Showing papers in "Bulletin of The London Mathematical Society in 2014"
TL;DR: In this article, iterated commutators of multilinear Calderon-Zygmund operators and pointwise multiplication with functions in $BMO$ are studied in products of Lebesgue spaces.
Abstract: Iterated commutators of multilinear Calderon-Zygmund operators and pointwise multiplication with functions in $BMO$ are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted results involving the vectors weights of the multilinear Calderon-Zygmund theory recently introduced in the literature. Some better than expected estimates for certain multilinear operators are presented too.
105 citations
86 citations
TL;DR: In this article, Sarkaria and Volovikov introduced a proof technique that combines a concept of Tverberg unavoidable subcomplexes with the observation that Tversberg points that equalize the distance from such a subcomplex can be obtained from maps to an extended target space.
Abstract: Many of the strengthenings and extensions of the topological Tverberg theorem can be derived with surprising ease directly from the original theorem: For this we introduce a proof technique that combines a concept of “Tverberg unavoidable subcomplexes” with the observation that Tverberg points that equalize the distance from such a subcomplex can be obtained from maps to an extended target space. Thus we obtain simple proofs for many variants of the topological Tverberg theorem, such as the colored Tverberg theorem of Živaljevic and Vrecica (1992). We also get a new strengthened version of the generalized van Kampen–Flores theorem by Sarkaria (1991) and Volovikov (1996), an affine version of their “j-wise disjoint” Tverberg theorem, and a topological version of Soberon’s (2013) result on Tverberg points with equal barycentric coordinates.
82 citations
TL;DR: In this paper, the authors use continuous model theory to obtain several results concerning isomorphisms and embeddings between II-1 factors and their ultrapowers, including a poor man's resolution of the Connes embedding problem.
Abstract: We use continuous model theory to obtain several results concerning isomorphisms and embeddings between II_1 factors and their ultrapowers. Among other things, we show that for any II_1 factor M, there are continuum many nonisomorphic separable II_1 factors that have an ultrapower isomorphic to an ultrapower of M. We also give a poor man's resolution of the Connes Embedding Problem: there exists a separable II_1 factor such that all II_1 factors embed into one of its ultrapowers.
78 citations
TL;DR: In this article, the boundedness and compactness of weighted composition operators on the Fock space over C were characterized. But the characterizations were restricted to normal or isometric composition operators.
Abstract: We obtain new and simple characterizations for the boundedness and compactness of weighted composition operators on the Fock space over C. We also describe all weighted composition operators that are normal or isometric.
76 citations
TL;DR: In this article, a generalized Bogomolov-Gieseker inequality for the smooth quadric was shown to imply the existence of a family of Bridgeland stability conditions.
Abstract: We prove a generalized Bogomolov-Gieseker inequality as conjectured by Bayer, Macri and Toda for the smooth quadric threefold. This implies the existence of a family of Bridgeland stability conditions.
49 citations
45 citations
TL;DR: In this article, the authors define and study a notion of discrete homology theory for metric spaces, which is related to the discrete homotopy theory of a metric space through a discrete analogue of the Hurewicz theorem.
Abstract: We define and study a notion of discrete homology theory for metric spaces. Instead of working with simplicial homology, our chain complexes are given by Lipschitz maps from an n
n
-dimensional cube to a fixed metric space. We prove that the resulting homology theory satisfies a discrete analogue of the Eilenberg–Steenrod axioms, and prove a discrete analogue of the Mayer–Vietoris exact sequence. Moreover, this discrete homology theory is related to the discrete homotopy theory of a metric space through a discrete analogue of the Hurewicz theorem. We study the class of groups that can arise as discrete homology groups and, in this setting, we prove that the fundamental group of a smooth, connected, metrizable, compact manifold is isomorphic to the discrete fundamental group of a ‘fine enough’ rectangulation of the manifold. Finally, we show that this discrete homology theory can be coarsened, leading to a new non-trivial coarse invariant of a metric space.
44 citations
TL;DR: In this paper, the R∞ property of free nilpotent groups of a given class and of finite rank was shown for groups with finite rank and a certain derived length.
