Bulletin of the London Mathematical Society - recent issues

Automorphisms of doubly even self-dual binary codes

Gunther, A., Nebe, G. — Tue, 27 Oct 2009 09:10:40 PDT

The automorphism group of a binary doubly even self-dual code is always contained in the alternating group. On the other hand, given a permutation group G of degree n there exists a doubly even self-dual G-invariant code if and only if n is a multiple of 8, every simple self-dual F₂G-module occurs with even multiplicity in F₂ⁿ, and G is contained in the alternating group.

Rigidity of the Mori cone for Fano manifolds

Wisniewski, J. A. — Tue, 27 Oct 2009 09:10:41 PDT

The Mori cone is rigid in smooth connected families of Fano manifolds.

Finitary group cohomology and Eilenberg-MacLane spaces

Hamilton, M. — Tue, 27 Oct 2009 09:10:41 PDT

We say that a group G has cohomology almost everywhere finitary if and only if the nth cohomology functors of G commute with filtered colimits for all sufficiently large n. In this paper, we show that if G is a group in Kropholler's class lhF with cohomology almost everywhere finitary, then G has an Eilenberg–MacLane space K(G, 1) that is dominated by a CW-complex with finitely many n-cells for all sufficiently large n. It is an open question as to whether this holds for arbitrary G. We also remark that the converse holds for any group G.

Free centre-by-nilpotent-by-abelian groups

Johnson, M., Stohr, R. — Tue, 27 Oct 2009 09:10:41 PDT

We prove that the free centre-by-(nilpotent-of-class-(c – 1))-by-abelian groups F/[_c(F'), F] are torsion-free for c = 6. This is in startling contrast to the cases when c is a prime and when c = 4, where these relatively free groups contain non-trivial elements of finite order.

Automorphism invariance and identities

Khukhro, E. I., Klyachko, Ant. A., Makarenko, N. Yu., Melnikova, Yu. B. — Tue, 27 Oct 2009 09:10:41 PDT

If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the word ‘large’, we obtain many interesting and useful facts. An example is produced showing that these results cannot be extended to arbitrary (non-multilinear) identities. As an application, a sharp estimate is given for the ‘virtual derived length’ of a (virtually solvable)-by-(virtually solvable) group.

Sum-product estimates for well-conditioned matrices

Solymosi, J., Vu, V. — Tue, 27 Oct 2009 09:10:41 PDT

We show that if A is a finite set of d x d well-conditioned matrices with complex entries, then the following sum–product estimate holds | A + A | x |A·A| = (|A| ^5/2).

Semigroups of chaotic operators

Bayart, F., Bermudez, T. — Tue, 27 Oct 2009 09:10:41 PDT

We prove the existence of chaotic semigroups of operators that do not contain any chaotic operator. In particular, we obtain a chaotic operator T such that T is not chaotic for some unimodular complex number .

Unconditional bases and strictly convex dual renormings

Smith, R. J., Troyanski, S. — Tue, 27 Oct 2009 09:10:41 PDT

We present equivalent conditions for a space X with an unconditional basis to admit an equivalent norm with a strictly convex dual norm.

Amalgams of designs and nets

McDonough, T. P., Mavron, V. C., Ward, H. N. — Tue, 27 Oct 2009 09:10:41 PDT

We present a procedure for amalgamating a net and a collection of designs into a single design. At first this amalgam is just point-regular, but it acquires additional regularities upon imposing restrictions on the ingredients. At its most regular, the amalgam is quasi-symmetric, and designs with the same parameters as those recently constructed by Bracken, McGuire and Ward appear. Along the way we discuss a class of designs generalising Hadamard designs, and we consider the problem of packing projective planes with disjoint line sets into the same point set.

A sharp combinatorial version of Vaaler's theorem

Ball, K. M., Prodromou, M. — Tue, 27 Oct 2009 09:10:42 PDT

In 1979 Vaaler proved that every d-dimensional central section of the cube [–1, 1]ⁿ has volume at least 2^d. We prove the following sharp combinatorial analogue. Let K be a d-dimensional subspace of Rⁿ. Then, there exists a probability measure P on the section [–1, 1]ⁿ K such that the quadratic form dominates the identity on K (in the sense that the difference is positive semi-definite).

