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作者：Shelukhin, Egor
作者单位：Universite de Montreal
摘要：We prove a conjecture of Viterbo from 2007 on the existence of a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in unit cotangent disk bundles, for bases given by compact rank one symmetric spaces S-n,RPn,CPn,HPn,n >= 1. We discuss generalizations and give applications, in particular to C0 symplectic topology. Our key method consists in a quantitative deformation argument for Floer persistence modules that allows to excise a divisor.
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作者：Banks, Peter; Panzer, Erik; Pym, Brent
作者单位：University of Oxford; University of Edinburgh; McGill University
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作者：Merle, Frank; Raphael, Pierre; Rodnianski, Igor; Szeftel, Jeremie
作者单位：CY Cergy Paris Universite; Princeton University; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Sorbonne Universite; Universite Paris Cite
摘要：We consider the energy supercritical defocusing nonlinear Schrodinger equation i partial derivative(t)u + Delta u - u vertical bar u vertical bar(p-1) = 0 in dimension d >= 5. In a suitable range of energy supercritical parameters (d, p), we prove the existence of C-infinity well localized spherically symmetric initial data such that the corresponding unique strong solution blows up in finite time. Unlike other known blowup mechanisms, the singularity formation does not occur by concentration ...
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作者：Dolgopyat, Dmitry; Dong, Changguang; Kanigowski, Adam; Nandori, Peter
作者单位：University System of Maryland; University of Maryland College Park; Yeshiva University; Nankai University; Nankai University
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作者：Beentjes, Sjoerd Viktor; Calabrese, John; Rennemo, Jorgen Vold
作者单位：University of Edinburgh; Heriot Watt University; University of Edinburgh; University of Oslo
摘要：We prove the crepant resolution conjecture for Donaldson-Thomas invariants of hard Lefschetz 3-Calabi-Yau (CY3) orbifolds, formulated by Bryan-Cadman-Young, interpreting the statement as an equality of rational functions. In order to do so, we show that the generating series of stable pair invariants on any CY3 orbifold is the expansion of a rational function. As a corollary, we deduce a symmetry of this function induced by the derived dualising functor. Our methods also yield a proof of the o...
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作者：Corvaja, Pietro; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M.
作者单位：University of Virginia; Scuola Normale Superiore di Pisa
摘要：We prove that if a linear group Gamma subset of GL(n)(K) over a field K of characteristic zero is boundedly generated by semi-simple (diagonalizable) elements then it is virtually solvable. As a consequence, one obtains that infinite S-arithmetic subgroups of absolutely almost simple anisotropic algebraic groups over number fields are never boundedly generated. Our proof relies on Laurent's theorem from Diophantine geometry and properties of generic elements.
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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...