Abstract: Let F be either a free nilpotent group of a given class and of finite rank or a free solvable group of a certain derived length and of finite rank. We show precisely which ones have the R∞ property. Finally, we also show that the free group of infinite rank does not have the R∞ property.
43 citations
TL;DR: The minimal innitesimal rigidity of bar-joint frameworks in the non-Euclidean spaces (R2, ||q) is characterised in terms of (2, 2)-tight graphs as mentioned in this paper.
Abstract: The minimal innitesimal rigidity of bar-joint frameworks in the non-Euclidean spaces (R2, ||.||q) are characterised in terms of (2,2)-tight graphs. Specifically, a generically placed bar-joint framework (G,p) in the plane is minimally infinitesimally rigid with respect to a non-Euclidean lq norm if and only if the underlying graph G = (V,E) contains 2|V|-2 edges and every subgraph H = (V (H),E(H)) contains at most 2|V(H)|-2 edges.
39 citations
TL;DR: In this article, an algorithm was proposed to decide whether or not a given automorphism is an irreducible automomorphism, given a fixed number of parameters, where n = 2.
Abstract: We produce an algorithm that, given $\phi\in Out(F_N)$, where $N\ge 2$, decides wether or not $\phi$ is an iwip ("fully irreducible") automorphism.
TL;DR: In this paper, it was shown that any standard parabolic subgroup of any Artin group is convex with respect to the standard generating set, and that any subgroup with a convex subgroup is also convex.
Abstract: We prove that any standard parabolic subgroup of any Artin group is convex with respect to the standard generating set.
TL;DR: The problem of determining when an integral quadratic form represents every positive integer has received much attention in recent years, culminating in the 15 and 290 Theorems of Bhargava-Conway-Schneeberger.
Abstract: The problem of determining when an integral quadratic form represents every positive integer has received much attention in recent years, culminating in the 15 and 290 Theorems of Bhargava-Conway-Schneeberger and Bhargava-Hanke. For ternary quadratic forms, there are always local obstructions, but one may ask whether there are ternary quadratic forms which represent every locally represented integer. Indeed, such forms exist and are called regular, and Jagy, Kaplansky, and Schiemann proved that there are at most 913; however, only 899 of these are actually known to be regular. We consider the remaining 14 forms, and establish the regularity of each under the generalized Riemann Hypothesis, following the method pioneered by Ono and Soundararajan. Moreover, we consider the exceptional arithmetic consequences if a large, locally represented integer is not globally represented by a ternary quadratic form, proving that some Dirichlet L-function would necessarily have a Siegel zero or that some quadratic twist of an elliptic curve would have an unusally large Tate-Shafarevich group.
TL;DR: This paper showed that the excellence axiom in the definition of Zilber's quasiminimal excellent classes is redundant, in that it follows from the other axioms.
Abstract: We show that the excellence axiom in the definition of Zilber's quasiminimal excellent classes is redundant, in that it follows from the other axioms. This substantially simplifies a number of categoricity proofs.
TL;DR: In this article, the authors proved the Zariski-Lipman conjecture for log canonical spaces, and proved the same conjecture for non-canonical spaces as well, in the sense that
Abstract: In this paper we prove the Zariski-Lipman conjecture for log canonical spaces.
TL;DR: In this article, it was shown that for a p-adic analytic self-map f on a closed unit polydisk, if every coefficient of f(x)-x has valuation greater than that of p 1/(p-1), then the iterates of f can be p-adically interpolated.
Abstract: Extending work of Bell and of Bell, Ghioca, and Tucker, we prove that for a p-adic analytic self-map f on a closed unit polydisk, if every coefficient of f(x)-x has valuation greater than that of p^{1/(p-1)}, then the iterates of f can be p-adically interpolated; i.e., there exists a function g(x,n) analytic in both x and n such that g(x,n) = f^n(x) whenever n is a nonnegative integer.
TL;DR: In this paper, the results of Ax and Konenigmann are generalized to a Henselian valuation ring with a convex p-regular subgroup that is not p-divisible.
