ALBERT — All Library Books, journals and Electronic Records Telegrafenberg

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Hausdorff dimensions of quasilines varying in the universal Teichmuller space (2013)

Huo, S., Wu, S.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: The aim of this paper is to study the relations between the Hausdorff dimensions of k -quasilines and the theory of extremal quasiconformal mappings. We show that there is an open and dense subset (Strebel points) of the universal Teichmüller space T (H) such that, for every [ f ] in the set, the Hausdorff dimension of the k -quasiline determined by [ f ] is strictly less than 1 + k 2 . We also show that there are some points [ f ] != [id] outside the open and dense set in the universal Teichmüller space such that the Hausdorff dimension of the quasiline determined by [ f ] is 1. Moreover, some results on the Hausdorff dimensions of the quasilines varying in the asymptotic Teichmüller space are also obtained.

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A Nagumo-type uniqueness result for an nth order differential equation (2013)

Ferreira, R. A. C.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: A new uniqueness result for a general n th order differential equation is obtained. We show that some previous results follow immediately from our theorem.

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Strong convergence to the homogenized limit of elliptic equations with random coefficients II (2013)

Conlon, J. G., Fahim, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: Consider a discrete uniformly elliptic divergence form equation on the d ≥3 dimensional lattice Z d with random coefficients. In Conlon and Spencer [ Trans. Amer. Math. Soc. , http://www.math.lsa.umich.edu/~conlon/paper/hom10.pdf ], rate of convergence results in homogenization and estimates on the difference between the averaged Green's function and the homogenized Green's function for random environments which satisfy a Poincaré inequality were obtained. Here, these results are extended to certain environments in which correlations can have arbitrarily small power law decay. These environments are simply related via a convolution to environments which do satisfy a Poincaré inequality.

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Infinitely many Carmichael numbers in arithmetic progressions (2013)

Wright, T.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: In this paper, we prove that, for any a , M N with ( a , M ) = 1, there are infinitely many Carmichael numbers m such that m a mod M .

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Geometric Auslander criterion for openness of an algebraic morphism (2013)

Adamus, J., Bierstone, E., Milman, P. D.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We give a topological analogue for openness of a criterion for flatness that originates with Auslander. Over a normal base of dimension n , failure of openness is detected by a vertical component in the n th fibred power of the morphism.

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Regular maps into real Fermat varieties (2013)

Kucharz, W.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: Investigated are regular maps from real algebraic varieties into real Fermat varieties. It is proved that under some natural assumptions, all such maps are null homotopic.

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Spectral positivity and Riemannian coverings (2013)

Berard, P., Castillon, P.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: Let ( M , g ) be a complete non-compact Riemannian manifold. We consider operators of the form g + V , where g is the non-negative Laplacian associated with the metric g , and V a locally integrable function. Let be a Riemannian covering, with Laplacian g and potential . If the operator + V is non-negative on ( M , g ), then the operator is non-negative on . In this note, we show that the converse statement is true provided that is a co-amenable subgroup of 1 ( M ).

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Noncommutative peak interpolation revisited (2013)

Blecher, D. P.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: Peak interpolation is concerned with a foundational kind of mathematical task: building functions in a fixed algebra A , which have prescribed values or behaviour on a fixed closed subset (or on several disjoint subsets). In this paper, we do the same but now A is an algebra of operators on a Hilbert space. We briefly survey this noncommutative peak interpolation , which we have studied with coauthors in a long series of papers, and whose basic theory now appears to be approaching its culmination. This programme developed from, and is based partly on, theorems of Hay and Read whose proofs were spectacular, but therefore inaccessible to an uncommitted reader. We give short proofs of these results, using recent progress in noncommutative peak interpolation, and conversely give examples of the use of these theorems in peak interpolation. For example, we prove a useful new noncommutative peak interpolation theorem.

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Inverse limits as attractors in parameterized families (2013)

Boyland, P., de Carvalho, A., Hall, T.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We show how a parameterized family of maps of the spine of a manifold can be used to construct a family of homeomorphisms of the ambient manifold which have the inverse limits of the spine maps as global attractors. We describe applications to unimodal families of interval maps, to rotation sets, and to the standard family of circle maps.

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Locally trivial torsors that are not Weil-Chatelet divisible (2013)

Creutz, B.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: For every prime p , we give infinitely many examples of torsors under abelian varieties over Q that are locally trivial but not divisible by p in the Weil–Châtelet group. We also give an example of a locally trivial torsor under an elliptic curve over Q that is not divisible by 4 in the Weil–Châtelet group. This gives a negative answer to a question of Cassels.

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On simple zeros of the Riemann zeta-function (2013)

Bui, H. M., Heath-Brown, D. R.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We show that at least of the zeros of the Riemann zeta-function are simple, assuming the Riemann hypothesis. This was previously established by Conrey, Ghosh and Gonek [ Proc. London Math. Soc. 76 (1998) 497–522] under the additional assumption of the generalized Lindelöf hypothesis. We are able to remove this hypothesis by careful use of the generalized Vaughan identity.

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Turaev torsion, definite 4-manifolds, and quasi-alternating knots (2013)

Greene, J. E., Watson, L.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We construct an infinite family of hyperbolic, homologically thin knots that are not quasi-alternating. To establish the latter, we argue that the branched double-cover of each knot in the family does not bound a negative-definite 4-manifold with trivial first homology and bounded second Betti number. This fact depends in turn on information from the correction terms in Heegaard Floer homology, which we establish by way of a relationship to, and calculation of, the Turaev torsion.

