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最新文章

• Babai's conjecture for high-rank classical groups with random generators AI翻译
  作者：Eberhard, Sean; Jezernik, Urban
  作者单位：University of Cambridge; University of Ljubljana
  摘要：Let G = SCln(q) be a quasisimple classical group with n large, and let x(1),..., x(k) is an element of G be random, where k >= q(C). We show that the diameter of the resulting Cayley graph is bounded by q(2)n(O(1)) with probability 1 - o(1). In the particular case G = SLn(p) with p a prime of bounded size, we show that the same holds for k = 3.
• On contact type hypersurfaces in 4-space AI翻译
  作者：Mark, Thomas E.; Tosun, Bulent
  作者单位：University of Virginia; University of Alabama System; University of Alabama Tuscaloosa
  摘要：We consider constraints on the topology of closed 3-manifolds that can arise as hypersurfaces of contact type in standard symplectic R-4. Using an obstruction derived from Heegaard Hoer homology we prove that no Brieskorn homology sphere admits a contact type embedding in R-4 , a result that has bearing on conjectures of Gompf and Kollar. This implies in particular that no rationally convex domain in C-2 has boundary diffeomorphic to a Brieskorn sphere. We also give infinitely many examples of...
• Rational elliptic surfaces and the trigonometry of tetrahedra AI翻译
  作者：Rudenko, Daniil
  作者单位：University of Chicago
  摘要：We study the trigonometry of non-Euclidean tetrahedra using tools from algebraic geometry. We establish a bijection between non-Euclidean tetrahedra and certain rational elliptic surfaces. We interpret the edge lengths and the dihedral angles of a tetrahedron as values of period maps for the corresponding surface. As a corollary we show that the cross-ratio of the exponents of the solid angles of a tetrahedron is equal to the cross-ratio of the exponents of the perimeters of its faces. The Reg...
• Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves AI翻译
  作者：Delecroix, Vincent; Goujard, Elise; Zograf, Peter; Zorich, Anton
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); Inria; Universite Paris Cite
  摘要：We study the combinatorial geometry of a random closed multi-curve on a surface of large genus g and of a random square-tiled surface of large genus g. We prove that primitive components , gamma(1), ...,gamma(k) of a random multicurve m(1)gamma(1) + ... + m(k)gamma(k) represent linearly independent homology cycles with asymptotic probability 1 and that all its weights m(i); are equal to 1 with asymptotic probability root 2/2. We prove analogous properties for random square-tiled surfaces. In p...
• Ancient asymptotically cylindrical flows and applications AI翻译
  作者：Choi, Kyeongsu; Haslhofer, Robert; Hershkovits, Or; White, Brian
  作者单位：Korea Institute for Advanced Study (KIAS); University of Toronto; Hebrew University of Jerusalem; Stanford University
  摘要：In this paper, we prove the mean-convex neighborhood conjecture for neck singularities of the mean curvature flow in R-n(+1) for all n >= 3: we show that if a mean curvature flow {M-t} in Rn+1 has an Sn-1 x R singularity at (x(0), t(0)), then there exists an epsilon = epsilon(x(0), t(0)) > 0 such that M-t boolean AND B(x(0), epsilon) is mean-convex for all t is an element of (t(0)-epsilon(2), t(0)+epsilon(2)). As in the case n = 2, which was resolved by the first three authors in Choi et al. (...
• On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives AI翻译
  作者：Liu, Yifeng; Tian, Yichao; Xiao, Liang; Zhang, Wei; Zhu, Xinwen
  作者单位：Zhejiang University; Chinese Academy of Sciences; Peking University; Massachusetts Institute of Technology (MIT); California Institute of Technology
  摘要：In this article, we study the Beilinson-Bloch-Kato conjecture for motives associated to Rankin-Selberg products of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the central critical value of the Rankin-Selberg L-function does not vanish, then the Bloch-Kato Selmer group with coefficients in a favorable field of the corresponding motive vanishes. We also show that if the class in the Bloch-Kato Selmer group constructed ...
• Lifting and automorphy of reducible mod p Galois representations over global fields AI翻译
  作者：Fakhruddin, Najmuddin; Khare, Chandrashekhar; Patrikis, Stefan
  作者单位：Tata Institute of Fundamental Research (TIFR); University of California System; University of California Los Angeles; University System of Ohio; Ohio State University
  摘要：We prove the modularity of most reducible, odd representations (rho) over bar : Gamma(Q) -> GL(2)(k) with k a finite field of characteristic an odd prime p. This is an analogue of Serre's celebrated modularity conjecture (which con- cerned irreducible, odd representations (rho) over bar : Gamma(Q) -> GL(2)(k)) for reducible, odd representations. Our proof lifts (rho) over bar to an irreducible geometric p-adic representation rho which is known to arise from a newform by results of Skinner-Wile...
• Strong Sard conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3 AI翻译
  作者：da Silva, A. Belotto; Figalli, A.; Parusinski, A.; Rifford, L.
  作者单位：Aix-Marseille Universite; Universite Paris Cite; Sorbonne Universite; Swiss Federal Institutes of Technology Domain; ETH Zurich; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite Cote d'Azur; Inria; Centre National de la Recherche Scientifique (CNRS)
  摘要：In this paper we prove the strong Sard conjecture for sub-Riemannian structures on 3-dimensional analytic manifolds. More precisely, given a totally nonholonomic analytic distribution of rank 2 on a 3-dimensional analytic manifold, we investigate the size of the set of points that can be reached by singular horizontal paths starting from a given point and prove that it has Hausdorff dimension at most 1. In fact, provided that the lengths of the singular curves under consideration are bounded w...
• Random integral matrices: universality of surjectivity and the cokernel AI翻译
  作者：Nguyen, Hoi H.; Wood, Melanie Matchett
  作者单位：University System of Ohio; Ohio State University; University of Wisconsin System; University of Wisconsin Madison
  摘要：For a random matrix of entries sampled independently from a fairly general distribution in Z we study the probability that the cokernel is isomorphic to a given finite abelian group, or when it is cyclic. This includes the probability that the linear map between the integer lattices given by the matrix is surjective. We show that these statistics are asymptotically universal (as the size of the matrix goes to infinity), given by precise formulas involving zeta values, and agree with distributi...
• Rigidity estimates for isometric and conformal maps from Sn-1 to Rn AI翻译
  作者：Luckhaus, Stephan; Zemas, Konstantinos
  作者单位：Leipzig University; University of Munster
  摘要：We investigate both linear and nonlinear stability aspects of rigid motions (resp. Mobius transformations) of Sn-1 among Sobolev maps from Sn-1 into R-n. Unlike similar in flavour results for maps defined on domains of R-n and mapping into R-n, not only an isometric (resp. conformal) deficit is necessary in this more flexible setting, but also a deficit measuring the distortion of Sn-1 under the maps in consideration. The latter is defined as an associated isoperimetric type of deficit. The fo...