3期

最新文章

• Canonical bases and moduli spaces of sheaves on curves AI翻译
  作者：Schiffmann, Olivier
• Quadratic forms on graphs AI翻译
  作者：Alon, N; Makarychev, K; Makarychev, Y; Naor, A
  作者单位：Tel Aviv University; Tel Aviv University; Institute for Advanced Study - USA; Princeton University; Microsoft
  摘要：We introduce a new graph parameter, called the Grothendieck constant of a graph G = ( V, E), which is defined as the least constant K such that for every A : E --> R, sup(f:V -->S\V\-1{u, v} is an element of E) Sigma A(u, v) . [f(u), f(v)] <= K sup(phi:V --> {-1, +1} {u, v} is an element of E) Sigma A(u, v) . phi*u)phi(v). The classical Grothendieck inequality corresponds to the case of bipartite graphs, but the case of general graphs is shown to have various algorithmic applications. Indeed, ...
• Murphy's law in algebraic geometry: Badly-behaved deformation spaces AI翻译
  作者：Vakil, R
  作者单位：Stanford University
  摘要：We consider the question: How bad can the deformation space of an object be? The answer seems to be: Unless there is some a priori reason otherwise, the deformation space may be as bad as possible. We show this for a number of important moduli spaces. More precisely, every singularity of finite type over Zeta (up to smooth parameters) appears on: the Hilbert scheme of curves in projective space; and the moduli spaces of smooth projective general-type surfaces (or higher-dimensional varieties),...
• The trajectories of particles in Stokes waves AI翻译
  作者：Constantin, Adrian
  作者单位：Trinity College Dublin; Lund University
  摘要：Analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat bed: within a period each particle experiences a backward-forward motion with a slight forward drift.
• Teichmuller curves in genus two: Torsion divisors and ratios of sines AI翻译
  作者：McMullen, Curtis T.
  作者单位：Harvard University
• 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.
• 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...
• 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...
• Quadratic estimates and functional calculi of perturbed Dirac operators AI翻译
  作者：Axelsson, A; Keith, S; McIntosh, A
  作者单位：Australian National University
  摘要：We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge-Dirac operator on compact manifolds depend analytically on L-infinity changes in the metric. We also recover a unified proof of many results in the Calderon program, including the Kato square root problem and the boundedness of the Cauchy operator on Lipschitz curves and surfaces.
• Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves AI翻译
  作者：Auroux, Denis; Katzarkov, Ludmil; Orlov, Dmitri
  作者单位：Massachusetts Institute of Technology (MIT); University of Miami; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
  摘要：We study homological mirror symmetry for Del Pezzo surfaces and their mirror Landau-Ginzburg models. In particular, we show that the derived category of coherent sheaves on a Del Pezzo surface X-k obtained by blowing up CP2 at k points is equivalent to the derived category of vanishing cycles of a certain elliptic fibration W-k :M-k -> C with k+3 singular fibers, equipped with a suitable symplectic form. Moreover, we also show that this mirror correspondence between derived categories can be e...