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Nonnegative polynomials from vector bundles on real curves (2013)

Bielawski, R.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We observe that E -resultant of a very ample rank 2 vector bundle E on a real projective curve (with no real points) is nonnegative when restricted to the space of real sections. Moreover, we show that if E has a section vanishing at exactly two points and the degree d of E satisfies d ( d – 6) ≥ 4( g – 1), then this polynomial cannot be written as a sum of squares.

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Ricci-flat deformations of metrics with exceptional holonomy (2013)

Nordstrom, J.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: Let G be one of the Ricci-flat holonomy groups SU( n ), Sp( n ), Spin(7) or G 2 , and M a compact manifold of dimension 2 n , 4 n , 8 or 7, respectively. We prove that the natural map from the moduli space of torsion-free G -structures on M to the moduli space of Ricci-flat metrics is open, and that the image is a smooth manifold. For the exceptional cases G = Spin(7) and G 2 , we extend the result to asymptotically cylindrical manifolds.

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Further refinements of the GL(2) converse theorem (2013)

Booker, A. R., Krishnamurthy, M.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We improve the results of Booker and Krishnamurthy ( Compos. Math. 147 (2011) 669–715) by allowing restricted sets of poles among the unramified twists. This allows for a clean statement of the GL(2) converse theorem which includes all cases of Eisenstein series.

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Finiteness of solvable automorphisms with null entropy on a compact Kahler manifold (2013)

Kim, J. H.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: Let G be a solvable subgroup of the automorphism group Aut( X ) of a compact Kähler manifold X of complex dimension n , and let N ( G ) be the normal subgroup of G consisting of elements with null entropy. Let us denote by G * the image of G under the natural map from Aut( X ) to GL( V , R ), where V is the Dolbeault cohomology group H 1, 1 ( X , R ). Assume that the Zariski closure of G * in GL( V C ) is connected. The main aim of this paper is to show that, when the rank r ( G ) of the quotient group G / N ( G ) is equal to n – 1 and the identity component of Aut( X ) is trivial, then the normal subgroup N ( G ) of G is finite. This affirmatively answers a question in Invent. Math. posed by D.-Q. Zhang.

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Two remarks on the reduction of Alperin's weight conjecture (2013)

Cabanes, M.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: The so-called inductive McKay condition on finite simple groups, due to Isaacs–Malle–Navarro, has recently been reformulated by Späth. We show that this reformulation applies to the reduction theorem for Alperin's weight conjecture, due to Navarro–Tiep. This also simplifies the checking of the inductive condition for Alperin's weight conjecture in the case of simple groups of Lie type with regard to the defining prime.

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Keum-Naie-Mendes Lopes-Pardini surfaces yield an irreducible component of the moduli space (2013)

Chen, Y.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We construct a family of minimal smooth surfaces of general type with K 2 = 3 and p g = 0, which are finite (Z/2Z) 2 -covers of the 4-nodal cubic surface. This turns out to be a five-dimensional subfamily of the six-dimensional family constructed by Mendes Lopes and Pardini, which realizes the Keum–Naie surfaces with K 2 = 3 as degenerations. We show that the base of the Kuranishi family of a general surface in our subfamily is smooth. We prove that the closure of the corresponding subset of the Keum–Naie–Mendes Lopes–Pardini surfaces is an irreducible component of the Gieseker moduli space. As an important byproduct, it is shown that, for the surfaces in this irreducible component, the degree of the bicanonical map can only be 2 or 4.

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The isometry group of the bounded Urysohn space is simple (2013)

Tent, K., Ziegler, M.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We show that the isometry group of the bounded Urysohn space is a simple group.

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On the Koszul cohomology of canonical and Prym-canonical binary curves (2013)

Colombo, E., Frediani, P.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: In this paper we study Koszul cohomology and the Green and Prym–Green conjectures for canonical and Prym-canonical binary curves. We prove that, if property N p holds for a canonical or a Prym-canonical binary curve of genus g , then it holds for a generic canonical or Prym-canonical binary curve of genus g + 1. We also verify the Green and Prym–Green conjectures for generic canonical and Prym-canonical binary curves of low genus (6 ≤ g ≤ 15, g != 8 for Prym-canonical and 3 ≤ g ≤ 12 for canonical).

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Jodeit's extensions for bilinear multipliers (Bull. London Math Soc. 40 (2008) 937-944) (2013)

Madan, S., Mohanty, P.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

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A Banach space in which every injective operator is surjective (2013)

Aviles, A., Koszmider, P.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We construct an infinite-dimensional Banach space of continuous functions C ( K ) such that every one-to-one operator T : C ( K )-〉 C ( K ) is onto.

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Some word maps that are non-surjective on infinitely many finite simple groups (2013)

Jambor, S., Liebeck, M. W., O'Brien, E. A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We provide the first examples of words in the free group of rank 2 that are not proper powers and for which the corresponding word maps are non-surjective on an infinite family of finite non-abelian simple groups.

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Characterization of the Haagerup property by fibred coarse embedding into Hilbert space (2013)

Chen, X., Wang, Q., Wang, X.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We show that a finitely generated, residually finite group has the Haagerup property (Gromov's a-T-menability) if and only if one (or equivalently, all) of its box spaces admits a fibred coarse embedding into Hilbert space. In contrast, the box spaces of a finitely generated, residually finite hyperbolic group with property (T) do not admit a fibred coarse embedding into Hilbert space, but do admit a fibred coarse embedding into an p -space for some p 〉2.

