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作者：Fehrman, Benjamin; Gess, Benjamin
作者单位：University of Oxford; University of Bielefeld; Max Planck Society
摘要：Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate parabolic-hyperbolic PDE with irregular drift. We develop a robust well-posedness theory for such PDEs in energy critical spaces based on concepts of renormalized solutions and the equation's kinetic form. We establish these properties by proving that renormalized solutions a...
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作者：Sun, Song; Zhang, Junsheng
作者单位：University of California System; University of California Berkeley
摘要：We discover a no semistability at infinity phenomenon for complete Calabi-Yau metrics asymptotic to cones, which is proved by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of Kahler-Einstein metrics. A byproduct of the proof is a polynomial convergence rate to the asymptotic cone for such manifolds, which bridges the gap between...
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作者：Belov, Yurii; Kulikov, Aleksei; Lyubarskii, Yurii
作者单位：Norwegian University of Science & Technology (NTNU)
摘要：We study the frame properties of the Gabor systems G(g; alpha, beta) := {e(2 pi i beta mx) g(x - an)} m,n is an element of Z. In particular, we prove that forHerglotzwindows g such systems always form a frame for L-2(R) if alpha, beta > 0, alpha beta <= 1. For general rationalwindows g is an element of L-2(R) we prove that G(g; alpha, beta) is a frame for L-2(R) if 0 < alpha, beta, alpha beta < 1, alpha beta is not an element of Q and (g) over bar(xi) not equal 0, xi > 0, thus confirming Daube...
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作者：Skorobogatov, Alexei N.; Sofos, Efthymios
作者单位：Imperial College London; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; University of Glasgow
摘要：We resolve Schinzel's Hypothesis (H) for 100% of polynomials of arbitrary degrees. We deduce that a positive proportion of diagonal conic bundles over Q with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Chatelet equations.
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作者：Bessonov, R.; Denisov, S.
作者单位：Saint Petersburg State University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; University of Wisconsin System; University of Wisconsin Madison
摘要：We give a dynamical characterization of measures on the real line with finite logarithmic integral. The general case is considered in the setting of evolution groups generated by de Branges canonical systems. Obtained results are applied to the Dirac operators and Krein strings.
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作者：Ford, Kevin; Ben Green; Koukoulopoulos, Dimitris
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Oxford; Universite de Montreal
摘要：We study the extent to which divisors of a typical integer n are concentrated. In particular, defining Delta(n) := max(t) #{d vertical bar n, log d is an element of [t, t + 1]}, we show that Delta(n) >= (log log n)(0.35332277...) for almost all n, a bound we believe to be sharp. This disproves a conjecture of Maier and Tenenbaum. We also prove analogs for the concentration of divisors of a random permutation and of a random polynomial over a finite field. Most of the paper is devoted to a stud...
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作者：De Simoi, Jacopo; Kaloshin, Vadim; Leguil, Martin
作者单位：University of Toronto; Institute of Science & Technology - Austria; Universite de Picardie Jules Verne (UPJV); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides a natural labeling of periodic orbits. We show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Geneva; Imperial College London
摘要：We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case...
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作者：Bakker, Benjamin; Brunebarbe, Yohan; Tsimerman, Jacob
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Universite de Bordeaux; University of Toronto
摘要：We prove a conjecture of Griffiths on the quasi-projectivity of images of period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop a theory of analytic spaces and coherent sheaves that are definable with respect to a given o-minimal structure, and prove a GAGA-type theorem algebraizing definable coherent sheaves on complex algebraic spaces. We then combine this with algebraization theorems of Artin to show that proper definable images of complex ...
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作者：Isenrich, Claudio Llosa; Py, Pierre
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
摘要：We prove that in a cocompact complex hyperbolic arithmetic lattice Gamma < PU(m, 1) of the simplest type, deep enough finite index subgroups admit plenty of homomorphisms to Z with kernel of type Fm-1 but not of type F-m. This provides many finitely presented non-hyperbolic subgroups of hyperbolic groups and answers an old question of Brady. Our method also yields a proof of a special case of Singer's conjecture for aspherical Kahler manifolds.
