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作者：Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer
作者单位：University of Munich; University of Cambridge; Harvard University
摘要：Consider the Dyson Brownian motion with parameter beta, where beta=1,2,4 corresponds to the eigenvalue flows for the eigenvalues of symmetric, hermitian and quaternion self-dual ensembles. For any beta a parts per thousand yen1, we prove that the relaxation time to local equilibrium for the Dyson Brownian motion is bounded above by N (-zeta) for some zeta > 0. The proof is based on an estimate of the entropy flow of the Dyson Brownian motion w.r.t. a pseudo equilibrium measure. As an applicati...
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作者：Cinkir, Zubeyir
作者单位：Zirve University
摘要：We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture, over a function field of characteristic 0 by proving Zhang's Conjecture about certain invariants of metrized graphs. In the function field case, these conjectures were previously known to be true only for curves of good reduction, for curves of genus at most 4 and a few other special cases. We also either verify or improve the previous results. We relate the invariants involved in Zhang's Conjecture to the tau consta...
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作者：Mueller, Carl; Mytnik, Leonid; Quastel, Jeremy
作者单位：University of Toronto; University of Rochester; Technion Israel Institute of Technology
摘要：We consider reaction-diffusion equations of KPP type in one spatial dimension, perturbed by a Fisher-Wright white noise, under the assumption of uniqueness in distribution. Examples include the randomly perturbed Fisher-KPP equations
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作者：Burns, David
作者单位：University of London; King's College London
摘要：We prove a natural refinement of a theorem of Lichtenbaum describing the leading terms of Zeta functions of curves over finite fields in terms of Weil-,tale cohomology. We then use this result to prove the validity of Chinburg's Omega(3)-Conjecture for all abelian extensions of global function fields, to prove natural refinements and generalisations of the refined Stark conjectures formulated by, amongst others, Gross, Tate, Rubin and Popescu, to prove a variety of explicit restrictions on the...
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作者：Rousset, Frederic; Tzvetkov, Nikolay
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite; Universite de Rennes
摘要：We prove the linear and nonlinear instability of the line solitary water waves with respect to transverse perturbations.
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作者：Cui, Guizhen; Tan, Lei
作者单位：Universite d'Angers; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We give a topological characterization of rational maps with disconnected Julia sets. Our results extend Thurston's characterization of post-critically finite rational maps. In place of iteration on Teichmuller space, we use quasiconformal surgery and Thurston's original result.
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作者：Maulik, D.; Oblomkov, A.; Okounkov, A.; Pandharipande, R.
作者单位：Princeton University; Columbia University
摘要：We prove the equivariant Gromov-Witten theory of a nonsingular toric 3-fold X with primary insertions is equivalent to the equivariant Donaldson-Thomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm, Marino, and Vafa of the Gromov-Witten theory of local Calabi-Yau toric 3-folds are proven to be correct in the full 3-leg setting.
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作者：Iwaniec, Tadeusz; Koh, Ngin-Tee; Kovalev, Leonid V.; Onninen, Jani
作者单位：Syracuse University; University of Helsinki
摘要：The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Among all homeomorphisms f : Omega ->(onto) Omega* between bounded doubly connected domains such that Omega <= Mod Omega* there exists, unique up to conformal authomorphisms of Omega, an energy-minimal diffeomorphism. Here Mod stands for the conformal modulus of a domain. No boundary conditions are imposed on f. Although any energy-minimal diffeomorphism is harmonic, our results...
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作者：Vollaard, Inken; Wedhorn, Torsten
作者单位：University of Paderborn
摘要：We complete the study of the supersingular locus M-ss in the fiber at p of a Shimura variety attached to a unitary similitude group GU( 1, n - 1) over Q in the case that p is inert. This was started by the first author in Can. J. Math. 62, 668-720 ( 2010) where complete results were obtained for n = 2, 3. The supersingular locus M-ss is uniformized by a formal scheme N which is a moduli space of so-called unitary p-divisible groups. It depends on the choice of a unitary isocrystal N. We define...
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作者：Brendle, Simon; Marques, Fernando C.; Neves, Andre
作者单位：Stanford University; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Imperial College London
摘要：Consider a compact Riemannian manifold M of dimension n whose boundary a,M is totally geodesic and is isometric to the standard sphere S (n-1). A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n-1), then M is isometric to the hemisphere S-+(n) equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo's ...