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Graham Everest 1957-2010 (2013)

Ward, T.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

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Toeplitz operators on Bergman spaces of polyanalytic functions (2012)

Cuckovic, Z., Le, T.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: We study algebraic properties of Toeplitz operators on Bergman spaces of polyanalytic functions on the unit disk. We obtain results on finite-rank commutators and semi-commutators of Toeplitz operators with harmonic symbols. We also raise and discuss some open questions.

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The numerical equivalence relation for height functions and ampleness and nefness criteria for divisors (2012)

Lee, C. G.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: In this paper, we study properties of Weil height functions associated with numerically trivial divisors. It helps us to define the fractional limit of h E with respect to h D on U , with D ample: The value of Flim D ( E , U ) contains numerical information about a divisor E , enough to determine whether E is ample, numerically effective (nef) or pseudo-effective.

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Scissor equivalence for torus links (2012)

Baader, S.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: We show that the cobordism distance of torus links is determined by the profiles of their signature functions, up to a constant factor.

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Descriptive topology in non-archimedean function spaces Cp(X, K). Part I (2012)

Kakol, J., Sliwa, W.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: Let K be a non-archimedean field and let X be an ultraregular space. We study the non-archimedean locally convex space C p ( X , K) of all K-valued continuous functions on X endowed with the pointwise topology. We show that K is spherically complete if and only if every polar metrizable locally convex space E over K is weakly angelic. This extends a result of Kiyosawa–Schikhof for polar Banach spaces. For any compact ultraregular space X we prove that C p ( X , K) is Fréchet–Urysohn if and only if X is scattered (a non-archimedean variant of Gerlits–Pytkeev's result). If K is locally compact, we show the following: (1) for any ultraregular space X , the space C p ( X , K) is K -analytic if and only if it has a compact resolution (a non-archimedean variant of Tkachuk's theorem); (2) for any ultrametrizable space X the space C p ( X , K) is analytic if and only if X is -compact (a non-archimedean variant of Christensen's theorem).

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Long time decay to the Leray solution of the two-dimensional Navier-Stokes equations (2012)

Benameur, J., Selmi, R.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: We give a new proof of the zero limit to the solution of the two-dimensional Navier–Stokes equations, as time goes to infinity. This proof is done in the frequency space; it is simpler and shorter compared to the existing proofs. Based on this limit, we derive some analytic properties of the solution. Mainly, it becomes infinitely differentiable with respect to time and has value in all Sobolev spaces. Moreover, its regularity grows in an exponential way and its L 2 ( R 2 ) norm decays exponentially fast, as time tends to infinity. Especially, we obtain, for any time t ≥0, that We describe the long time behaviour of its homogeneous Sobolev norm for any positive, real exponent, by comparing to usual functions and we ameliorate some existing results. We establish that the Leray solution is stable as time increases.

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Existence and regularity of weakly harmonic maps into a Finsler manifold with a special structure (2012)

Tachikawa, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: We study Dirichlet problems for harmonic maps from a Riemannian m -manifold ( M , g ) into a Finsler n -manifold ( N , F ). We assume that the dimension of the source manifold M is less than or equal to 4, and that the Finsler structure F ( u , X ) is given as where ( h ij ) is a Riemannian metric and B( u , X ) is a function on TN with positive homogeneity of degree 2 with respect to X . Under these assumptions, an existence and interior regularity result will be given.

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Linear relations among Poincare series (2012)

Das, S., Ganguly, S.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: We study general linear relations among Poincaré series of different indices with arbitrary but fixed level and weight. We establish several conditions the coefficients involved must satisfy. In particular, we show under some mild assumptions that two Poincaré series of distinct indices cannot be identically equal unless they are both identically zero.

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On the cardinality of sumsets in torsion-free groups (2012)

Boroczky, K. J., Palfy, P. P., Serra, O.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: Let A , B be finite subsets of a torsion-free group G . We prove that, for every positive integer k , there is a c ( k ) such that if | B | ≥ c ( k ), then the inequality | AB | ≥ | A |+| B |+ k holds unless a left translate of A is contained in a cyclic subgroup. We obtain c ( k ) 〈 c 0 k 6 for arbitrary torsion-free groups, and c ( k )〈 c 0 k 3 for groups with the unique product property, where c 0 is an absolute constant. We give examples to show that c ( k ) is at least quadratic in k .

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Translation invariant equations and the method of Sanders (2012)

Bloom, T. F.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: We extend the recent improvement of Roth's theorem on three-term arithmetic progressions by Sanders to obtain similar results for the problem of locating non-trivial solutions to translation invariant linear equations in many variables in both Z/ N Z and F q [ t ].

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Primes whose sum of digits is prime and metric number theory (2012)

Harman, G.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: It is shown that almost all real x contain infinitely many primes in their decimal expansions (to any base) whose sum of digits is also prime, generalizing a previous result by the author. To do this, the earlier method in metric number theory is combined with recent work by Drmota, Mauduit and Rivat on primes with prescribed sum of digits.

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Tree modules (2012)

Weist, T.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: After stating several tools which can be used to construct indecomposable tree modules for quivers without oriented cycles, we use these methods to construct indecomposable tree modules for every imaginary Schur root. These methods also give a recipe for the construction of tree modules for every root. Moreover, we give several examples illustrating the results.

