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作者：Li, Haozhao; Wang, Bing
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow IN R-3
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作者：Bakker, Benjamin; Tsimerman, Jacob
作者单位：University System of Georgia; University of Georgia; University of Toronto
摘要：We extend the Ax-Schanuel theorem recently proven for Shimura varieties by Mok-Pila-Tsimerman to all varieties supporting a pure polarizable integral variation of Hodge structures. In fact, Hodge theory provides a number of conceptual simplifications to the argument. The essential new ingredient is a volume bound for Griffiths transverse subvarieties of period domains.
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作者：Naber, Aaron; Valtorta, Daniele
作者单位：Northwestern University; University of Zurich
摘要：Given a principal bundle PM over a Riemannian manifold with compact structure group G, let us consider a stationary Yang-Mills connection A with energy M|FA|2. If we consider a sequence of such connections Ai, then it is understood by Tian (Ann Math 151(1):193-268, 2000) that up to subsequence we can converge AiA to a singular limit connection such that the energy measures converge |FAi|2dvg|FA|2dvg+, where =e(x)dn-4 is the n-4 rectifiable defect measure. Our main result is to show, without ad...
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作者：Bridgeland, Tom
作者单位：University of Sheffield
摘要：We study a class of Riemann-Hilbert problems arising naturally in Donaldson-Thomas theory. In certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions. We briefly explain connections with Gromov-Witten theory and exact WKB analysis.
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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：Cai, Yuanqing; Friedberg, Solomon; Ginzburg, David; Kaplan, Eyal
作者单位：Boston College; Weizmann Institute of Science; Tel Aviv University; Bar Ilan University
摘要：We present an integral representation for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and lo...
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作者：Eskenazis, Alexandros; Mendel, Manor; Naor, Assaf
作者单位：Princeton University; Open University Israel
摘要：We prove that not every metric space embeds coarsely into an Alexandrov space of nonpositive curvature. This answers a question ofGromov (Geometric group theory, Cambridge University Press, Cambridge, 1993) and is in contrast to the fact that any metric space embeds coarsely into an Alexandrov space of nonnegative curvature, as shown by Andoni et al. (Ann Sci Ec Norm Super (4) 51(3):657-700, 2018). We establish this statement by proving that a metric space which is q- barycentric for some q is...
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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：Chung, Yong Moo; Rivera-Letelier, Juan; Takahasi, Hiroki
作者单位：Hiroshima University; University of Rochester; Keio University
摘要：We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation Principle holds for every non-renormalizable quadratic map. This includes the maps without physical measure found by Hofbauer and Keller, and challenges the widely-shared view of the Large Deviation Principle as a refinement of laws of large numbers.
