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作者：Li, Xiannan
作者单位：Kansas State University
摘要：We prove an asymptotic for the second moment of quadratic twists of a modular L-function. This was previously known conditionally on GRH by the work of Soundararajan and Young
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作者：Polimeni, Davide; Terracini, Susanna
作者单位：University of Turin
摘要：We deal, for the classical N-body problem, with the existence of action minimizing half entire expansive solutions with prescribed asymptotic direction and initial configuration of the bodies. We tackle the cases of hyperbolic, hyperbolic-parabolic and parabolic arcs in a unified manner. Our approach is based on the minimization of a renormalized Lagrangian action on a suitable functional space. With this new strategy, we are able to confirm the already-known results of the existence of both h...
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作者：De Roeck, Wojciech; Elgart, Alexander; Fraas, Martin
作者单位：KU Leuven; Virginia Polytechnic Institute & State University
摘要：This work justifies the linear response formula for the Hall conductance of a two-dimensional disordered system. The proof rests on controlling the dynamics associated with a random time-dependent Hamiltonian. The principal challenge is related to the fact that spectral and dynamical localization are intrinsically unstable under perturbation, and the exact spectral flow - the tool used previously to control the dynamics in this context - does not exist. We resolve this problem by proving a loc...
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作者：Ji, Ran; Wu, Yunhui
作者单位：Tsinghua University; Capital Normal University; Tsinghua University
摘要：In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M$\end{document} of finite volume with sectional curvature -1 <= K <= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...
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作者：Karpukhin, Mikhail; Stern, Daniel
作者单位：California Institute of Technology; University of Chicago
摘要：We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold (M-n,g) of dimension n>2 to any closed, non-aspherical manifold N containing no stable minimal two-spheres. In particular, this gives the first general existence result for harmonic maps from higher-dimensional manifolds to a large class of positively curved targets. In the special case of the round spheres N=S-k, k >= 3, we obtain a distinguished family of nonconstant harmonic maps M ->...
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作者：Baldi, Gregorio; Klingler, Bruno; Ullmo, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Humboldt University of Berlin
摘要：Given a polarizable Z-variation of Hodge structures V over a complex smooth quasi-projective base S, a classical result of Cattani, Deligne and Kaplan says that its Hodge locus (i.e. the locus where exceptional Hodge tensors appear) is a countable union of irreducible algebraic subvarieties of S, called the special subvarieties for V. Our main result in this paper is that, if the level of V is at least 3, this Hodge locus is in fact a finite union of such special subvarieties (hence is algebra...
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作者：Feng, Tony; Yun, Zhiwei; Zhang, Wei
作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT)
摘要：We construct special cycles on the moduli stack of hermitian shtukas. We prove an identity between (1) the rth central derivative of non-singular Fourier coefficients of a normalized Siegel-Eisenstein series, and (2) the degree of special cycles of virtual dimension 0 on the moduli stack of hermitian shtukas with r legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein seri...
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作者：Louder, Larsen; Wilton, Henry
作者单位：University of London; University College London; University of Cambridge
摘要：Previously, the authors proved that the presentation complex of a one-relator group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document} satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepack...
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作者：Gomez, Jaime; Guerra, Andre; Ramos, Joao P. G.; Tilli, Paolo
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; ETH Zurich; Polytechnic University of Turin
摘要：We prove a sharp quantitative version of the Faber-Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit delta(f;omega)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\delta (f;\Omega )$\end{document} which measures by how much the STFT of a function f is an element of L2(R)\d...
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作者：Brendle, Simon
作者单位：Columbia University
摘要：We prove a scalar curvature rigidity theorem for convex polytopes. The proof uses the Fredholm theory for Dirac operators on manifolds with boundary. A variant of a theorem of Fefferman and Phong plays a central role in our analysis.