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Approximation up to the boundary of homeomorphisms of finite Dirichlet energy (2012)

Iwaniec, T., Kovalev, L. V., Onninen, J.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: Let XC and YC be Jordan domains of the same finite connectivity, Y being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h : X-〉Y in the Sobolev space W 1, 2 extends to a continuous map h : X-〉Y. We prove that there exist homeomorphisms h k : X-〉Y that converge to h uniformly and in W 1, 2 (X , Y). The problem of approximation of Sobolev homeomorphisms, raised by J. M. Ball and L. C. Evans, is deeply rooted in a study of energy-minimal deformations in non-linear elasticity. The new feature of our main result is that approximation takes place also on the boundary, where the original map need not be a homeomorphism.

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The classification of the indecomposable liftable modules in blocks with cyclic defect groups (2012)

Hiss, G., Naehrig, N.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: Let G be a finite group, let k be an algebraically closed field of positive characteristic p and let B be a block of kG with cyclic defect groups. We classify the indecomposable B -modules which are liftable with respect to a splitting p -modular system with residue class field k . The indecomposable non-projective modules in B are constructed from certain paths in the Brauer tree of B [G. J. Janusz, ‘Indecomposable modules for finite groups’, Ann. Math. 2 (1969) 209–224.]. We determine those paths that give rise to liftable modules. We also find the characters of the lifts of these modules.

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Packing dimension profiles and Levy processes (2012)

Khoshnevisan, D., Schilling, R. L., Xiao, Y.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: We extend the concept of packing dimension profiles, due to Falconer and Howroyd [‘Packing dimensions of projections and dimension profiles’, Math. Proc. Cambridge Philos. Soc. 121 (1997) 269–286] and Howroyd [‘Box and packing dimensions of projections and dimension profiles’, Math. Proc. Cambridge Philos. Soc. 130 (2001) 135–160], and use our extension in order to determine the packing dimension of an arbitrary image of a general Lévy process.

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A spectral analysis of compact linear operators in Banach spaces (2012)

Edmunds, D. E., Evans, W. D., Harris, D. J.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

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From Cardano's great art to Lagrange's reflections: filling a gap in the history of algebra (Heritage of European Mathematics) By Jacqueline Stedall (2012)

Robertson, E. F.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

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Monodromy groups of parameterized linear differential equations with regular singularities (2012)

Mitschi, C., Singer, M. F.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: We study the notion of regular singularities for parameterized complex ordinary linear differential systems, prove an analogue of the Schlesinger theorem for systems with regular singularities and solve both a parameterized version of the weak Riemann–Hilbert Problem and a special case of the inverse problem in parameterized Picard–Vessiot theory.

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A proof of a conjecture of Y. Morita (2012)

Lee, D. U.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: A conjecture of Morita says that if an abelian variety defined over a number field has the Mumford–Tate group which does not have any non-trivial Q-rational unipotent element, then it has potentially good reduction everywhere. In this article, we prove this conjecture. The main ingredients of the proof include some newly established cases of the conjecture due to Vasiu, a generalization of a criterion of Paugam on good reduction of abelian varieties, and the local–global principle of isotropy for Mumford–Tate groups of abelian varieties.

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Some non-collarable slices of Lagrangian surfaces (2012)

Chantraine, B.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-09-18

Description: In this note, we define the notion of collarable slices of Lagrangian submanifolds. These are slices of Lagrangian submanifolds which can be isotoped through Lagrangian submanifolds to a cylinder over a Legendrian embedding near a contact hypersurface. Such a notion arises naturally when studying intersections of Lagrangian submanifolds with contact hypersurfaces. We then give two explicit examples of Lagrangian disks in C 2 transverse to S 3 whose slices are non-collarable.

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Inverse system characterizations of the (hereditarily) just infinite property in profinite groups (2012)

Reid, C. D.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

Description: We give criteria on an inverse system of finite groups that ensure that the limit is just infinite or hereditarily just infinite. More significantly, these criteria are ‘universal’ in that all (hereditarily) just infinite profinite groups arise as limits of the specified form. Inspired by a recent paper of Wilson, we give special consideration to (hereditarily) just infinite profinite groups that are not virtually pro- p .

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Topology of definable abelian groups in o-minimal structures (2012)

Baro, E., Berarducci, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

Description: In this note, we prove that every definably connected, definably compact abelian definable group G in an o-minimal expansion of a real closed field with dim( G )!=4 is definably homeomorphic to a torus of the same dimension. Moreover, in the semialgebraic case the result holds for all dimensions.

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Product decompositions in finite simple groups (2012)

Liebeck, M. W., Nikolov, N., Shalev, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

Description: We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of Lie type of bounded rank. Some of our arguments apply recent advances in the theory of growth in finite simple groups of Lie type, and provide a variety of new product decompositions of these groups.

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Composition operators on Hardy spaces of a half-plane (2012)

Elliott, S., Jury, M. T.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

Description: We prove that a composition operator is bounded on the Hardy space H 2 of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative there. In this case the norm, essential norm and spectral radius of the operator are all equal to .

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Local constancy for the reduction mod p of 2-dimensional crystalline representations (2012)

Berger, L.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

Description: Irreducible crystalline representations of dimension 2 of are all twists of some representations which depend on two parameters, the weight k and the trace of the Frobenius map a p . We show that the reduction modulo p of is a locally constant function of a p (with an explicit radius), and a locally constant function of the weight k if a p !=0. We then give (for p !=2) an algorithm for computing the reduction modulo p of . The main ingredient is Fontaine's theory of ( , )-modules, as well as the theory of Wach modules.

