which ( among other things) extends the Duflo theorem to germs of biinvariant distributions on the Lie group G. The main results of the present paper are as follows. ( 1) Using a recent result of Torossian ( 2002), we establish t...