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作者：Aggarwal, Amol
作者单位：Harvard University
摘要：In this paper we consider the six-vertex model at ice point on an arbitrary three-bundle domain, which is a generalization of the domain-wall ice model on the square (or, equivalently, of a uniformly random alternating sign matrix). We show that this model exhibits the arctic boundary phenomenon, whose boundary is given by a union of explicit algebraic curves. This was originally predicted by Colomo and Sportiello (J Stat Phys 164:1488-1523, 2016) as one of the initial applications of a genera...
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作者：Gray, Robert D.
作者单位：University of East Anglia
摘要：We prove the following results: (1) There is a one-relator inverse monoid Inv⟨A|w=1⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {Inv}\langle A\,|\,w=1 \rangle $$\end{document} with undecidable word problem; and (2) There are one-relator groups with undecidable submonoid membership problem. The second ...
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作者：Hesselholt, Lars; Larsen, Michael; Lindenstrauss, Ayelet
作者单位：Nagoya University; University of Copenhagen; Indiana University System; Indiana University Bloomington
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作者：Bianchini, Stefano; Bonicatto, Paolo
作者单位：International School for Advanced Studies (SISSA)
摘要：Given a vector field.(1, b). L1 loc(R+ x Rd, Rd+1) such that divt, x(.(1, b)) is a measure, we consider the problem of uniqueness of the representation. of.(1, b)Ld+1 as a superposition of characteristics. : (t ., t +.). Rd,.. (t) = b(t,. (t)). We give conditions in terms of a local structure of the representation. on suitable sets in order to prove that there is a partition of Rd+1 into disjoint trajectories Pa, a. A, such that the PDE divt, x u.(1, b). M(Rd+1), u. L 8 (R+ x Rd), can be disin...
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作者：Chen, Lvzhou
作者单位：University of Chicago
摘要：Let G be a group acting on a tree with cyclic edge and vertex stabilizers. Then stable commutator length (scl) is rational in G. Furthermore, scl varies predictably and converges to rational limits in so-called surgery families. This is a homological analog of the phenomenon of geometric convergence in hyperbolic Dehn surgery.
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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：Kim, Sang-hyun; Koberda, Thomas
作者单位：Korea Institute for Advanced Study (KIAS); University of Virginia
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作者：Li, Xin
作者单位：University of London; Queen Mary University London
摘要：We construct Cartan subalgebras in all classifiable stably finite C*-algebras. Together with known constructions of Cartan subalgebras in all UCT Kirchberg algebras, this shows that every classifiable simple C*-algebra has a Cartan subalgebra.
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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：Colmez, Pierre; Dospinescu, Gabriel; Niziol, Wieslawa
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We compute p-adic etale and pro-etale cohomologies of Drinfeld half-spaces. In the pro-etale case, the main input is a comparison theorem for p-adic Stein spaces; the cohomology groups involved here are much bigger than in the case of etale cohomology of algebraic varieties or proper analytic spaces considered in all previous works. In the etale case, the classical p-adic comparison theorems allow us to pass to a computation of integral differential forms cohomologies which can be done because...