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Hilbert series of PI relatively free G-graded algebras are rational functions (2012)

Aljadeff, E., Kanel-Belov, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

Description: Given a finite group G and a field F of characteristic zero, we let F 〈 x 1, g 1 ,..., x r , g r 〉 be the free G -graded F -algebra generated by homogeneous variables { x i , g i } g i G . Let I be a G -graded T -ideal of F 〈 x 1, g 1 ,..., x r , g r 〉 which is PI (that is, the algebra F 〈 x 1, g 1 ,..., x r , g r 〉/I is PI). We prove that the Hilbert series of F 〈 x 1, g 1 ,..., x r , g r 〉/I is a rational function. More generally, we show that the Hilbert series which corresponds to any g -homogeneous component of F 〈 x 1, g 1 ,..., x r , g r 〉/I is a rational function.

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The structure of spider's web fast escaping sets (2012)

Osborne, J. W.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

Description: Building on recent work by Rippon and Stallard, we explore the intricate structure of the spider's web fast escaping sets associated with certain transcendental entire functions. Our results are expressed in terms of the components of the complement of the set (the ‘holes’ in the web). We describe the topology of such components and give a characterization of their possible orbits under iteration. We show that there are uncountably many components having each of a number of orbit types, and we prove that components with bounded orbits are quasiconformally homeomorphic to components of the filled Julia set of a polynomial. We also show that there are singleton periodic components and that these are dense in the Julia set.

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Geometric structure in the tempered dual of SL(4) (2012)

Chao, K. F., Plymen, R.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

Description: We exhibit a definite geometric structure in the tempered dual of SL(4, Q p ). Especially interesting is the case of SL(4, Q 2 ), when we reveal a tetrahedron of reducibility in the tempered dual. This conforms to a recent geometric conjecture.

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Thomas Kovari, 1930-2010 (2012)

Hayman, W. K.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

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Algebraic theories (Cambridge Tracts in Mathematics 184) By J. Adamek, J. Rosicky and E. M. Vitale (2012)

Prest, M.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

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On the representation of integers by indefinite binary Hermitian forms (2011)

Parkkonen, J., Paulin, F.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with an absolute value at most s by f , as s tends to + .

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G-complete reducibility and semisimple modules (2011)

Bate, M., Herpel, S., Martin, B., Rohrle, G.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Let G be a connected reductive algebraic group defined over an algebraically closed field of characteristic p 〉 0. Our first aim in this note is to give concise and uniform proofs for two fundamental and deep results in the context of Serre's notion of G -complete reducibility, at the cost of less favourable bounds. Here are some special cases of these results: Suppose that the index ( H : H ° ) is prime to p and that p 〉 2 dim V –2 for some faithful G -module V . Then the following hold: (i) V is a semisimple H -module if and only if H is G -completely reducible; (ii) H ° is reductive if and only if H is G -completely reducible. We also discuss two new related results. (i) If p ≥ dim V for some G -module V and H is a G -completely reducible subgroup of G , then V is a semisimple H -module; this generalizes Jantzen's semisimplicity theorem (which is the case H = G ). (ii) If H acts semisimply on V V * for some faithful G -module V , then H is G -completely reducible.

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Function spectra and continuous G-spectra (2011)

Davis, D. G.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Let G be a profinite group, { X α } α be a cofiltered diagram of discrete G -spectra, and Z be a spectrum with trivial G -action. We show how to define the homotopy fixed point spectrum F ( Z , holim α X α ) hG and that when G has finite virtual cohomological dimension (vcd), it is equivalent to F ( Z , holim α ( X α ) hG ). With these tools, we show that the K ( n )-local Spanier–Whitehead dual is always a homotopy fixed point spectrum, a well-known Adams-type spectral sequence is actually a descent spectral sequence, and, for a sufficiently nice k -local profinite G -Galois extension E , with K G and closed, the equivalence (due to Behrens and the author), where denotes k -local homotopy fixed points, can be upgraded to an equivalence that just uses ordinary ( non-local ) homotopy fixed points, when G / K has finite vcd.

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The groups of self-homotopy equivalences and the Tits alternative (2011)

Maruyama, K.-i.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: In this paper, we study the group of self-homotopy equivalences. We prove a theorem that is analogous to Tits’ well-known theorem for linear groups. Using this result, we determine a condition for the group of self-homotopy equivalences to be of finite rank.

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Directional discrepancy in two dimensions (2011)

Bilyk, D., Ma, X., Pipher, J., Spencer, C.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: In the present paper, we study the geometric discrepancy with respect to families of rotated rectangles. The well-known extremal cases are the axis-parallel rectangles (logarithmic discrepancy) and rectangles rotated in all possible directions (polynomial discrepancy). We study several intermediate situations: lacunary sequences of directions, lacunary sets of finite order, and sets with small Minkowski dimension. In each of these cases, extensions of a lemma due to Davenport allow us to construct appropriate rotations of the integer lattice which yield small discrepancy.

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Cellular automata and groups (Springer Monographs in Mathematics) By Tullio Ceccherini-Silberstein and Michel Coornaert (2011)

Machi, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

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Nonlinear Markov processes and kinetic equations (Cambridge Tracts in Mathematics 182) By Vassili N. Kolokoltsov (2011)

Applebaum, D.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

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Root separation for irreducible integer polynomials (2011)

Bugeaud, Y., Dujella, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We establish new results on root separation of integer, irreducible polynomials of degree at least 4. These improve earlier bounds of Bugeaud and Mignotte (for even degree) and of Beresnevich, Bernik, and Götze (for odd degree).

