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作者：Bridson, Martin R.; Evans, David M.; Liebeck, Martin W.; Segal, Dan
作者单位：University of Oxford; Imperial College London; University of Oxford
摘要：We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains infinitely many alternating groups, or contains classical groups of unbounded dimensions, we prove that there is no such algorithm. On the other hand, for families of simple groups of Lie type of bound...
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作者：Nguyen, Hop Dang; Trung, Ngo Viet
作者单位：Vietnam Academy of Science & Technology (VAST); Vietnam Academy of Science & Technology (VAST)
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作者：Brendle, Simon; Choi, Kyeongsu
作者单位：Columbia University; Massachusetts Institute of Technology (MIT)
摘要：A well-known question of Perelman concerns the classification of noncompact ancient solutions to the Ricci flow in dimension 3 which have positive sectional curvature and are -noncollapsed. In this paper, we solve the analogous problem for mean curvature flow in R3, and prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in R3 which is strictly convex and noncollapsed.
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作者：Schrader, Gus; Shapiro, Alexander
作者单位：Columbia University; University of Edinburgh
摘要：We construct an injective algebra homomorphism of the quantum group Uq(sln+1) into a quantum cluster algebra Ln associated to the moduli space of framed PGLn+1-local systems on a marked punctured disk. We obtain a description of the coproduct of Uq(sln+1) in terms of the corresponding quantum cluster algebra associated to the marked twice punctured disk, and express the action of the R-matrix in terms of a mapping class group element corresponding to the half-Dehn twist rotating one puncture a...
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作者：Frisch, Joshua; Tamuz, Omer; Ferdowsi, Pooya Vahidi
作者单位：California Institute of Technology
摘要：A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.
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作者：Mikhalkin, Grigory; Orevkov, Stepan
作者单位：University of Geneva; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Oleg Viro introduced an invariant of rigid isotopy for real algebraic knots and links in RP3 which is not a topological isotopy invariant. In this paper we study real algebraic links of degree d with the maximal value of this invariant. We show that these links admit entirely topological description. In particular, these links are characterized by the property that any of their planar diagram has at least (d-1)(d-2)/2-g-1 crossing points where g is the genus of the complexification. Also we sh...
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作者：Bitoun, Thomas
作者单位：University of Oxford
摘要：For a smooth variety Y over a perfect field of positive characteristic, the sheaf DY of crystalline differential operators on Y (also called the sheaf of PD-differential operators) is known to be an Azumaya algebra over TY, the cotangent space of the Frobenius twist Y of Y. Thus to a sheaf of modules M over DY one can assign a closed subvariety of TY, called the p-support, namely the support of M seen as a sheaf on TY. We study here the family of p-supports assigned to the reductions modulo pr...
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作者：Shokrieh, Farbod; Wu, Chenxi
作者单位：Cornell University; Rutgers University System; Rutgers University New Brunswick
摘要：We extend the notion of canonical measures to all (possibly non-compact) metric graphs. This will allow us to introduce a notion of hyperbolic measures on universal covers of metric graphs. Kazhdan's theorem for Riemann surfaces describes the limiting behavior of canonical (Arakelov) measures on finite covers in relation to the hyperbolic measure. We will prove a generalized version of this theorem for metric graphs, allowing any infinite Galois cover to replace the universal cover. We will sh...
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作者：Aprodu, Marian; Farkas, Gavril; Papadima, Stefan; Raicu, Claudiu; Weyman, Jerzy
作者单位：Institute of Mathematics of the Romanian Academy; University of Bucharest; Humboldt University of Berlin; University of Notre Dame; University of Connecticut; Jagiellonian University
摘要：We prove a strong vanishing result for finite length Koszul modules, and use it to derive Green's conjecture for every g-cuspidal rational curve over an algebraically closed field documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbf {k}}}$$\end{document}, with char(k)=0\documentclass[12pt]{minimal} \usepackage{...
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作者：Krishna, Amalendu
作者单位：Tata Institute of Fundamental Research (TIFR)
摘要：We show that the Levine-Weibel Chow group of 0-cycles CHd(A) of a reduced affine algebra A of dimension d >= 2 over an algebraically closed field is torsion-free. Among several applications, it implies an affirmative solution to an old conjecture of Murthy in classical K-theory.