Gorenstein dimension and proper actions

Bahlekeh, A., Dembegioti, F., Talelli, O. — Tue, 27 Oct 2009 09:10:42 PDT

We conjecture that a group G admits a finite-dimensional classifying space for proper actions if and only if the Gorenstein projective dimension of G is finite. We verify the one-dimensional case of this conjecture. Some evidence are given for the hypothesis that the Gorenstein projective ZG-modules are precisely Benson's class of cofibrant modules.

Positive solutions to a higher-order nonlinear delay boundary value problem on the half-line

Philos, Ch. G. — Tue, 27 Oct 2009 09:10:42 PDT

The main result of this paper establishes sufficient conditions that guarantee the existence of positive solutions to a boundary value problem on the half-line for nth-order (n > 2) nonlinear differential equations with positive delays. The application of the main result to the particular case of Emden–Fowler-type differential equations with constant delays as well as to the special case of linear differential equations with constant delays, is also presented. Moreover, some (general or specific) examples demonstrating the applicability of our result are included.

Reversibility in the group of homeomorphisms of the circle

Gill, N., O'Farrell, A. G., Short, I. — Tue, 27 Oct 2009 09:10:42 PDT

The group of orientation-preserving homeomorphisms of the circle is simple, and, because there are non-trivial involutions in this group, it must be generated by its involutions. We show that, in this group of homeomorphisms, each element can be expressed as a product of three involutions. We also characterise those elements of the group that can be expressed as a composite of two involutions, and perform a similar characterisation in the full group of homeomorphisms of the circle.

Vector product algebras

Darpo, E. — Tue, 27 Oct 2009 09:10:42 PDT

Vector products can be defined on spaces of dimensions 0, 1, 3 and 7 only, and their isomorphism types are determined entirely by their adherent symmetric bilinear forms. We present a short and elementary proof for this classical result.

Eigenvalue decay of operators on harmonic function spaces

Bandtlow, O. F., Chu, C.-H. — Tue, 27 Oct 2009 09:10:42 PDT

Let be an open set in R^d (d > 1) and let h() be the Fréchet space of harmonic functions on . Given a bounded linear operator L : h () -> h(), we show that its eigenvalues _n, arranged in decreasing order and counting multiplicities, satisfy |_n| ≤ K exp(–cn^1/(d–1)), where K and c are two explicitly computable positive constants.

The structure of finite groups of conjugate rank 2

Dolfi, S., Jabara, E. — Tue, 27 Oct 2009 09:10:42 PDT

We give a structure theorem for the finite groups with three conjugacy class sizes. In particular, they are solvable groups with derived length at most 3 or nilpotent groups.

Decompositions of complete graphs into long cycles

Bryant, D., Horsley, D. — Tue, 27 Oct 2009 09:10:42 PDT

The problem of decomposing complete graphs into cycles of arbitrary specified lengths has attracted much attention, but remains largely unsolved. In this paper, the problem is settled in the case where the specified cycle lengths are each more than about half the order of the complete graph. The proof is based on a result that modifies certain existing cycle decompositions to produce new ones in which the lengths of two of the cycles are altered.

Generation of ray class fields by elliptic units

Jung, H. Y., Koo, J. K., Shin, D. H. — Tue, 27 Oct 2009 09:10:42 PDT

We show that a certain special value of a Siegel function generates the ray class field over the Hilbert class field for an imaginary quadratic field, from which we settle the Schertz's conjecture.

Harold Scott Macdonald Coxeter, FRS, 1907-2003

Roberts, S., Weiss, A. I. — Tue, 27 Oct 2009 09:10:42 PDT

Morris's pigeonhole principle and the Helly theorem for unions of convex sets

Eckhoff, J., Nischke, K.-P. — Wed, 22 Jul 2009 09:12:41 PDT

In 1973, H. C. Morris devised a combinatorial scheme, a ‘generalized pigeonhole principle’, which he used to prove a conjecture of Grünbaum and Motzkin from 1961. This conjecture proposed, in an abstract setting, a Helly-type theorem for certain families of disjoint unions of sets. A geometric instance dealing with disjoint unions of convex sets in R^d was proved in a special case by Larman in 1968 and in the general case by Amenta in 1996. Also covered by the conjecture is a topological extension of Amenta's theorem obtained by Kalai and Meshulam in 2008.

