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  • Articles  (340)
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  • Articles  (340)
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  • 1
    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
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  • 2
    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
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  • 3
    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
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  • 4
    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.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 5
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    Oxford University Press
    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.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 6
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    Oxford University Press
    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.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 7
    Publication Date: 2018-03-06
    Description: We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 8
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    Oxford University Press
    Publication Date: 2018-03-06
    Description: We develop a theory of minors for alternating dimaps—orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that they are related by the triality relation of Tutte. They do not commute in general, though do in many circumstances, and we characterize the situations where they do. We give a characterization of alternating dimaps of at most a given genus, using a finite set of excluded minors. We also use the minor operations to define simple Tutte invariants for alternating dimaps and characterize them. We establish a connection with the Tutte polynomial, and pose the problem of characterizing universal Tutte-like invariants for alternating dimaps based on these minor operations.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 9
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    Oxford University Press
    Publication Date: 2018-03-06
    Description: We prove an analog of the Szemerédi–Trotter Theorem in the plane for definable curves and points in any o-minimal structure over an arbitrary real closed field R. One new ingredient in the proof is an extension of the well known crossing number inequality for graphs to the case of embeddings in any o-minimal structure over an arbitrary real closed field.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 10
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    Oxford University Press
    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).
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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