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作者：Bartholdi, Laurent; Erschler, Anna
作者单位：University of Gottingen; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：We study the geometry of a class of group extensions, containing permutational wreath products, which we call permutational extensions. We construct for all k is an element of N a torsion group K-k with growth function upsilon K-k (n) similar to exp(n(1-(1-alpha)k)), 2(3-3/alpha) + 2(2-2/alpha) + 2(1-1/alpha) = 2, and a torsion-free group H-k with growth function upsilon H-k (n) similar to exp(log(n)n(1-(1-alpha)k)). These are the first examples of groups of intermediate growth for which the a...
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作者：Lin, Chang-Shou; Wei, Juncheng; Ye, Dong
作者单位：National Taiwan University; Chinese University of Hong Kong; Universite de Lorraine
摘要：We consider the following Toda system Delta u(i) + Sigma(n)(j=1)a(ij)e(uj) = 4 pi gamma(i)delta(0) in R-2, integral(R2)e(ui)dx < infinity, for all 1 <= i <= n, where gamma (i) >-1, delta (0) is Dirac measure at 0, and the coefficients a (ij) form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result: Sigma(n)(j=1)a(ij) integral(R2)e(uj)dx = 4 pi(2 + gamma(i) + gamma(n+1-i)), for all 1 <= i <= n This generalizes the c...
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作者：Bridgeland, Tom; Laredo, Valerio Toledano
作者单位：University of Oxford; Northeastern University; Institute for Advanced Study - USA
摘要：Let A be the category of modules over a complex, finite-dimensional algebra. We show that the space of stability conditions on A parametrises an isomonodromic family of irregular connections on P-1 with values in the Hall algebra of A. The residues of these connections are given by the holomorphic generating function for counting invariants in A constructed by D. Joyce (in Geom. Topol. 11, 667-725, 2007).
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作者：Belinschi, Serban; Collins, Benoit; Nechita, Ion
作者单位：University of Ottawa; University of Saskatchewan; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Institute of Mathematics of the Romanian Academy; Romanian Academy
摘要：Given two positive integers n and k and a parameter ta(0,1), we choose at random a vector subspace V (n) aS,a, (k) aSua, (n) of dimension N similar to tnk. We show that the set of k-tuples of singular values of all unit vectors in V (n) fills asymptotically (as n tends to infinity) a deterministic convex set K (k,t) that we describe using a new norm in ae (k) . Our proof relies on free probability, random matrix theory, complex analysis and matrix analysis techniques. The main result comes tog...
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作者：Smith, Ivan
作者单位：University of Cambridge
摘要：There is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces. We investigate symplectic aspects of this relationship, with a view to applications in low-dimensional topology.
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作者：Ein, Lawrence; Lazarsfeld, Robert
作者单位：University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We study the asymptotic behavior of the syzygies of a smooth projective variety as the positivity of the embedding line bundle grows. The main result asserts that the syzygy modules are non-zero in almost all degrees allowed by Castelnuovo-Mumford regularity. We also give an effective statement for Veronese varieties that we conjecture to be optimal.
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作者：Hou, Xuanji; You, Jiangong
作者单位：Nanjing University
摘要：In this paper, we prove that a quasi-periodic linear differential equation in sl(2,ae) with two frequencies (alpha,1) is almost reducible provided that the coefficients are analytic and close to a constant. In the case that alpha is Diophantine we get the non-perturbative reducibility. We also obtain the reducibility and the rotations reducibility for an arbitrary irrational alpha under some assumption on the rotation number and give some applications for Schrodinger operators. Our proof is a ...
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作者：Gordon, I. G.
作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University
摘要：Using the Harish-Chandra D-module, we give a proof of Haiman's theorem on the positivity of Macdonald polynomials. Ginzburg's work on the connection between this D-module and the isospectral commuting variety is fundamental to this approach.
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作者：Chen, Xuezhang; Xu, Xingwang
作者单位：National University of Singapore; Nanjing University; Nanjing University; Peking University
摘要：For the problem of finding a geometry on S-n, for n >= 3, with a prescribed scalar curvature, there is a well- known result which is called the perturbation theorem; it is due to Chang and Yang (Duke Math. J. 64, 27-69, 1991). Their key assumption is that the candidate f for the prescribed scalar curvature is sufficiently near the scalar curvature of the standard metric in the sup norm. It is important to know how large that difference in sup norm can possibly be. Here we consider prescribing ...
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作者：Melbourne, Ian; Terhesiu, Dalia
作者单位：University of Surrey
摘要：We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates L (n) of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In ...