Morris's proof of the generalized pigeonhole principle is extremely involved, and the validity of some of his arguments is open to dispute. In the present paper, the principle is placed on a sound basis and established in a relatively short and transparent manner. This includes a particular case, left open by Morris, which is applied here to families of disjoint unions of boxes in R^d.

On modular forms for some noncongruence subgroups of SL2(Z) II

Kurth, C., Long, L. — Wed, 22 Jul 2009 09:12:41 PDT

In this paper we show every type I(A) noncongruence character group of ₀(M) with M square-free satisfies the so-called unbounded denominator property.

Linear groups with many two-generator soluble subgroups

Wilson, J. S. — Wed, 22 Jul 2009 09:12:41 PDT

Let G be a linear group of degree n over a field and let S be any generating set. It is proved that (a) if every pair of products of at most elements of S S^{– 1} generates a soluble group then G is soluble and (b) if G is soluble and every pair of products of at most elements of S S^–1 generates a nilpotent group then G is locally nilpotent.

A note on the Coates-Sinnott conjecture

Aoki, M. — Wed, 22 Jul 2009 09:12:41 PDT

Let K be a finite abelian extension of a totally real number field. The Brumer conjecture asserts that the Stickelberger element annihilates the ideal class group of K. In this article, we will prove under some assumptions that the conjecture implies the Coates–Sinnott conjecture which is an analogue of the Brumer conjecture for higher K-groups.

The Riesz energy of the Nth roots of unity: an asymptotic expansion for large N

Brauchart, J. S., Hardin, D. P., Saff, E. B. — Wed, 22 Jul 2009 09:12:41 PDT

We derive the complete asymptotic expansion in terms of powers of N for the Riesz s-energy of N equally spaced points on the unit circle as N -> . For s ≥ – 2, such points form optimal energy N-point configurations with respect to the Riesz potential 1/r^s, s != 0, where r is the Euclidean distance between points. By analytic continuation we deduce the expansion for all complex values of s. The Riemann zeta function plays an essential role in this asymptotic expansion.

A geometric proof of the Karpelevich-Mostow theorem

Di Scala, A. J., Olmos, C. — Wed, 22 Jul 2009 09:12:41 PDT

In this paper we give a geometric proof of Karpelevich's theorem that asserts that a semisimple Lie subgroup of isometries, of a symmetric space of non-compact type, has a totally geodesic orbit. In fact, this is equivalent to a well-known result of Mostow about the existence of compatible Cartan decompositions.

A direct proof of Z-stability for approximately homogeneous C*-algebras of bounded topological dimension

Dadarlat, M., Phillips, N. C., Toms, A. S. — Wed, 22 Jul 2009 09:12:41 PDT

We prove that a unital simple approximately homogeneous C*-algebra with no dimension growth absorbs the Jiang–Su algebra tensorially without appealing to the classification theory of these algebras. Our main result continues to hold under the slightly weaker hypothesis of exponentially slow dimension growth.

The ring of reciprocal polynomials and rank varieties

Woodcock, C. — Wed, 22 Jul 2009 09:12:41 PDT

Let p be a prime and let G be a finite p-group. In a recent paper we introduced a commutative graded Z-algebra R_G (which classifies the so-called convolutions on G). Now let K be an algebraically closed field of characteristic p and let M be a non-zero finitely generated K[G]-module. A general rank variety W_G(M) is constructed quite explicitly as a determinantal subvariety of the variety of K-valued points of the spectrum of R_G. Further, it is shown that the quotient variety W_G(M)/G is inseparably isogenous to the usual cohomological support variety V_G(M).

