3期

最新文章

• Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups AI翻译
  作者：Monod, Nicolas; Nariman, Sam
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Purdue University System; Purdue University
  摘要：We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring generated by the bounded Euler class. These seem to be the first examples of groups for which the entire bounded cohomology can be described without being trivial. We further prove that the C-r-diffeomorphisms groups of the circle and of the c...
• Unbounded Hankel operators and the flow of the cubic Szego equation AI翻译
  作者：Gerard, Patrick; Pushnitski, Alexander
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of London; King's College London
  摘要：We prove that, for any Hankel operator with a symbol from the Hardy class H-2, the maximal and minimal domains coincide. As an application, we prove that the evolution flow of the cubic Szeg & oacute; equation on the unit circle can be continuously extended to the whole class H-2.
• Potential automorphy for G Ln AI翻译
  作者：Qian, Lie
  作者单位：Stanford University
  摘要：We prove potential automorphy results for a single Galois representation G(F) -> GL(n)((Q) over bar (l)) where F is a CM number field. The strategy is to use the p, q switch trick to go between the p-adic and q-adic realisation of a certain variant of the Dwork motive. We choose this variant to break self-duality shape of the motives, but not the Hodge-Tate weights. Another key result to prove is that certain p-adic representations we choose that come from the Dwork motives is ordinarily autom...
• Closed three-dimensional vacuum static spaces AI翻译
  作者：Xu, Xingwang; Ye, Jian
  作者单位：Nanjing University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
  摘要：This article is devoted to the study of the closed vacuum static spaces. Based on the argument of maximum principle, we show that three-dimensional closed vacuum static spaces with scalar curvature 6 must be isometric to either the standard unit sphere S-3 (1) or a finite quotient of the torus S-1 (root 1/3) x S-2 (root 1/3).
• A Chabauty-Coleman bound for surfaces AI翻译
  作者：Caro, Jerson; Pasten, Hector
  作者单位：Pontificia Universidad Catolica de Chile
  摘要：Building on work by Chabauty from 1941, Coleman proved in 1985 an explicit bound for the number of rational points of a curve C of genus g = 2 defined over a number field F, with Jacobian of rank at most g - 1. Namely, in the case F = Q, if p > 2g is a prime of good reduction, then the number of rational points of C is at most the number of F-p-points plus a contribution coming from the canonical class of C. We prove a result analogous to Coleman's bound in the case of a hyperbolic surface X o...
• Local models for Galois deformation rings and applications AI翻译
  作者：Le, Daniel; Le Hung, Bao V.; Levin, Brandon; Morra, Stefano
  作者单位：Purdue University System; Purdue University; Northwestern University; Rice University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-VIII
  摘要：We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois deformation rings for unramified extensions of Q(p) with small regular Hodge-Tate weights. We establish several significant facts about their geometry including a unibranch property at special points and a representation theoretic description of the irreducible components of their special fibers. We derive from these geometric results a number of...
• One dimensional representations of finite W-algebras, Dirac reduction and the orbit method AI翻译
  作者：Topley, Lewis
  作者单位：University of Bath
  摘要：In this paper we study the variety of one dimensional representations of a finite W algebra attached to a classical Lie algebra, giving a precise description of the dimensions of the irreducible components. We apply this to prove a conjecture of Losev describing the image of his orbit method map. In order to do so we first establish new Yangian-type presentations of semiclassical limits of the W-algebras attached to distinguished nilpotent elements in classical Lie algebras, using Dirac reduct...
• Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps AI翻译
  作者：Li, Jialun; Pan, Wenyu
  作者单位：University of Zurich; University of Chicago
  摘要：Let Gamma be a geometrically finite discrete subgroup in SO(d + 1, 1)degrees with parabolic elements. We establish exponential mixing of the geodesic flow on the unit tangent bundle T-1 (Gamma\Hd+1) with respect to the Bowen-Margulis- Sullivan measure, which is the unique probability measure on T-1 (Gamma\Hd+1) with maximal entropy. As an application, we obtain a resonance-free region for the resolvent of the Laplacian on Gamma\Hd+1. Our approach is to construct a coding for the geodesic flow ...
• Large prime gaps and probabilistic models AI翻译
  作者：Banks, William; Ford, Kevin; Tao, Terence
  作者单位：University of Missouri System; University of Missouri Columbia; University of Illinois System; University of Illinois Urbana-Champaign; University of California System; University of California Los Angeles
  摘要：We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a specific bound. From a rigorous analysis of this model, we obtain heuristic upper and lower bounds for the size of the largest prime gap in the interval [1, x]. Our results are stated in terms of the extremal bounds in the interval sieve problem. The same methods also allow us to rigorously relate the validity of th...
• Time quasi-periodic vortex patches of Euler equation in the plane AI翻译
  作者：Berti, Massimiliano; Hassainia, Zineb; Masmoudi, Nader
  作者单位：International School for Advanced Studies (SISSA); New York University; New York University Abu Dhabi; New York University
  摘要：We prove the existence of time quasi-periodic vortex patch solutions of the 2d-Euler equations in R2, close to uniformly rotating Kirchhoff elliptical vortices, with aspect ratios belonging to a set of asymptotically full Lebesgue measure. The problem is reformulated into a quasi-linear Hamiltonian equation for a radial displacement from the ellipse. A major difficulty of the KAM proof is the presence of a zero normal mode frequency, which is due to the conservation of the angular momentum. Th...