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作者：Magee, Michael; Puder, Doron
作者单位：Durham University; Tel Aviv University
摘要：Since the 1970's, physicists and mathematicians who study random matrices in the GUE or GOE models are aware of intriguing connections between integrals of such random matrices and enumeration of graphs on surfaces. We establish a new aspect of this theory: for random matrices sampled from the group U (n) of unitary matrices. More concretely, we study measures induced by free words on U (n). Let F-r be the free group on r generators. To sample a random element from U (n) according to the measu...
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作者：Horing, Andreas; Peternell, Thomas
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); University of Bayreuth
摘要：Given a reflexive sheaf on a mildly singular projective variety, we prove a flatness criterion under certain stability conditions. This implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical bundle such that the second Chern class does not vanish. Combined with the recent works of Druel and Greb-Guenancia-Kebekus this establishes the Beauville-Bogomolov decomposition for minimal models with trivial canonical class.
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作者：Levin, Aaron
作者单位：Michigan State University
摘要：We give results and inequalities bounding the greatest common divisor of multivariable polynomials evaluated at S-unit arguments, generalizing to an arbitrary number of variables results of Bugeaud-Corvaja-Zannier, Hernandez-Luca, and Corvaja-Zannier. In closely related results, and in line with observations of Silverman, we prove special cases of Vojta's conjecture for blowups of toric varieties. As an application, we classify when terms from simple linear recurrence sequences can have a larg...
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作者：Bridson, Martin R.; Evans, David M.; Liebeck, Martin W.; Segal, Dan
作者单位：University of Oxford; Imperial College London; University of Oxford
摘要：We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains infinitely many alternating groups, or contains classical groups of unbounded dimensions, we prove that there is no such algorithm. On the other hand, for families of simple groups of Lie type of bound...
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作者：Krishna, Amalendu
作者单位：Tata Institute of Fundamental Research (TIFR)
摘要：We show that the Levine-Weibel Chow group of 0-cycles CHd(A) of a reduced affine algebra A of dimension d >= 2 over an algebraically closed field is torsion-free. Among several applications, it implies an affirmative solution to an old conjecture of Murthy in classical K-theory.
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作者：Zhou, Xin; Zhu, Jonathan J.
作者单位：University of California System; University of California Santa Barbara; Harvard University; Princeton University
摘要：In this paper, we develop a min-max theory for the construction of constant mean curvature (CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold. As a corollary, we prove the existence of a nontrivial, smooth, closed, almost embedded, CMC hypersurface of any given mean curvature c. Moreover, if c is nonzero then our min-max solution always has multiplicity one.
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作者：Nicaise, Johannes; Shinder, Evgeny
作者单位：Imperial College London; KU Leuven; University of Sheffield; HSE University (National Research University Higher School of Economics)
摘要：We prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities. Our proof is based on motivic specialization techniques and the criterion of Larsen and Lunts for stable rationality in the Grothendieck ring of varieties.