Abstract: On a Henselian valued field (K, V), where V is the valuation ring, if the value group contains a convex p-regular subgroup that is not p-divisible, then V is definable in the language of rings. A Henselian valuation ring with a regular non-divisible value group is always 0-definable. In particular, some results of Ax and of Konenigmann are generalized.
TL;DR: In this paper, several one-parameter families of explicit self-similar solutions are constructed for the porous medium equations with fractional operators, also called Barenblatt profiles.
Abstract: Several one-parameter families of explicit self-similar solutions are constructed for the porous medium equations with fractional operators. The corresponding self-similar profiles, also called Barenblatt profiles, have the same forms as those of the classic porous medium equations. These new exact solutions complement current theoretical analysis of the underlying equations and are expected to provide insights for further quantitative investigations.
TL;DR: Lalin et al. as mentioned in this paper, 2013, ACTA MATH HUNG, V138, P85, DOI 10.1112-blms-2.2.
Abstract: [Anonymous], 2008, VERS 2 3 4; Berndt B. C., 1985, RAMANUJANS NOTEBOO 2; Cohn A, 1922, MATH Z, V14, P110, DOI 10.1007-BF01215894; Conrey JB, 2013, INT MATH RES NOTICES, P4758, DOI 10.1093-imrn-rns183; GOSH A., 2012, J EUR MATH SOC, V14, P465; Grosswald E., 1970, NACHR AKAD WISS G MP, VII, P9; Gun S, 2011, B LOND MATH SOC, V43, P939, DOI 10.1112-blms-bdr031; Holowinsky R., 2010, ANN MATH, V172, P85; Kohnen W., 2004, KYUSHU J MATH, V58, P251, DOI 10.2206-kyushujm.58.251; Kohnen W., 1984, E HORWOOD SER MATH A, P197; Lalin MN, 2013, ACTA MATH HUNG, V138, P85, DOI 10.1007-s10474-012-0225-4; Lalin MN, 2013, FUNCT APPROX COMM MA, V48, P91, DOI 10.7169-facm-2013.48.1.7; Murty MR, 2011, J RAMANUJAN MATH SOC, V26, P107; Rankin F. K. C., 1970, B LOND MATH SOC, V2, P169, DOI 10.1112-blms-2.2.169; ZAGIER D, 1991, INVENT MATH, V104, P449, DOI 10.1007-BF01245085
TL;DR: In this paper, it was shown that if the average of the degrees of the irreducible characters of a finite group G is less than 16/5, then G is solvable.
Abstract: We prove that if the average of the degrees of the irreducible characters of a finite group G is less than 16/5, then G is solvable. This solves a conjecture of I. M. Isaacs, M. Loukaki and the first author. We discuss related questions.
TL;DR: In this article, it was shown that a finite group in which any two nontrivial p-elements are conjugate has Sylow p-subgroups which are either elementary abelian or extraspecial of order p and exponent p.
Abstract: We prove that a finite group in which any two nontrivial p-elements are conjugate have Sylow p-subgroups which are either elementary abelian or extraspecial of order p and exponent p.
TL;DR: In this article, the authors introduced the notion of front Sm-spinning for Legendrian submanifolds of R2n+1 and proved that there are infinitely many pairs of exact Lagrangian cobordant and not pairwise Legendrian isotopic S1×Si1×…×Sik which have the same classical invariants if one of the ij is odd.
Abstract: In this paper, we introduce a notion of front Sm-spinning for Legendrian submanifolds of R2n+1. It generalizes the notion of front S1-spinning which was invented by Ekholm, Etnyre and Sullivan. We use it to prove that there are infinitely many pairs of exact Lagrangian cobordant and not pairwise Legendrian isotopic Legendrian S1×Si1×…×Sik which have the same classical invariants if one of the ij is odd.
TL;DR: In this article, Hotz and Huckemann showed that the Central Limit Theorem holds for any complete and connected Riemannian manifold, assuming that there are at least two minimal geodesics between the Frechet mean and any point in its cut locus.