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Finite generation of Hochschild cohomology of Hecke algebras of finite classical type in characteristic zero (2011)

Linckelmann, M.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We show that the Hochschild cohomology HH *(H) of a Hecke algebra H of finite classical type over a field k of characteristic zero and a non-zero parameter q in k is finitely generated, unless possibly if q has even order in k x and H is of type B or D .

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Ricci solitons on Lorentzian manifolds with large isometry groups (2011)

Batat, W., Brozos-Vazquez, M., Garcia-Rio, E., Gavino-Fernandez, S.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We show that Lorentzian manifolds whose isometry group is of dimension at least 1/2 n ( n –1)+1 admit different vector fields resulting in expanding, steady and shrinking Ricci solitons. Moreover, it is proved that those Ricci solitons are gradient (only) in the steady case. This provides examples of complete locally conformally flat and symmetric Lorentzian gradient Ricci solitons that are not rigid.

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Gonality, apolarity and hypercubics (2011)

De Poi, P., Zucconi, F.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We show that any Fermat hypercubic is apolar to a trigonal curve, and vice versa. We show also that the Waring number of the polar hypercubic associated to a tetragonal curve of genus g is at most , and for a large class of them is at most .

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Transcendental values of certain Eichler integrals (2011)

Gun, S., Murty, M. R., Rath, P.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We study the transcendence of certain Eichler integrals associated to Eisenstein series and more generally to modular forms using functional identities due to Ramanujan, Grosswald, Weil et al . The special values of such integrals at algebraic points in the upper half-plane are linked to Riemann zeta values at odd positive integers.

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On the unique continuation property for Kadomtsev-Petviashvili-I and Benjamin-Ono-Zakharov-Kuznetsov equations (2011)

Esfahani, A., Pastor, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We prove unique continuation results for the Kadomtsev–Petviashvili-I and Benjamin–Ono–Zakharov–Kuznetsov equations. Our method of proof goes back to the complex variable techniques introduced by Bourgain. The approach is quite similar to that used by Panthee for the Kadomtsev–Petviashvili-II and Zakharov–Kuznetsov equations.

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Almost-isometry between Teichmuller metric and length-spectrum metric on moduli space (2011)

Liu, L., Su, W.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We prove an analogue of Farb–Masur's theorem that the length-spectrum metric on moduli space is ‘almost isometric’ to a simple model V( S ) which is induced by the cone metric over the complex of curves. As an application, we know that the Teichmüller metric and the length-spectrum metric are ‘almost isometric’ on moduli space, while they are not even quasi-isometric on Teichmüller space.

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Asymptotic growth and least common multiples in groups (2011)

Bou-Rabee, K., McReynolds, D. B.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: In this article, we relate word and normal subgroup growth to certain functions that arise in the quantification of residual finiteness. One consequence of this endeavor is a pair of results that equate the virtual nilpotency of a finitely generated group with the asymptotic behavior of these functions. The second half of this article investigates the asymptotic behavior of two of these functions. Our main result in this area resolves a question of Bogopolski from the Kourovka notebook concerning lower bounds of one of these functions for non-abelian free groups.

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Kulikov's problem on universal torsion-free abelian groups revisited (2011)

Shelah, S., Strungmann, L.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Let T be a torsion abelian group. We consider the class of all torsion-free abelian groups G satisfying Ext( G , T ) = 0 and search for -universal objects in this class. We show that, for certain T there is no -universal group. However, for uncountable cardinals there is always a -universal group if we assume ( V = L ). Together with results by the second author this solves completely a problem by Kulikov.

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71

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When is the second local multiplier algebra of a C*-algebra equal to the first? (2011)

Ara, P., Mathieu, M.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We discuss necessary as well as sufficient conditions for the second iterated local multiplier algebra of a separable C *-algebra to agree with the first.

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Morse theory, random subgraphs, and incoherent groups (2011)

Wise, D. T.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We prove that certain polygons of finite groups have finitely generated infinite index normal subgroups, and are hence incoherent. This gives a new family of incoherent Kleinian groups. The method of proof suggests an effective approach toward related problems.

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73

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Subclasses of the separable permutations (2011)

Albert, M. H., Atkinson, M. D., Vatter, V.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: The separable permutations are those that can be obtained from the trivial permutation by two operations called direct sum and skew sum. This class of permutations contains the class of stack sortable permutations, Av(231), which are enumerated by the Catalan numbers. We prove that all subclasses of the separable permutations which do not contain Av(231) or a symmetry of this class have rational generating functions. Our principal tools include partial well-order (the lack of an infinite antichain), atomicity (the joint embedding property), and the theory of strongly rational permutation classes which is introduced here for the first time.

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74

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Fermat quotients: exponential sums, value set and primitive roots (2011)

Shparlinski, I. E.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: For a prime p and an integer u with gcd( u , p )=1, we define Fermat quotients by the conditions Heath-Brown has given a bound of exponential sums with N consecutive Fermat quotients that is non-trivial for N ≥ p 1/2+ for any fixed 〉0. We use a recent idea of Garaev together with a form of the large sieve inequality due to Baier and Zhao to show that, on average over p , one can obtain a non-trivial estimate for much shorter sums starting with N ≥ p . We also obtain lower bounds on the image size of the first N consecutive Fermat quotients and use them to prove that there is a positive integer n ≤ p 3/4+ o (1) such that q p ( n ) is a primitive root modulo p .

