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作者：Maulik, Davesh; Toda, Yukinobu
作者单位：Massachusetts Institute of Technology (MIT); University of Tokyo
摘要：In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT in...
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作者：Buhovsky, Lev; Humiliere, Vincent; Seyfaddini, Sobhan
作者单位：Tel Aviv University; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected symplectic manifold must have at least as many fixed points as the minimal number of critical points of a smooth function on M. It is well known that the Arnold conjecture holds for Hamiltonian homeomorphisms of closed symplectic surfaces. The goal of this paper is to provide a counterexample to the Arnold conjecture for Hamiltonian homeomorphisms in dimensions four and higher. More precisely, we prove tha...
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作者：Brotbek, Damian; Darondeau, Lionel
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; KU Leuven
摘要：Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.
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作者：Zhang, Hui-Chun; Zhu, Xi-Ping
作者单位：Sun Yat Sen University
摘要：In 1997, Jost (Calc Var PDE 5:1-19, 1997) and Lin (Collection of papers on geometry, analysis and mathematical physics, World Sci. Publ., River Edge, 1997), independently proved that every energy minimizing harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov space with non-positive curvature is locally Holder continuous. Lin (1997) proposed an open problem: can the Holder continuity be improved to Lipschitz continuity? J. Jost also asked a similar problem a...
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作者：Gui, Changfeng; Moradifam, Amir
作者单位：Hunan University; University of Texas System; University of Texas at San Antonio; University of California System; University of California Riverside
摘要：In this paper, we showthat the total area of two distinct surfaces with Gaussian curvature equal to 1, which are also conformal to the Euclidean unit disk with the same conformal factor on the boundary, must be at least 4p. In otherwords, the areas of these surfaces must cover the whole unit sphere after a proper rearrangement. We refer to this lower bound of total area as the Sphere Covering Inequality. The inequality and its generalizations are applied to a number of open problems related to...
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作者：Latala, Rafal; van Handel, Ramon; Youssef, Pierre
作者单位：University of Warsaw; Princeton University; Universite Paris Cite
摘要：Let X be a symmetric random matrix with independent but non-identically distributed centered Gaussian entries. We show that E parallel to X parallel to(Sp) asymptotic to E[(Sigma i(Sigma j Xij2)p/2)1/p] for any 2 <= p <= infinity, where Sp denotes the p-Schatten class and the constants are universal. The right-hand side admits an explicit expression in terms of the variances of thematrix entries. This settles, in the case p = infinity, a conjecture of the first author, and provides a complete ...
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作者：De Simoi, Jacopo; Liverani, Carlangelo
作者单位：University of Toronto; University of Rome Tor Vergata
摘要：We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and conclude with a completely new result (a local limit theorem) on the distribution of the process determined by the fluctuations around the average. The method of proof is based on a mixture of standard pairs and transfer operators that we expect to be applicable ...
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作者：Myerson, Simon L. Rydin
作者单位：University of London; University College London
摘要：Let be quadratic forms with integer coefficients in n variables. When and the variety is a smooth complete intersection, we prove an asymptotic formula for the number of integer points in an expanding box at which these forms simultaneously vanish, which in particular implies the Hasse principle for . Previous work in this direction required n to grow at least quadratically with R. We give a similar result for R forms of degree d, conditional on an upper bound for the number of solutions to an...
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作者：Xie, Song-Yan
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：For the intersection family of general Fermat-type hypersurfaces in defined over an algebraically closed field , we extend Brotbek's symmetric differential forms by a geometric approach, and we further exhibit unveiled families of lower degree symmetric differential forms on all possible intersections of with coordinate hyperplanes. Thereafter, we develop what we call the 'moving coefficients method' to prove a conjecture made by Olivier Debarre: for a generic choice of hypersurfaces of degree...
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作者：Gouezel, Sebastien; Matheus, Frederic; Maucourant, Francois
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Nantes Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes
摘要：The fundamental inequality of Guivarc'h relates the entropy and the drift of random walks on groups. It is strict if and only if the random walk does not behave like the uniform measure on balls. We prove that, in any nonelementary hyperbolic group which is not virtually free, endowed with a word distance, the fundamental inequality is strict for symmetric measures with finite support, uniformly for measures with a given support. This answers a conjecture of S. Lalley. For admissible measures,...