Non-linear factorization of linear operators

Johnson, W. B., Maurey, B., Schechtman, G. — Wed, 22 Jul 2009 09:12:41 PDT

We show, in particular, that a linear operator between finite-dimensional normed spaces, which factors through a third Banach space Z via Lipschitz maps, factors linearly through the identity from L([0, 1], Z) to L₁([0, 1], Z) (and thus, in particular, through each L_p(Z), for 1 ≤ p ≤ ) with the same factorization constant. It follows that, for each 1 ≤ p ≤ , the class of L_p spaces is closed under uniform (and even coarse) equivalences. The case p = 1 is new and solves a problem raised by Heinrich and Mankiewicz in 1982. The proof is based on a simple local–global linearization idea.

Ideals of denominators in the disk-algebra

Mortini, R., Sasane, A. — Wed, 22 Jul 2009 09:12:41 PDT

We show that there do not exist finitely generated, non-principal ideals of denominators in the disk-algebra A(D). Our proof involves a new factorization theorem for A(D) that is based on Treil's determination of the Bass stable rank for H.

Diophantine approximation with arithmetic functions, II

Alkan, E., Ford, K., Zaharescu, A. — Wed, 22 Jul 2009 09:12:41 PDT

We prove that real numbers can be well approximated by the normalized Fourier coefficients of newforms.

A brief note on the spectrum of the basic Dirac operator

Habib, G., Richardson, K. — Wed, 22 Jul 2009 09:12:41 PDT

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation (M, F) with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on spin flows in terms of the O’Neill tensor and the first eigenvalue of the Dirac operator on M. We discuss examples and also define a new version of the basic Laplacian whose spectrum does not depend on the choice of bundle-like metric.

Zeros and the universality for the Euler-Zagier-Hurwitz type of multiple zeta-functions

Nakamura, T. — Wed, 22 Jul 2009 09:12:41 PDT

In this paper, we show relations between the zero-free region and the universality for the Euler–Zagier–Hurwitz type of multiple zeta-functions. Roughly speaking these relations imply that we can obtain the universality for the Euler–Zagier–Hurwitz type of multiple zeta-functions by their zero-free property, and vice versa. Moreover, we obtain the non-trivial zeros, joint denseness and functional independence for the Euler–Zagier–Hurwitz type of multiple zeta-functions.

Area of small disks

Croke, C. B. — Wed, 22 Jul 2009 09:12:41 PDT

This paper considers Riemannian metrics on 2-dimensional disks where all geodesics are minimizing. A sharp reverse isoperimetric inequality is proved. This in turn yields near optimal bounds for the area of disks as well as near optimal upper bounds on the first non-zero Neumann eigenvalue of the Laplacian in terms only of the radius.

A Cauchy integral formula in superspace

De Bie, H., Sommen, F. — Wed, 22 Jul 2009 09:12:41 PDT

In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. In this paper a Cauchy integral formula is obtained in this new framework by exploiting techniques from orthogonal Clifford analysis. After introducing Clifford algebra-valued surface- and volume-elements, a purely fermionic Cauchy formula is proved. Combining this formula with the already well-known bosonic Cauchy formula yields the general case. Here the integration over the boundary of a supermanifold is an integration over the even as well as the odd boundary (in a formal way). Finally, some additional results such as a Cauchy–Pompeiu formula and a representation formula for monogenic functions are proved.

A priori analysis of initial data for the Riccati equation and asymptotic properties of its solutions

Chernyavskaya, N. A., Schiff, J., Shuster, L. A. — Wed, 22 Jul 2009 09:12:41 PDT

We obtain two main results for the Cauchy problem where x₀, y₀ R, r > 0, q ≥ 0, 1/r L₁^loc(R), q L₁^loc(R) and (1) For given initial data x₀, y₀ and functions r and q, we give a condition that can be used to determine whether the solution of the problem can be continued to the whole of R. (2) When the solution is defined on an infinite interval, we study its asymptotic properties as the argument tends to infinity.

A criterion of convergence in the augmented Teichmuller space

Mondello, G. — Wed, 22 Jul 2009 09:12:41 PDT

We prove a criterion of convergence in the augmented Teichmüller space that can be phrased in terms of convergence of the hyperbolic metrics or of quasiconformal convergence away from the nodes.

