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作者：Walsh, Miguel N.
作者单位：University of Buenos Aires; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); University of Buenos Aires
摘要：We introduce a strategy to tackle some known obstructions of current approaches to the Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for intervals of length at least (logX)psi(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\log X)<^>{\psi (X)}$\end{document}, with psi(X)->infinit...
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作者：Abdurrahman, Amina; Venkatesh, Akshay
作者单位：Princeton University; Institute for Advanced Study - USA
摘要：We propose (and prove under some restrictions) that the square class of the central value of the L-function of an everywhere unramified symplectic Galois representation is given by a universal cohomological formula. This phenomenon is parallel to the appearance of metaplectic groups in quantization. In the course of the proof we also establish a topological analogue of this statement, concerning Reidemeister torsion of 3-manifolds.
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作者：Logunov, A.; Malinnikova, E.; Nadirashvili, N.; Nazarov, F.
作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); University System of Ohio; Kent State University; Kent State University Kent; Kent State University Salem
摘要：Consider a solution u to Delta u + Vu = 0 on R-2, where V is real-valued, measurable and |V|<= 1. If |u(x)| <= exp (-C|x|log(1/2)|x|), |x| > 2, where C is a sufficiently large absolute constant, then u equivalent to 0.
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作者：Donvil, Milan; Vaes, Stefaan
作者单位：KU Leuven
摘要：We construct countable groups G with the following new degree of W*-superrigidity: if L(G) is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra L(Lambda), then the groups G and Lambda must be virtually isomorphic. Moreover, we allow both group von Neumann algebras to be twisted by an arbitrary 2-cocycle. We also give examples of II1 factors N that are indecomposable in every sense: they are not virtually isomorphic to any cocycle twis...
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作者：Dong, Conghan; Song, Antoine
作者单位：State University of New York (SUNY) System; Stony Brook University; California Institute of Technology
摘要：We show that the Euclidean 3-space R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}<^>{3}$\end{document} is stable for the Positive Mass Theorem in the following sense. Let (Mi,gi)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackag...
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作者：Spaeth, Britta
作者单位：University of Wuppertal
摘要：We determine the action of the automorphism group Aut(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm {Aut}(G)$\end{document} on the set of irreducible characters Irr(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \us...
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作者：Heinavaara, Otte
作者单位：Princeton University
摘要：Given two Hermitian matrices, A and B, we introduce a new type of spectral measure, a tracial joint spectral measure mu A, B on the plane. Existence of this measure implies the following two results: 1) any two-dimensional subspace of the Schatten-p class is isometric to a subspace of Lp, and 2) if f : R R has non-negative kth derivative and A and B are Hermitian matrices with A positive semidefinite, then t trf (tA + B) has non-negative kth derivative. We also give an explicit expression for ...
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作者：Hassainia, Zineb; Hmidi, Taoufik; Masmoudi, Nader
作者单位：New York University; New York University Abu Dhabi; New York University
摘要：This paper investigates the leapfrogging phenomenon in inviscid planar flows, specifically for the 2D Euler equations, showing that under suitable constraints, four concentrated vortex patches leapfrog indefinitely. Observing this system from a translating reference frame reveals a non-rigid time-periodic motion of the vortex patches. These solutions are shown to evolve near singular time-periodic relative equilibria of the point vortex system. Our proof hinges upon two main components. First,...
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作者：Gerber, Marlies; Kunde, Philipp
作者单位：Indiana University System; Indiana University Bloomington; Jagiellonian University; Oregon State University
摘要：A time change of a flow {Tt}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{T_{t}\}$\end{document}, t is an element of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsi...
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作者：Zlatos, Andrej
作者单位：University of California System; University of California San Diego
摘要：We show that smooth solutions to the Euler equation on the half-plane can exhibit double-exponential growth of their vorticity gradients. We also determine the maximal possible growth rate and construct solutions that saturate it. These are the first such results on an unbounded resp. any 2D domain.
