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作者：Berger, Pierre
作者单位：Universite Paris 13
摘要：We show, for every or , the existence of a Baire generic set of -families of -maps of a manifold M of dimension 2, so that for every a small the map has infinitely many sinks. When the dimension of the manifold is 3, the generic set is formed by families of diffeomorphisms. When M is the annulus, this generic set is formed by local diffeomorphisms. This is a counter example to a conjecture of Pugh and Shub.
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作者：De Simoi, Jacopo; Liverani, Carlangelo
作者单位：University of Toronto; University of Rome Tor Vergata
摘要：We consider a class of partially hyperbolic systems on described by maps where are expanding maps of the circle. For sufficiently small and generic in an open set, we precisely classify the SRB measures for and their statistical properties, including exponential decay of correlation for Holder observables with explicit and nearly optimal bounds on the decay rate.
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作者：Uhlmann, Gunther; Vasy, Andras
作者单位：University of Washington; University of Washington Seattle; University of Helsinki; Hong Kong University of Science & Technology; Stanford University
摘要：Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces the geodesic X-ray transform is globally injective. In addition we prove stability estimates and propose a layer stripping type algorithm for reconstruction.
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作者：Aizenbud, Avraham; Avni, Nir
作者单位：Weizmann Institute of Science; Northwestern University
摘要：Let G be a semisimple algebraic group defined over , and let be a compact open subgroup of . We relate the asymptotic representation theory of and the singularities of the moduli space of G-local systems on a smooth projective curve, proving new theorems about both:We prove that there is a constant C, independent of G, such that the number of n-dimensional representations of grows slower than , confirming a conjecture of Larsen and Lubotzky. In fact, we can take . We also prove the same bounds...
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作者：Kim, Inkang; Lecuire, Cyril; Ohshika, Ken'ichi
作者单位：Korea Institute for Advanced Study (KIAS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Osaka
摘要：We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective lamination. We prove that if this limit projective lamination is doubly incompressible, then the sequence has compact closure in the deformation space. As a consequence we generalise Thurston's double limit theorem and solve his conjecture on convergence of fun...
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作者：McMullen, Curtis T.
作者单位：Harvard University
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作者：Abe, Takuro
作者单位：Kyoto University
摘要：Let be the triple of hyperplane arrangements. We show that the freeness of and the division of by imply the freeness of . This division theorem improves the famous addition-deletion theorem, and it has several applications, which include a definition of divisionally free arrangements. It is a strictly larger class of free arrangements than the classical important class of inductively free arrangements. Also, whether an arrangement is divisionally free or not is determined by the combinatorics....
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作者：Bonahon, Francis; Wong, Helen
作者单位：University of Southern California; Carleton College
摘要：We study finite-dimensional representations of the Kauffman bracket skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter is a root of unity. The main one of these invariants is a point in the character variety consisting of group homomorphisms from the fundamental group to , or in a twisted version of this character variety. The proof relies on certain miraculous cancellations that occur for the quantum trace hom...
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作者：Angel, Omer; Hutchcroft, Tom; Nachmias, Asaf; Ray, Gourab
作者单位：University of British Columbia; Tel Aviv University; University of Cambridge
摘要：We show that the circle packing type of a unimodular random plane triangulation is parabolic if and only if the expected degree of the root is six, if and only if the triangulation is amenable in the sense of Aldous and Lyons [1]. As a part of this, we obtain an alternative proof of the Benjamini-Schramm Recurrence Theorem [19]. Secondly, in the hyperbolic case, we prove that the random walk almost surely converges to a point in the unit circle, that the law of this limiting point has full sup...
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作者：Danciger, Jeffrey; Gueritaud, Francois; Kassel, Fanny
作者单位：University of Texas System; University of Texas Austin; Centre National de la Recherche Scientifique (CNRS); Universite de Lille
摘要：We study strip deformations of convex cocompact hyperbolic surfaces, defined by inserting hyperbolic strips along a collection of disjoint geodesic arcs properly embedded in the surface. We prove that any deformation of the surface that uniformly lengthens all closed geodesics can be realized as a strip deformation, in an essentially unique way. The infinitesimal version of this result gives a parameterization, by the arc complex, of the moduli space of Margulis spacetimes with fixed convex co...