Recovering Baire one functions on ultrametric spaces

Duncan, J., Solecki, S. — Wed, 22 Jul 2009 09:12:41 PDT

We find a characterization of those Polish ultrametric spaces on which each Baire one function is first return recoverable. The notion of pseudo-convergence originating in the theory of valuation fields plays a crucial role in the characterization.

Affine divisibility of convex sets

Richter, C. — Wed, 22 Jul 2009 09:12:41 PDT

A subset C of a linear topological space X is called m-divisible with respect to a group G of affine homeomorphisms of X if there exists a disjoint decomposition of C into m subsets C_i pairwise congruent with respect to G. We ask for the possibility of m-divisibility, mainly for m {2, 3, ...}, in the following cases: (I) G contains all affine homeomorphisms, C is bounded, closed, and convex, and m = 2; (II) X is normed and strictly convex, G consists of all isometries of X, and C is shaped like a ball; and (III) G is the group of translations and C is closed or open and convex. A geometric characterization of the reflexivity of a Banach space is obtained as a corollary.

The fundamental group of a p-compact group

Dwyer, W. G., Wilkerson, C. W. — Thu, 21 May 2009 06:43:59 PDT

We compute the fundamental group of a connected p-compact group in terms of the map from the homology of the classifying space of a maximal torus to the homology of the classifying space of its normalizer.

Intermediate convergents and a metric theorem of Khinchin

Haynes, A. K. — Thu, 21 May 2009 06:43:59 PDT

A landmark theorem in the metric theory of continued fractions begins this way: Select a non-negative real function f defined on the positive integers and a real number x, and form the partial sums s_n of f evaluated at the partial quotients a₁, ..., a_n in the continued fraction expansion for x. Does the sequence {s_n/n} have a limit as n -> ? In 1935 Khinchin proved that the answer is yes for almost every x, provided that the function f does not grow too quickly. In this article we are going to explore a natural reformulation of this problem in which the function f is defined on the rationals and the partial sums in question are over the intermediate convergents to x with denominators less than a prescribed amount. By using some of Khinchin's ideas together with more modern results we are able to provide a quantitative asymptotic theorem analogous to the classical one mentioned above.

Integral means and boundary limits of Dirichlet series

Saksman, E., Seip, K. — Thu, 21 May 2009 06:43:59 PDT

This paper deals with the boundary behaviour of functions in the Hardy spaces ^p for ordinary Dirichlet series. The main result, answering a question of Hedenmalm, shows that the classical Carlson theorem on integral means does not extend to the imaginary axis for functions in , that is, for the ordinary Dirichlet series in H of the right half-plane. We discuss an important embedding problem for ^p, the solution of which is only known when p is an even integer. Viewing ^p as Hardy spaces of the infinite-dimensional polydisc, we also present analogues of Fatou's theorem.

On theta functions of order 4

Kopeliovich, Y., Pauly, C., Serman, O. — Thu, 21 May 2009 06:43:59 PDT

We prove that the fourth powers of theta functions with even characteristics form a basis of the space H⁰(A, O_A(4))₊ of even theta functions of order 4 on a principally polarized Abelian variety (A, ) without a vanishing theta-null.

Fields with measure and automorphism

Tomasic, I. — Thu, 21 May 2009 06:43:59 PDT

We consider a difference field (K, ) such that finite-dimensional definable sets over K can be compared in size, or measured. Let k be the fixed field of the automorphism . We show that curves of genus 1 defined over k are approximately the size of the affine line over k, an ‘approximative version’ of the Riemann hypothesis for curves of genus 1.

The regular part of symmetric forms associated with second-order elliptic differential expressions

Vogt, H. — Thu, 21 May 2009 06:43:59 PDT

Let be a (not necessarily closable) positive symmetric form associated with a second-order elliptic differential expression. We show that the regular part of (in the sense of B. Simon) can be obtained by modifying the coefficients of suitably; in particular, the regular part is again associated with a second-order elliptic differential expression.

