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  • Articles  (340)
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  • Articles  (340)
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  • 1
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    A sharp signature bound for positive four-braids (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: We provide the optimal linear bound for the signature of positive four-braids in terms of the three-genus of their closures. As a consequence, we improve previously known linear bounds for the signature in terms of the first Betti number for all positive braid links. We obtain our results by combining bounds for positive three-braids with Gordon and Litherland’s approach to signature via unoriented surfaces and their Goeritz forms. Examples of families of positive four-braids for which the bounds are sharp are provided.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 2
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    Second-Order deformations of associative submanifolds in nearly parallel G2-manifolds (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: Associative submanifolds A in nearly parallel G 2 -manifolds Y are minimal 3-submanifolds in spin 7-manifolds with a real Killing spinor. The Riemannian cone over Y has the holonomy group contained in Spin(7) and the Riemannian cone over A is a Cayley submanifold.Infinitesimal deformations of associative submanifolds were considered by the author. This paper is a continuation of the work. We give a necessary and sufficient condition for an infinitesimal associative deformation to be integrable (unobstructed) to second order explicitly. As an application, we show that the infinitesimal deformations of a homogeneous associative submanifold in the 7-sphere given by Lotay, which he called A 3 , are unobstructed to second order.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 3
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    On the critical points of random matrix characteristic polynomials and of the Riemann ξ-function (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: A one-parameter family of point processes describing the distribution of the critical points of the characteristic polynomial of large random Hermitian matrices on the scale of mean spacing is investigated. Conditionally on the Riemann hypothesis and the multiple correlation conjecture, we show that one of these limiting processes also describes the distribution of the critical points of the Riemann ξ-function on the critical line. We prove that each of these processes boasts stronger level repulsion than the sine process describing the limiting statistics of the eigenvalues: the probability to find k critical points in a short interval is comparable to the probability to find k + 1 eigenvalues there. We also prove a similar property for the critical points and zeros of the Riemann ξ -function, conditionally on the Riemann hypothesis, but not on the multiple correlation conjecture.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 4
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    Point counting on curves using a gonality preserving lift (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: We study the problem of lifting curves from finite fields to number fields in a genus and gonality preserving way. More precisely, we sketch how this can be done efficiently for curves of gonality at most four, with an in-depth treatment of curves of genus at most five over finite fields of odd characteristic, including an implementation in Magma. We then use such a lift as input to an algorithm due to the second author for computing zeta functions of curves over finite fields using p -adic cohomology.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 5
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    The Norm of Gaussian Periods (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: Gaussian periods are cyclotomic integers with a long history in number theory and connections to problems in combinatorics. We investigate the asymptotic behavior of the absolute norm of a Gaussian period and prove a case of Myerson’s Conjecture for periods of arbitrary odd length and provide a rate of convergence. Our method involves a result of Bombieri et al . on unlikely intersections in the algebraic torus as well as work of the author on the diophantine approximations to a set definable in an o-minimal structure. In the appendix, we make a result of Lawton on Mahler measures quantitative.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 6
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    On the Quantized Dynamics of Factorial Languages (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: We study local piecewise conjugacy of the quantized dynamics arising from factorial languages. We show that it induces a bijection between allowable words of same length and thus it preserves entropy. In the case of sofic factorial languages we prove that local piecewise conjugacy translates to unlabeled graph isomorphism of the follower set graphs. Moreover, it induces an unlabeled graph isomorphism between the Fischer covers of irreducible subshifts. We verify that local piecewise conjugacy does not preserve finite type nor irreducibility; but it preserves soficity. Moreover, it implies identification (up to a permutation) for factorial languages of type 1 if, and only if, the follower set function is one-to-one on the symbol set.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 7
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    On coarse embeddings into c0(Γ) (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: Let λ be a large enough cardinal number (assuming the Generalized Continuum Hypothesis it suffices to let λ=ℵω). If X is a Banach space with dens(X)≥λ, which admits a coarse (or uniform) embedding into any c0(Γ), then X fails to have non-trivial cotype, i.e. X contains ℓ∞n C -uniformly for every C〉1. In the special case when X has a symmetric basis, we may even conclude that it is linearly isomorphic with c0(densX).
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 8
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    PSL(2, ℂ), the exponential and some new free groups (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: We prove a normal form result for the groupoid of germs generated by PSL(2,ℂ) and the exponential map. We discuss three consequences of this result: (1) a generalization of a result of Cohen about the group of translations and powers, which gives a positive answer to a problem posed by Higman; (2) as proof that the subgroup of Homeo(ℝ,+∞) generated by the positive affine maps and the exponential map is isomorphic to an HNN-extension; (3) a finitary version of the immiscibility conjecture of Ecalle–Martinet–Moussu–Ramis.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 9
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    The value of the Kac polynomial at one (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: We establish a formula for the value of the Kac polynomial at one in terms of Kac polynomials, evaluated at one, of the universal (abelian) covering quiver by applying torus localization methods to quiver varieties introduced by Hausel–Letellier–Rodriguez-Villegas.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 10
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    A fast amortized algorithm for computing quadratic Dirichlet L-functions (2018)
    Oxford University Press
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    Publication Date: 2018-03-06
    Description: An algorithm to compute Dirichlet L -functions for many quadratic characters is derived. The algorithm is optimal (up to logarithmic factors) provided that the conductors of the characters under consideration span a dyadic window.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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