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作者：Bowen, Lewis
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We determine the range of Furstenberg entropy for stationary ergodic actions of nonabelian free groups by an explicit construction involving random walks on random coset spaces.
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作者：Petersen, Dan; Tommasi, Orsola
作者单位：Royal Institute of Technology; Leibniz University Hannover
摘要：We prove that for N equal to at least one of the integers 8, 12, 16, 20 the tautological ring is not Gorenstein. In fact, our N equals the smallest integer such that there is a non-tautological cohomology class of even degree on . By work of Graber and Pandharipande, such a class exists on , and we present some evidence indicating that N is in fact 20.
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作者：Hairer, M.
作者单位：University of Warwick
摘要：We introduce a new notion of regularity structure that provides an algebraic framework allowing to describe functions and/or distributions via a kind of jet or local Taylor expansion around each point. The main novel idea is to replace the classical polynomial model which is suitable for describing smooth functions by arbitrary models that are purpose-built for the problem at hand. In particular, this allows to describe the local behaviour not only of functions but also of large classes of dis...
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作者：Seidel, Paul
摘要：We consider open symplectic manifolds which admit dilations (in the sense previously introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian submanifolds which are pairwise disjoint (or pairwise disjoinable by Hamiltonian isotopies) inside such manifolds. This includes the Milnor fibres of isolated hypersurface singularities which have been stabilized (by adding quadratic terms) sufficiently often.
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作者：Alarcon, Antonio; Forstneric, Franc
作者单位：University of Granada; University of Ljubljana
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作者：Koropecki, Andres; Tal, Fabio Armando
作者单位：Universidade Federal Fluminense; Universidade de Sao Paulo
摘要：This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points is shown to be a disjoint union of periodic topological disks (...
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作者：Gan, Wee Teck; Ichino, Atsushi
作者单位：National University of Singapore; Kyoto University
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作者：Grabowski, Lukasz
作者单位：University of Warwick
摘要：Main theorems of the article concern the problem of Atiyah on possible values of -Betti numbers. It is shown that all non-negative real numbers are -Betti numbers, and that many (for example all non-negative algebraic) real numbers are -Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental -Betti number with respect to an action of the threefold direct product...
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作者：Guionnet, A.; Shlyakhtenko, D.
作者单位：Massachusetts Institute of Technology (MIT); Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); University of California System; University of California Los Angeles
摘要：By solving a free analog of the Monge-AmpSre equation, we prove a non-commutative analog of Brenier's monotone transport theorem: if an n-tuple of self-adjoint non-commutative random variables Z (1),aEuro broken vertical bar,Z (n) satisfies a regularity condition (its conjugate variables xi (1),aEuro broken vertical bar,xi (n) should be analytic in Z (1),aEuro broken vertical bar,Z (n) and xi (j) should be close to Z (j) in a certain analytic norm), then there exist invertible non-commutative ...
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作者：Cook, Brian; Magyar, Akos
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of British Columbia
摘要：Let p = (p(1), ... , p(r)) be a system of r polynomials with integer coefficients of degree d in n variables x = (x(1), ... , x(n)). For a given r-tuple of integers, say s, a general local to global type statement is shown via classical Hardy-Littlewood type methods which provides sufficient conditions for the solubility of p(x) = s under the condition that each of the x(i)'s is prime.