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Bounds for coefficients of cusp forms and extremal lattices (2011)

Jenkins, P., Rouse, J.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: A cusp form f ( z ) of weight k for SL 2 (Z) is determined uniquely by its first := dim S k Fourier coefficients. We derive an explicit bound on the n th coefficient of f in terms of its first coefficients. We use this result to study the non-negativity of the coefficients of the unique modular form of weight k with Fourier expansion In particular, we show that k =81632 is the largest weight for which all the coefficients of F k , 0 ( z ) are non-negative. This result has applications to the theory of extremal lattices.

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76

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Slopes of smooth curves on Fano manifolds (2011)

Hwang, J.-M., Kim, H., Lee, Y., Park, J.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Ross and Thomas introduced the concept of slope stability to study K -stability, which has conjectural relation with the existence of constant scalar curvature Kähler metric. This paper presents a study of slope stability of Fano manifolds of dimension n ≥3 with respect to smooth curves. The question turns out to be easy for curves of genus at least 1 and the interest lies in the case of smooth rational curves. Our main result classifies completely the cases when a polarized Fano manifold ( X ,– K X ) is not slope stable with respect to a smooth curve. Our result also states that a Fano three-fold X with Picard number 1 is slope stable with respect to every smooth curve unless X is the projective space.

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77

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Quasi-tree expansion for the Bollobas-Riordan-Tutte polynomial (2011)

Champanerkar, A., Kofman, I., Stoltzfus, N.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Bollobás and Riordan introduced a three-variable polynomial extending the Tutte polynomial to oriented ribbon graphs, which are multi-graphs embedded in oriented surfaces, such that complementary regions (faces) are disks. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. By generalizing Tutte's concept of activity to quasi-trees, we prove a quasi-tree expansion of the Bollobás–Riordan–Tutte polynomial.

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78

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Fixed points of elements of linear groups (2011)

Liebeck, M. W., Shalev, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We prove that for any finite group G , such that | G / R ( G )|〉120 (where R ( G ) is the soluble radical of G ), and any finite-dimensional vector space V on which G acts, there is a non-identity element of G with fixed-point space of dimension at least dim V . This bound is best possible.

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79

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On the number of branches of real curve singularities (2011)

Nowel, A., Szafraniec, Z.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We present a method for computing the number of branches of a real analytic curve germ V ( f 1 , ..., f m ) R n ( m ≥ n ) having a singular point at the origin, and the number of half-branches of the set of double points of an analytic germ u : (R 2 , 0 ) -〉 (R 3 , 0 ).

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Global aspects of ergodic group actions (Mathematical Surveys and Monographs 160) By Alexander S. Kechris (2011)

Rosendal, C.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

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81

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Effective Siegel's theorem for modular curves (2011)

Bilu, Y., Illengo, M.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We prove that integral points can be effectively determined on all but finitely many modular curves, and on all but one modular curve of prime power level.

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An open-image theorem for a general class of abelian varieties (2011)

Hall, C.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Let K be a number field and A / K be a polarized abelian variety with absolutely trivial endomorphism ring. We show that if the Néron model of A / K has at least one fiber with potential toric dimension 1, then, for almost all rational primes , the Galois group of the splitting field of the -torsion of A is GSp 2 g (Z/).

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83

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On the predual of non-commutative H{infty} (2011)

Ueda, Y.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: The liftability property of weakly relatively compact subsets in M / A to M is established for any non-commutative H -algebra A = H ( M , ). Some supplementary results to our previous works are also given.

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84

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Nielsen-Thurston orders and the space of braid orderings (2011)

Navas, A., Wiest, B.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We study the topological space of left-orderings of the braid group, and its subspace of Nielsen–Thurston orderings. Our main result is that no Nielsen–Thurston ordering is isolated in the space of braid orderings. In the course of the proof, we classify the convex subgroups and calculate the Conradian soul for any Nielsen–Thurston ordering of B n . We also prove that, for a large class of Nielsen–Thurston orderings, including all those of infinite type, a stronger result holds: they are approximated by their own conjugates. On the other hand, we suggest an example of a Nielsen–Thurston ordering that may not be approximated by its conjugates.

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85

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Approximation of functions and their derivatives by analytic maps on certain Banach spaces (2011)

Azagra, D., Fry, R., Keener, L.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Let X be a separable Banach space that admits a separating polynomial; in particular, let X be a separable Hilbert space. Let f : X -〉 R be bounded and Lipschitz, with uniformly continuous derivative. Then, for each 〉 0, there exists an analytic function g : X -〉 R with | g – f | 〈 and || g ' – f ' || 〈 .

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86

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Gluing Borel-Smith functions and the group of endo-trivial modules (2011)

Coskun, O.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: The aim of this paper is to describe the group of endo-trivial modules for a p -group P , in terms of the obstruction group for the gluing problem of Borel–Smith functions. Explicitly, we shall prove that there is a split exact sequence of abelian groups where T ( P ) is the endo-trivial group of P , and C b ( P ) is the group of Borel–Smith functions on P . As a consequence, we obtain a set of generators of the group T ( P ) that coincides with the relative syzygies found by Alperin. In order to prove the result, we solve gluing problems for the functor B * of super class functions, the functor R Q * of rational class functions and the functor C b of Borel–Smith functions.

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Algebraic methods in unstable homotopy theory (New Mathematical Monographs 12) By Joseph Neisendorfer (2011)

Theriault, S.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

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Trianguline representations (2011)

Berger, L.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Trianguline representations are a certain class of p -adic representations of Gal( p / Q p ), like the crystalline, semistable and de Rham representations of Fontaine. Their definition involves the theory of (, )-modules. In this survey, we explain the theory of (, )-modules and the definition and properties of trianguline representations. After that, we give some examples of their occurrence in arithmetic geometry.

