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作者：Good, Chris; Meddaugh, Jonathan
作者单位：University of Birmingham; Baylor University
摘要：Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in the study of dynamical systems. In this paper we prove that there is a deep and fundamental relationship between these two concepts. Let X be a compact totally disconnected space and f:X -> X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69p...
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作者：Wei, Fu-Tsun
作者单位：National Tsing Hua University
摘要：We establish a general Kronecker limit formula of arbitrary rank over global function fields with Drinfeld period domains playing the role of upper-half plane. The Drinfeld-Siegel units come up as equal characteristic modular forms replacing the classical Delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ...
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作者：Barthel, Tobias; Schlank, Tomer; Stapleton, Nathaniel
作者单位：Max Planck Society; Hebrew University of Jerusalem; University of Kentucky
摘要：Inspired by the Ax-Kochen isomorphism theorem, we develop a notion of categorical ultraproducts to capture the generic behavior of an infinite collection of mathematical objects. We employ this theory to give an asymptotic solution to the approximation problem in chromatic homotopy theory. More precisely, we show that the ultraproduct of the E(n, p)-local categories over any non-principal ultrafilter on the set of prime numbers is equivalent to the ultraproduct of certain algebraic categories ...
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作者：Agostiniani, Virginia; Fogagnolo, Mattia; Mazzieri, Lorenzo
作者单位：University of Verona; University of Trento
摘要：In this paper we consider complete noncompact Riemannian manifolds (M, g) with nonnegative Ricci curvature and Euclidean volume growth, of dimension n >= 3. For every bounded open subset Omega subset of M with smooth boundary, we prove that integral(partial derivative Omega)vertical bar H/n-1 vertical bar(n-1) d sigma >= AVR(g)vertical bar Sn-1 vertical bar, where H is the mean curvature of partial derivative Omega and AVR(g) is the asymptotic volume ratio of (M, g). Moreover, the equality hol...
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作者：Hutchcroft, Tom; Pete, Gabor
作者单位：University of Cambridge; Budapest University of Technology & Economics
摘要：We prove that every countably infinite group with Kazhdan's property (T) has cost 1, answering a well-known question of Gaboriau. It remains open if they have fixed price 1.
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作者：Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan
作者单位：University of Zurich; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Universite Paris Cite; Imperial College London; Institute for Advanced Study - USA
摘要：We prove that a Ck\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>k$$\end{document}, k >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{do...
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作者：Hahn, Jeremy; Shi, XiaoLin Danny
作者单位：Massachusetts Institute of Technology (MIT); University of Chicago
摘要：We show that Lubin-Tate spectra at the prime 2 are Real oriented and Real Landweber exact. The proof is by application of the Goerss-Hopkins-Miller theorem to algebras with involution. For each height n, we compute the entire homotopy fixed point spectral sequence for E-n with its C-2-action given by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these C-2-fixed points.
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作者：Azzam, Jonas; Hofmann, Steve; Maria Martell, Jose; Mourgoglou, Mihalis; Tolsa, Xavier
作者单位：University of Edinburgh; University of Missouri System; University of Missouri Columbia; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); University of Basque Country; Basque Foundation for Science; ICREA; Autonomous University of Barcelona; Autonomous University of Barcelona
摘要：It is well-known that quantitative, scale invariant absolute continuity (more precisely, the weak-A(infinity) property) of harmonic measure with respect to surface measure, on the boundary of an open set Omega subset of Rn+1 with Ahlfors-David \regular boundary, is equivalent to the solvability of the Dirichlet problem in Omega, with data in L-p(partial derivative Omega) for some p < infinity. In this paper, we give a geometric characterization of the weak-A(infinity) property, of harmonic mea...
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作者：Alper, Jarod; Blum, Harold; Halpern-Leistner, Daniel; Xu, Chenyang
作者单位：University of Washington; University of Washington Seattle; Utah System of Higher Education; University of Utah; Cornell University; Massachusetts Institute of Technology (MIT)
摘要：We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and Theta-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open condition, we prove that the Artin stack parametrizing K-semistable Fano varieties admits a separated good moduli space.
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作者：Brown, Aaron; Fisher, David; Hurtado, Sebastian
作者单位：University of Chicago; Indiana University System; Indiana University Bloomington
摘要：We prove Zimmer's conjecture for C2 actions by finite-index subgroups of SL(m, Z) provided m > 3. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in SL(m, R) (Brown et al. in Zimmer's conjecture: subexponential growth, measure rigidity, and strong property (T), 2016. arXiv:1608.04995) but new ideas are needed to overcome the lack of compactness of the space (G x M)/ (admitting the induced G-action). Non-compactness allows both mea...
