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作者：Guo, Yan; Pausader, Benoit; Widmayer, Klaus
作者单位：Brown University; University of Zurich; University of Vienna
摘要：We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform rigid body rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter linearly, thanks to the dispersive effect induced by the rotation. To establish this, we introduce a framework that builds on the symmetries of the problem and precisely captures the anisotropic, dispersive mechanism due to rotation. This enables a fine analysis...
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作者：Bary-Soroker, Lior; Koukoulopoulos, Dimitris; Kozma, Gady
作者单位：Tel Aviv University; Universite de Montreal; Weizmann Institute of Science
摘要：Let mu be a probability measure on Z that is not a Dirac mass and that has finite support. We prove that if the coefficients of a monic polynomial f (x) is an element of Z[x] of degree n are chosen independently at random according to mu while ensuring that f (0) not equal 0, then there is a positive constant theta = theta (mu) such that f (x) has no divisors of degree <= theta n with probability that tends to 1 as n -> infinity. Furthermore, in certain cases, we show that a random polynomial ...
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作者：Mooney, Connor; Yang, Yang
作者单位：University of California System; University of California Irvine
摘要：We construct nonlinear entire anisotropic minimal graphs over R-4, completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of nonlinear entire minimal graphs over R-n, n >= 8.
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作者：De Filippis, Cristiana; Mingione, Giuseppe
作者单位：University of Parma
摘要：Local Schauder theory holds in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic problems are locally Holder continuous if so are their coefficients.
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作者：Laba, Izabella; Londner, Itay
作者单位：University of British Columbia; Weizmann Institute of Science
摘要：It is well known that if a finite set A subset of Z tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a factorization A circle plus B = Z(M) of a finite cyclic group. We are interested in characterizing all finite sets A subset of Z that have this property. Coven and Meyerowitz (J Algebra 212:161-174, 1999) proposed conditions (T1), (T2) that are sufficient for A to tile, and necessary when the cardinality of A has at most two di...
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作者：Blomer, Valentin
摘要：Strong bounds-going beyond Sarnak's density hypothesis-are obtained for the number of automorphic forms for the group Gamma(0)(q) subset of SL(n, Z) violating the Ramanujan conjecture at any given unramified place. The proof is based on a relative trace formula of Kuznetsov type and best-possible bounds for certain Kloosterman sums for GL(n). Further applications are given.
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作者：Kim, Dongryul M.; Oh, Hee
作者单位：Yale University; Korea Institute for Advanced Study (KIAS)
摘要：Let Gamma < PSL2( C) similar or equal to Isom(+) (H-3) be a finitely generated non-Fuchsian Kleinian group whose ordinary set Omega = S-2 - Lambda has at least two components. Let rho : Gamma -> PSL2( C) be a faithful discrete non-Fuchsian representation with boundary map f : Lambda -> S-2 on the limit set. In this paper, we obtain a new rigidity theorem: if f is conformal on Lambda, in the sense that f maps every circular slice of Lambda into a circle, then f extends to a Mobius transformatio...
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作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：We consider directed polymers in random environment in the critical dimension d = 2, focusing on the intermediate disorder regime when the model undergoes a phase transition. We prove that, at criticality, the diffu-sively rescaled random field of partition functions has a unique scaling limit: a universal process of random measures on R-2 with logarithmic correlations, which we call the Critical 2d Stochastic Heat Flow. It is the natural candidate for the long sought solution of the critical ...
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作者：Canzani, Yaiza; Galkowski, Jeffrey
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of London; University College London
摘要：We obtain new quantitative estimates on Weyl Law remainders under dynamical assumptions on the geodesic flow. On a smooth compact Riemannian manifold (M, g) of dimension n, let H(lambda )denote the kernel of the spectral projector for the Laplacian, (1)[0,lambda(2)](-delta(g)). Assuming only that the set of near periodic geodesics over W subset of M has small measure, we prove that as lambda -> infinity integral(W) Pi(lambda) (x, x)dx = (2 pi)(-n) vol(R)(n)(B) volg(W) lambda(n) + O (lambda(n-1...
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作者：Pstragowski, Piotr
作者单位：Harvard University
摘要：To an Adams-type homology theory we associate the notion of a synthetic spectrum; this is a product-preserving sheaf on the site of finite spectra with projective E-homology. We show that the infinity-category SynE of synthetic spectra based on E is in a precise sense a deformation of the infinity-category of spectra into quasi-coherent sheaves over a certain algebraic stack, and show that this deformation encodes the E*-based Adams spectral sequence. We describe a symmetric monoidal functor f...