Sufficiency of jets with line singularities

Brodersen, H. — Thu, 21 May 2009 06:43:59 PDT

Let z: (R ^{n + 1}, 0) -> (R, 0) be an r-jet with a singular set containing a 1-dimensional manifold L. Let be the set of homeomorphism germs h : (R ^{n + 1}, 0) -> (R ^{n + 1}, 0) leaving L invariant. Let be the set of C^r germs, f : (R ^{n + 1}, 0) -> (R , 0), with singular sets containing L. We say that z is sufficient in if any two f and g in with are -equivalent. In this paper we give necessary and sufficient conditions in terms of Lojasiewicz inequalities for such a jet z to be sufficient in .

Stability of projective Poincare and Picard bundles

Biswas, I., Brambila-Paz, L., Newstead, P. E. — Thu, 21 May 2009 06:43:59 PDT

Let X be an irreducible smooth projective curve of genus g ≥ 3 defined over the complex numbers, and let M denote the moduli space of stable vector bundles on X of rank n and determinant , where is a fixed line bundle of degree d. If n and d have a common divisor, then there is no universal vector bundle on X x M. We prove that there is a projective bundle on X x M with the property that its restriction to X x {E} is isomorphic to P(E) for all E M and that this bundle (called the projective Poincaré bundle) is stable with respect to any polarization; moreover its restriction to {x} x M is also stable for any x X. We also prove stability results for bundles induced from the projective Poincaré bundle by homomorphisms PGL(n) -> H for any reductive H. We further show that there is a projective Picard bundle on a certain open subset M' of M for any d > n(g–1) and that this bundle is also stable. Also, we obtain new results on the stability of the Picard bundle even when n and d are coprime.

Hochschild homology and global dimension

Bergh, P. A., Madsen, D. — Thu, 21 May 2009 06:43:59 PDT

We prove that, for certain classes of graded algebras (Koszul, local and cellular), infinite global dimension implies that Hochschild homology does not vanish in high degrees, provided that the characteristic of the ground field is zero. Our proof uses Igusa's formula relating the Euler characteristic of relative cyclic homology to the graded Cartan determinant.

The generating condition for coalgebras

Iovanov, M. C. — Thu, 21 May 2009 06:44:00 PDT

For a ring R, the properties of being (left) self-injective or being a cogenerator for the left R-modules do not imply one another, and the two combined give rise to the important notion of pseudo-Frobenius-rings. For a coalgebra C, (left) self-projectivity implies that C is a generator for right comodules and the coalgebras with this property are called right quasi-co-Frobenius; however, whether the converse implication is true is an open question. We provide an extensive study of this problem. We show that this implication does not hold, by giving a large class of examples of coalgebras having the ‘generating property’. In fact, we show that any coalgebra C can be embedded in a coalgebra C that generates its right comodules, and, if C is local over an algebraically closed field, then C can be chosen local as well. We also give some general conditions under which the implication ‘C-projective (left) C generator for right comodules’ does work, and such conditions are when C is right semiperfect or when C has finite coradical filtration.

'High spots' theorems for sloshing problems

Kulczycki, T., Kuznetsov, N. — Thu, 21 May 2009 06:44:00 PDT

We investigate several 2D and 3D cases of the classical eigenvalue problem that arises in hydrodynamics and is referred to as the sloshing problem. In particular, for a domain W R² (canal's cross-section), where W = F B and F (cross-section of the free surface of fluid) is an interval of the x-axis, whereas B (bottom's cross-section) is the graph of a negative function, the following result is proved. The fundamental eigenfunction u₁ of the sloshing problem (the corresponding eigenvalue is simple) has monotonic traces on F and B; moreover, u₁ attains its maximum and minimum values at the end-points of F. It is established that for the 2D (3D) ice-fishing problem with a single (circular) hole, the function u₁ (both fundamental eigenfunctions) attains its maximum value at an inner point of F. A relationship between the high spots and hot spots theorems is considered.

Schwarz lemma for the tetrablock

Edigarian, A., Zwonek, W. — Thu, 21 May 2009 06:44:00 PDT

We describe all complex geodesics in the tetrablock passing through the origin thus obtaining the form of all extremals in the Schwarz lemma for the tetrablock. Some other extremals for the Lempert function and geodesics are also given. The paper may be seen as a continuation of the results from Abouhajar et al. [‘A Schwarz lemma for a domain related to mu-synthesis’, J. Geom. Anal. 17 (2007) 717–750]. The proofs rely on a necessary form of complex geodesics in general domains which is also proven in the paper.

