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作者：Gutman, Yonatan; Tsukamoto, Masaki
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Kyushu University
摘要：We study the problem of embedding minimal dynamical systems into the shift action on the Hilbert cube mml:mfenced close=) open=([0,1]NZ\ This problem is intimately related to the theory of mean dimension, which counts the average number of parameters for describing a dynamical system. Lindenstrauss proved that minimal systems of mean dimension less than cN for c=1/36 can be embedded in mml:mfenced close=) open=([0,1]NZ and asked what is the optimal value for c. We solve this problem by showing...
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作者：Kanigowski, Adam; Lemanczyk, Mariusz; Ulcigrai, Corinna
作者单位：University System of Maryland; University of Maryland College Park; University of Zurich; University of Bristol
摘要：The Ratner property, a quantitative form of divergence of nearby trajectories, is a central feature in the study of parabolic homogeneous flows. Discovered by Marina Ratner and used in her 1980th seminal works on horocycle flows, it pushed forward the disjointness theory of such systems. In this paper, exploiting a recent variation of the Ratner property, we prove new disjointness phenomena for smooth parabolic flows beyond the homogeneous world. In particular, we establish a general disjointn...
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作者：Matomaki, Kaisa; Radziwill, Maksym; Tao, Terence
作者单位：University of Turku; California Institute of Technology; University of California System; University of California Los Angeles
摘要：Let lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, integral X2Xsup alpha n-ary sumation x<= x+H lambda(n)e(-alpha n)dx=o(XH)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \u...
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作者：Dudko, Artem; Sutherland, Scott
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; State University of New York (SUNY) System; Stony Brook University
摘要：We show that the Julia set of the Feigenbaum polynomial has Hausdorff dimension less than 2 (and consequently it has zero Lebesgue measure). This solves a long-standing open question.
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作者：Banks, Peter; Panzer, Erik; Pym, Brent
作者单位：University of Oxford; University of Edinburgh; McGill University
摘要：Kontsevich's 1997 formula for the deformation quantization of Poisson brackets is a Feynman expansion involving volume integrals over moduli spaces of marked disks. We develop a systematic theory of integration on these moduli spaces via suitable algebras of polylogarithms, and use it to prove that Kontsevich's integrals can be expressed as integer-linear combinations of multiple zeta values. Our proof gives a concrete algorithm for calculating the integrals, which we have used to produce the ...
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作者：Marrakchi, Amine
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We show that a factor M is full if and only if the C*-algebra generated by its left and right regular representations contains the compact operators. We prove that the bicentralizer flow of a type III1 factor is always ergodic. As a consequence, for any type III1 factor M and any lambda is an element of]0, 1], there exists an irreducible AFD type III lambda subfactor with expectation in M. Moreover, any type III1 factor M which satisfies M congruent to M (circle times) over bar R-lambda for so...
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作者：Xi, Ping
作者单位：Xi'an Jiaotong University
摘要：By elaborating a two-dimensional Selberg sieve with asymptotics and equidistributions of Kloosterman sums from l\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-adic cohomology, as well as a Bombieri-Vinogradov type mean value theorem for Kloosterman sums in arithmetic progressions, it is prove...
