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作者：de Lizaur, Francisco Torres
作者单位：University of Toronto
摘要：We construct finite dimensional families of non-steady solutions to the Euler equations, existing for all time, and exhibiting all kinds of qualitative dynamics in the phase space, for example: strange attractors and chaos, invariant manifolds of arbitrary topology, and quasiperiodic invariant tori of any dimension. The main theorem of the paper, from which these families of solutions are obtained, states that for any given vector field X on a closed manifold N, there is a Riemannian manifold ...
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作者：Xu, Daxin; Zhu, Xinwen
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; California Institute of Technology
摘要：We construct the Frobenius structure on a rigid connection Be (sic) on G(m) for a split reductive group (sic) introduced by Frenkel-Gross. These data form a (sic)-valued overconvergent F-isocrystal Be-(sic)(dagger) on G(m), F-p, which is the p-adic companion of the Kloosterman (sic)-local system Kl((sic)) constructed by Heinloth-Ngo-Yun. By studying the structure of the underlying differential equation, we calculate themonodromy group of Be-(sic)(dagger) when (sic) is almost simple (which reco...
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作者：Deng, Yu; Nahmod, Andrea R.; Yue, Haitian
作者单位：University of Southern California; University of Massachusetts System; University of Massachusetts Amherst; ShanghaiTech University
摘要：We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work (Deng et al. in: Invariant Gibbs measures and global strong solutions for 4009 nonlinear Schrodinger equations in dimension two, ), to study the propagation of randomness under nonlinear dispersive equations. By applying this theory we establish almost-sure local well-posedness for semilinear Schrodinger equations in the full subcritical range relative to the probabil...
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作者：Sawin, Will; Shusterman, Mark
作者单位：Columbia University; Harvard University
摘要：We establish cancellation in short sums of certain special trace functions over F-q [u] belowthe Polya-Vinogradov range, with savings approaching square-root cancellation as q grows. This is used to resolve the F-q [u]-analog of Chowla's conjecture on cancellation in Mobius sums over polynomial sequences, and of the Bateman-Horn conjecture in degree 2, for some values of q. A final application is to sums of trace functions over primes in F-q [u].
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作者：Chaidez, J.; Edtmair, O.
作者单位：University of California System; University of California Berkeley
摘要：Let X subset of R-4 be a convex domain with smooth boundary Y. We use a relation between the extrinsic curvature of Y and the Ruelle invariant of the Reeb flow on Y to prove that there are constants C > c > 0 independent of Y such that c <= ru(Y).sys(Y)(1/2) <= C Here sys(Y) is the systolic ratio of Y, i.e. the square of the minimal period of a closed Reeb orbit of Y divided by twice the volume of X, and ru(Y) is the volume-normalized Ruelle invariant. We then construct dynamically convex cont...
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作者：Li, Chao
作者单位：Stanford University
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作者：Dunfield, Nathan M.; Garoufalidis, Stavros; Rubinstein, J. Hyam
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Southern University of Science & Technology; University of Melbourne
摘要：We consider the natural problem of counting isotopy classes of essential surfaces in 3-manifolds, focusing on closed essential surfaces in a broad class of hyperbolic 3-manifolds. Our main result is that the count of (possibly disconnected) essential surfaces in terms of their Euler characteristic always has a short generating function and hence has quasi-polynomial behavior. This gives remarkably concise formulae for the number of such surfaces, as well as detailed asymptotics. We give algori...
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作者：Balister, Paul; Bollobas, Bela; Morris, Robert; Sahasrabudhe, Julian; Tiba, Marius
作者单位：University of Oxford; University of Memphis; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Since their introduction by Erdos in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and numerous questions and conjectures have been posed regarding the existence of covering systems with various properties. In particular, Erdos asked if the moduli can be distinct and all arbitrarily large, Erdos and Selfridge asked if themoduli can be distinct and all odd, and Schinzel conjectured that in any covering syst...
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作者：Briggs, Benjamin
作者单位：Utah System of Higher Education; University of Utah
摘要：For any ideal I of finite projective dimension in a commutative noetherian local ring R, we prove that if the conormal module I/I-2 has finite projective dimension over R/I, then I must be generated by a regular sequence. This resolves a conjecture of Vasconcelos. We prove a similar result for the first Koszul homology module of I. When R is a localisation of a polynomial ring over a field K of characteristic zero, Vasconcelos conjectured that R/I is a reduced complete intersection if the modu...
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作者：Carmeli, Shachar; Schlank, Tomer M.; Yanovski, Lior
作者单位：Weizmann Institute of Science; Hebrew University of Jerusalem; Max Planck Society
摘要：We extend the theory of ambidexterity developed by M. J. Hopkins and J. Lurie and show that the infinity-categories of T (n)-local spectra are infinity-semiadditive for all n, where T (n) is the telescope on a vn-self map of a type n spectrum. This generalizes and provides a newproof for the analogous result of Hopkins-Lurie on K(n)-local spectra. Moreover, we showthat K(n)-local and T (n)-local spectra are respectively, the minimal and maximal 1-semiadditive localizations of spectra with resp...