The equivariant Euler characteristic of real Coxeter toric varieties

Henderson, A., Lehrer, G. — Thu, 21 May 2009 06:44:00 PDT

Let W be a Weyl group, and let T_W be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of W, and its weight lattice. The real locus T_W(R) is a smooth, connected, compact manifold with a W-action. We give a formula for the equivariant Euler characteristic of T_W(R) as a generalised character of W. In type A_n–1 for n odd, one obtains a generalised character of Sym_n whose degree is (up to sign) the nth Euler number.

On the definition of pseudospectra

Shargorodsky, E. — Thu, 21 May 2009 06:44:00 PDT

It is well known that the -pseudospectrum of a bounded linear operator defined with the help of a strict inequality is equal to the union of the spectra of all perturbed operators with perturbations that have norms strictly less than . The aim of the paper is to show that the same is not true in the case of non-strict inequalities.

Twisted Alexander polynomials and representation shifts

Silver, D. S., Williams, S. G. — Thu, 21 May 2009 06:44:00 PDT

For any knot, the following are equivalent. (1) The infinite cyclic cover has uncountably many finite covers; (2) there exists a finite-image representation of the knot group for which the twisted Alexander polynomial vanishes; (3) the knot group admits a finite-image representation such that the image of the fundamental group of an incompressible Seifert surface is a proper subgroup of the image of the commutator subgroup of the knot group.

Capitulation for locally free class groups of orders of group algebras over number fields

Greither, C., Johnston, H. — Thu, 21 May 2009 06:44:00 PDT

We prove a capitulation result for locally free class groups of orders of group algebras over number fields. This result allows some control over ramification, and so, as a corollary, we obtain an ‘arithmetically disjoint capitulation result’ for the Galois module structure of rings of integers.

Local well-posedness of nonlinear dispersive equations on modulation spaces

Benyi, A., Okoudjou, K. A. — Thu, 21 May 2009 06:44:00 PDT

By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the nonlinear Schrödinger, nonlinear wave and nonlinear Klein–Gordon equations with Cauchy data in modulation spaces M_0,s^p,1.

Centralizers in domains of finite Gelfand-Kirillov dimension

Bell, J. P. — Thu, 21 May 2009 06:44:00 PDT

We study centralizers of elements in domains. We extend a result of the author and Small ‘Centralizers in domains of Gelfand–Kirillov dimension 2’, Bull. London Math. Soc. 36 (2004) 779–785, showing that if A is a finitely generated domain of finite Gelfand–Kirillov (GK) dimension and a A is not algebraic over the extended center of A, then the centralizer of a has GK dimension at most one less than the GK dimension of A. In the case that A is a finitely generated noetherian domain of GK dimension 3 over the complex numbers, we show that the centralizer of an element a A that is not algebraic over the extended center of A satisfies a polynomial identity.

The group of automorphisms of a real rational surface is n-transitive

Huisman, J., Mangolte, F. — Thu, 21 May 2009 06:44:00 PDT

Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-transitively on X, for all natural integers n. As an application we give a new and simpler proof of the fact that two rational nonsingular compact connected real algebraic surfaces are isomorphic if and only if they are homeomorphic as topological surfaces.

Classifying spaces of sporadic groups * (Mathematical Surveys and Monographs 147) * By David J. Benson and Stephen D. Smith: 289 pp., US$85.00, * ISBN 978-0821-84474-8 * (American Mathematical Society, Providence, RI, 2008)

Lazarev, A. — Thu, 21 May 2009 06:44:00 PDT

Quantum groups: A path to current algebra * (Australian Mathematical Society Lecture Series 19) * By Ross Street: 141 pp., {pound}28.99 (US$57.00), ISBN 0-5216-9524-4 * (Cambridge University Press, Cambridge, 2007)

Launois, S. — Thu, 21 May 2009 06:44:00 PDT

Honorary Members 2008

Thu, 21 May 2009 06:44:00 PDT