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Indecomposables live in all smaller lengths (2011)

Ringel, C. M.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Let be a finite-dimensional k -algebra with k algebraically closed. Bongartz has recently shown that the existence of an indecomposable -module of length n 〉 1 implies that also indecomposable -modules of length n – 1 exist. Using a slight modification of his arguments, we strengthen the assertion as follows: If there is an indecomposable module of length n , then there is also an accessible one. Here, the accessible modules are defined inductively, as follows. First, the simple modules are accessible. Second, a module of length n ≥ 2 is accessible provided it is indecomposable and that there is a submodule or a factor module of length n – 1 which is accessible.

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90

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Near inclusions of amenable operator algebras (2011)

Roydor, J.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We prove that if an amenable operator algebra is nearly contained in a complemented dual operator algebra, then it can be embedded inside this dual operator algebra via a similarity. The proof relies on a Johnson Theorem on approximately multiplicative maps.

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The radial curvature of an end that makes eigenvalues vanish in the essential spectrum II (2011)

Kumura, H.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: In quantum mechanics, the non-existence of L 2 -eigenfunction of the Schrödinger operator implies that particles recede to infinity as time tends to infinity or minus infinity in the sense of time average, that is, the non-existence of L 2 -eigenfunction expresses the scattering state. In this paper, we shall consider an analogue of this fact on Riemannian manifolds with a specific end: we assume that the radial curvature of one of its ends tends to zero at infinity with some quadratic order. Then, we shall derive growth estimates of solutions to the eigenvalue equation of the Laplacian and show the absence of eigenvalues. Compared to the case that the radial curvature of one of its ends tends to a negative constant at infinity, this case that the radial curvature of one of its ends tends to zero at infinity is much more difficult . The consequence of this paper will have an important role in the proof of the limiting absorption principle and absolute continuity.

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92

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Covers of multiplicative groups of algebraically closed fields of arbitrary characteristic (2011)

Bays, M., Zilber, B.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We show that algebraic analogues of universal group covers, surjective group homomorphisms from a Q-vector space to F x with ‘standard kernel’, are determined up to isomorphism of the algebraic structure by the characteristic and transcendence degree of F and, in positive characteristic, the restriction of the cover to finite fields. This extends the main result of ‘Covers of the Multiplicative Group of an Algebraically Closed Field of Characteristic Zero’ (Zilber, JLMS 2007), and our proof fills a hole in the proof given there.

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On simple endotrivial modules (2011)

Robinson, G. R.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We show that when G is a finite group that contains an elementary Abelian subgroup of order p 2 and k is an algebraically closed field of characteristic p , then the study of simple endotrivial kG -modules that are not monomial may be reduced to the case when G is quasi-simple.

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Relativizations of randomness and genericity notions (2011)

Franklin, J. N. Y., Stephan, F., Yu, L.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: A set A is a base for Schnorr randomness if it is Turing reducible to a set R that is Schnorr random relative to A , and the notion of a base for weak 1-genericity can be defined similarly. We show that A is a base for Schnorr randomness if and only if A is a base for weak 1-genericity if and only if the halting set K is not Turing reducible to A . Furthermore, we define a set A to be high for Schnorr randomness versus Martin-Löf randomness if and only if every set that is Schnorr random relative to A is also Martin-Löf random unrelativized, and we show that A is high for Schnorr randomness versus Martin-Löf randomness if and only if K is Turing reducible to A . Results concerning highness for other pairs of randomness notions are also presented.

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Constructing projective varieties in weighted flag varieties (2011)

Qureshi, M. I., Szendroi, B.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We compute the Hilbert series of general weighted flag varieties and discuss a computer-aided method to determine their defining equations. We apply our results to weighted flag varieties coming from the Lie groups of type G 2 and GL(6), to construct some families of polarized projective varieties in codimensions 8 and 6, respectively.

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Finite descent obstruction on curves and modularity (2011)

Helm, D., Voloch, J. F.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of S integral points on integral models of twists of modular curves over Q , for any finite set of primes S . We deduce this from an existence theorem for elliptic curves over Q satisfying certain local conditions.

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Eigenvalue bounds for Schrodinger operators with complex potentials (2011)

Frank, R. L.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L p -norms of the potential. This extends an inequality of Abramov, Aslanyan and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our main ingredient are the uniform Sobolev inequalities of Kenig, Ruiz and Sogge.

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Difference algebra (Algebra and Applications 8) By Alexander Levin (2011)

Ovchinnikov, A.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

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A parametrized version of the Borsuk-Ulam theorem (2011)

Schick, T., Simon, R. S., Spiez, S., Torunczyk, H.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: We show that for a ‘continuous’ family of Borsuk–Ulam situations, parametrized by points of a compact manifold W , its solution set also depends ‘continuously’ on the parameter space W . By such a family we understand a compact set Z W x S m x R m , the solution set consists of points ( w , x , v ) Z such that also ( w ,– x , v ) Z . Here, ‘continuity’ means that the solution set supports a homology class that maps onto the fundamental class of W . We also show how to construct such a family starting from a ‘continuous’ family Y W x R m when W is a compact top-dimensional subset in R m +1 . This solves a problem related to a conjecture that is relevant for the construction of equilibrium strategies in repeated two-player games with incomplete information. A new method (of independent interest) used in this context is a canonical symmetric squaring construction in Cech homology with Z/2-coefficients.

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