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作者：Bakker, Benjamin; Guenancia, Henri; Lehn, Christian
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Technische Universitat Chemnitz
摘要：We extend the decomposition theorem for numerically K-trivial varieties with log terminal singularities to the Kahler setting. Along the way we prove that all such varieties admit a strong locally trivial algebraic approximation, thus completing the numerically K-trivial case of a conjecture of Campana and Peternell.
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作者：Dotsenko, Vladimir
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：We show that the integer cohomology rings of the moduli spaces of stable rational marked curves are Koszul. This answers an open question of Manin. Using the machinery of Koszul spaces developed by Berglund, we compute the rational homotopy Lie algebras of those spaces, and obtain some estimates for Betti numbers of their free loop spaces in case of torsion coefficients. We also prove and conjecture some generalisations of our main result.
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作者：Freitag, James; Jaoui, Remi; Moosa, Rahim
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Freiburg; University of Waterloo
摘要：Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any number of distinct nonalgebraic solutions, along with their derivatives, then there is already such a relation between three solutions. In the autonomous situation when the equation is over constant parameters the assumption that the order be greater than one can be dropped, and a nontrivial algebraic relation exists already between two solutions. These...
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作者：Bedrossian, Jacob; Blumenthal, Alex; Punshon-Smith, Sam
作者单位：University System of Maryland; University of Maryland College Park; University System of Georgia; Georgia Institute of Technology; Institute for Advanced Study - USA
摘要：We put forward a new method for obtaining quantitative lower bounds on the top Lyapunov exponent of stochastic differential equations. Our method combines (i) a new identity connecting the top Lyapunov exponent to a Fisher information-like functional of the stationary density of the Markov process tracking tangent directions with (ii) a novel, quantitative version of Hormander's hypoelliptic regularity theory in an L-1 framework which estimates this (degenerate) Fisher information from below b...
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作者：Bowden, Jonathan; Gironella, Fabio; Moreno, Agustin
作者单位：University of Regensburg; Monash University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Humboldt University of Berlin; University of Augsburg; Uppsala University; Institute for Advanced Study - USA
摘要：Given a contact structure on a manifold V together with a supporting open book decomposition, Bourgeois gave an explicit construction of a contact structure on V x T-2. We prove that all such structures are universally tight in dimension 5, independent of whether the original contact manifold is itself tight or overtwisted. In arbitrary dimensions, we provide obstructions to the existence of strong symplectic fillings of Bourgeois manifolds. This gives a broad class of new examples of weakly b...
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作者：Liu, Ruochuan; Wang, Guozhen
作者单位：Fudan University; Peking University
摘要：We introduce a new approach to determining the structure of topological cyclic homology by means of a descent spectral sequence. We carry out the computation for a p-adic local field with F-p-coefficients, including the case p = 2 which was only covered by motivic methods except in the totally unramified case.
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作者：Okounkov, A.; Smirnov, A.
作者单位：Columbia University; HSE University (National Research University Higher School of Economics); University of North Carolina; University of North Carolina Chapel Hill; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：For an arbitrary Nakajima quiver variety X, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the fundamental groupoid of a certain periodic locally finite hyperplane arrangement in Pic(X) circle times C. We identify the lattice part of this groupoid with the operators of quantum difference equation for X. The cases of quivers of finite and affine type are illustrated by explicit examples.
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作者：Buterus, P.; Goetze, F.; Hille, T.; Margulis, G.
作者单位：University of Gottingen; University of Bielefeld; Northwestern University; Yale University
摘要：The number of lattice points in d-dimensional hyperbolic or elliptic shells {m : a < Q[m] < b}, which are restricted to rescaled and growing domains r Omega, is approximated by the volume. An effective error bound of order o(r(d-2)) for this approximation is proved based on Diophantine approximation properties of the quadratic form Q. These results allow to show effective variants of previous non-effective results in the quantitative Oppenheim problem and extend known effective results in dime...
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作者：Berti, Massimiliano; Maspero, Alberto; Ventura, Paolo
作者单位：International School for Advanced Studies (SISSA)
摘要：Small-amplitude, traveling, space periodic solutions -called Stokes waves- of the 2 dimensional gravity water waves equations in deep water are linearly unstable with respect to long-wave perturbations, as predicted by Benjamin and Feir in 1967. We completely describe the behavior of the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent is turned on. We prove in particular the conjecture that a pair of non-purely imaginary eigenvalues depict...
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作者：De Rosa, Antonio; Tione, Riccardo
作者单位：University System of Maryland; University of Maryland College Park; Max Planck Society
摘要：We prove that m-dimensional Lipschitz graphs with anisotropic mean curvature bounded in L-p, p > m, are regular almost everywhere in every dimension and codimension. This provides partial or full answers to multiple open questions arising in the literature. The anisotropic energy is required to satisfy a novel ellipticity condition, which holds for instance in a C-1,C-1 neighborhood of the area functional. This condition is proved to imply the atomic condition. In particular we provide the fir...
