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作者：Angles, Bruno; Pellarin, Federico
作者单位：Universite de Caen Normandie; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We prove that the maximal abelian extension tamely ramified at infinity of the rational function field over is generated by the values at the points in the algebraic closure of of the higher derivatives of the so-called Anderson and Thakur function We deduce a similar property for the special values of the higher derivatives of a new kind of -series introduced by the second author.
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作者：Andersen, Jorgen Ellegaard; Ueno, Kenji
作者单位：Aarhus University; Hosei University
摘要：In Andersen and Ueno (J Knot Theory Ramif 16:127-202, 2007) we constructed the vacua modular functor based on the sheaf of vacua theory developed in Tsuchiya et al. (Adv Stud Pure Math 19:459-566, 1989) and the abelian analog in Andersen and Ueno (Int J Math 18:919-993, 2007). We here provide an explicit isomorphism from the modular functor underlying the skein-theoretic model for the Witten-Reshetikhin-Turaev TQFT due to Blanchet, Habbeger, Masbaum and Vogel to the vacua modular functor. This...
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作者：Preiss, David; Speight, Gareth
作者单位：University of Warwick; Scuola Normale Superiore di Pisa
摘要：We show that if then there exists a Lebesgue null set in containing a point of differentiability of each Lipschitz function ; in combination with the work of others, this completes the investigation of when the classical Rademacher theorem admits a converse. Avoidance of -porous sets, arising as irregular points of Lipschitz functions, plays a key role in the proof.
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作者：Bridson, Martin R.; Wilton, Henry
作者单位：University of Oxford; University of London; University College London
摘要：We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, non-positively curved square complexes. We deduce that many other properties of groups are undecidable. For hyperbolic groups, there cannot exist algorithms to determine largeness, the existence of a linear representation with infinite image (over any infinite field), or the rank of...
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作者：Sato, Yasuhiko; White, Stuart; Winter, Wilhelm
作者单位：Kyoto University; University of Glasgow; University of Munster
摘要：Simple, separable, unital, monotracial and nuclear C*-algebras are shown to have finite nuclear dimension whenever they absorb the Jiang-Su algebra Z tensorially. This completes the proof of the Toms-Winter conjecture in the unique trace case. The structure theory of simple nuclear C*-algebras is currently undergoing revolutionary progress, driven by the discovery of regularity properties of various flavours: topological, functional analytic and algebraic. Despite the diverse nature of these r...
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作者：Hsu, Tim; Wise, Daniel T.
作者单位：California State University System; San Jose State University; McGill University
摘要：Let be a group splitting as a graph of groups where each vertex group acts properly on a CAT(0) cube complex. When is hyperbolic relative to virtually abelian subgroups, we examine conditions producing a proper action of on a CAT(0) cube complex. When is hyperbolic this action is also cocompact.
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作者：Pera, Keerthi Madapusi
作者单位：Harvard University
摘要：We show that the classical Kuga-Satake construction gives rise, away from characteristic , to an open immersion from the moduli of primitively polarized K3 surfaces (of any fixed degree) to a certain regular integral model for a Shimura variety of orthogonal type. This allows us to attach to every polarized K3 surface in odd characteristic an abelian variety such that divisors on the surface can be identified with certain endomorphisms of the attached abelian variety. In turn, this reduces the...
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作者：Eldan, Ronen
作者单位：University of Washington; University of Washington Seattle
摘要：The Gaussian noise-stability of a set is defined by where are standard jointly Gaussian vectors satisfying . Borell's inequality states that for all , among all sets with a given Gaussian measure, the quantity is maximized when is a half-space. We give a novel short proof of this fact, based on stochastic calculus. Moreover, we prove an almost tight, two-sided, dimension-free robustness estimate for this inequality: by introducing a new metric to measure the distance between the set and its co...
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作者：Dujardin, Romain; Lyubich, Mikhail
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); State University of New York (SUNY) System; Stony Brook University; State University of New York (SUNY) System; Stony Brook University
摘要：We study stability and bifurcations in holomorphic families of polynomial automorphisms of . We say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there. We first show that this defines a meaningful notion of stability, which parallels in many ways the classical notion of -stability in one-dimensional dynamics. Define the bifurcation locus to be the complement of the weak stability locus. In the second part of the paper, we prove that under a...
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作者：Bramham, Barney
作者单位：Ruhr University Bochum
摘要：It is an open question in smooth ergodic theory whether there exists a Hamiltonian disk map with zero topological entropy and (strong) mixing dynamics. Weak mixing has been known since Anosov and Katok first constructed examples in 1970. Currently all known examples with weak mixing are irrational pseudo-rotations with Liouvillean rotation number on the boundary. Our main result however implies that for a dense subset of Liouville numbers (strong) mixing cannot occur. Our approach involves app...
