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作者：Cai, Yuanqing; Friedberg, Solomon; Ginzburg, David; Kaplan, Eyal
作者单位：Boston College; Weizmann Institute of Science; Tel Aviv University; Bar Ilan University
摘要：We present an integral representation for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and lo...
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作者：Eskenazis, Alexandros; Mendel, Manor; Naor, Assaf
作者单位：Princeton University; Open University Israel
摘要：We prove that not every metric space embeds coarsely into an Alexandrov space of nonpositive curvature. This answers a question ofGromov (Geometric group theory, Cambridge University Press, Cambridge, 1993) and is in contrast to the fact that any metric space embeds coarsely into an Alexandrov space of nonnegative curvature, as shown by Andoni et al. (Ann Sci Ec Norm Super (4) 51(3):657-700, 2018). We establish this statement by proving that a metric space which is q- barycentric for some q is...
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作者：Levin, Aaron
作者单位：Michigan State University
摘要：We give results and inequalities bounding the greatest common divisor of multivariable polynomials evaluated at S-unit arguments, generalizing to an arbitrary number of variables results of Bugeaud-Corvaja-Zannier, Hernandez-Luca, and Corvaja-Zannier. In closely related results, and in line with observations of Silverman, we prove special cases of Vojta's conjecture for blowups of toric varieties. As an application, we classify when terms from simple linear recurrence sequences can have a larg...
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作者：Chung, Yong Moo; Rivera-Letelier, Juan; Takahasi, Hiroki
作者单位：Hiroshima University; University of Rochester; Keio University
摘要：We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation Principle holds for every non-renormalizable quadratic map. This includes the maps without physical measure found by Hofbauer and Keller, and challenges the widely-shared view of the Large Deviation Principle as a refinement of laws of large numbers.
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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...