Abstract: One of the fundamental differences between the Central Limit Theorem for empirical Frechet means obtained in [Kendall and Le, ‘Limit theorems for empirical Frechet means of independent and non‐identically distributed manifold‐valued random variables’, Braz. J. Probab. Stat. 25 (2011) 323–352] and that for empirical Euclidean means lies on the assumption that the probability measure of the cut locus of the true Frechet mean is zero. In [Hotz and Huckemann, ‘Intrinsic means on the circle: uniqueness, locus and asymptotics’, Preprint, 2011, arXiv:1108.2141v1], the authors show that, in the case of a circle, this assumption holds automatically. This paper shows that this holds for any complete and connected Riemannian manifold, assuming that there are at least two minimal geodesics between the Frechet mean and any point in its cut locus and that, in fact, it can also be generalized to local minima of the
TL;DR: In this paper, it was shown that for any compact Lie group G with identity component N and component group W = G/N, the category of free rational G-spectra is equivalent to the class of torsion modules over the twisted group ring H ∗ (BN)[W].
Abstract: We show that for any compact Lie group G with identity component N and component group W = G/N, the category of free rational G-spectra is equivalent to the category of torsion modules over the twisted group ring H ∗ (BN)[W]. This gives an algebraic classification of rational G-equivariant cohomology theories on free G-spaces and a practical method for calculating the groups of natural transformations between them.
TL;DR: In this article, a classification of surface homeomorphisms via the dynamics of the corresponding mapping class elements on Teichmuller space is presented. But this classification is restricted to random products of homeomorphism and not to holomorphic self-maps.
Abstract: Thurston obtained a classification of individual surface homeomorphisms via the dynamics of the corresponding mapping class elements on Teichmuller space. In this paper we present certain extended versions of this, first, to random products of homeomorphisms and second, to holomorphic self-maps of Teichmuller spaces.
TL;DR: In this paper, the authors established local-to-global results for a function space which is larger than the well-known bounded mean oscillation space, and was also introduced by John and Nirenberg.
Abstract: We establish local-to-global results for a function space which is larger than the well-known bounded mean oscillation space, and was also introduced by John and Nirenberg
TL;DR: In this paper, it was shown that the maximal subfield spectrum of a division algebra does not necessarily determine the isomorphism class of a quaternion division algebra over some fields.
Abstract: To what extent does the maximal subfield spectrum of a division algebra determine the isomorphism class of that algebra? It has been shown that over some fields a quaternion division algebra's isomorphism class is largely if not entirely determined by its maximal subfield spectrum. However in this paper, we show that there are fields for which the maximal subfield spectrum says little to nothing about a quaternion division algebra's isomorphism class. We give an explicit construction of a division algebra with infinite genus. Along the way we introduce the notion of a "linking field extension," which we hope will be of independent interest. We go on to show that there exists a field K for which (1) there are infinitely many nonisomorphic quaternion division algebras with center K, and (2) any two quaternion division algebra with center K are pairwise weakly isomorphic. In fact we show that there are infinitely many nonisomorphic fields satisfying these two conditions.
TL;DR: In this paper, it was shown that given a finite idempotent algebra A in a finite language, there is a polynomial-time algorithm that determines whether the variety generated by A is n-permutable.
Abstract: One of the important classes of varieties identified in tame congruence theory is the class of varieties which are n-permutable for some n .I n this paper, we prove two results: (1) for every n> 1, there is a polynomial-time algorithm that, given a finite idempotent algebra A in a finite language, determines whether the variety generated by A is n-permutable and (2) a variety is npermutable for some n if and only if it interprets an idempotent variety that is not interpretable in the variety of distributive lattices.
TL;DR: In this paper, the authors established a slow divergence counterpart of their result for a non-negative function, where the inequality is the set of real numbers for which the inequality holds.
Abstract: For a non-negative function $\psi: ~ \N \mapsto \R$, let $W(\psi)$ denote the set of real numbers $x$ for which the inequality $|n x - a| 0$}. $$ In the present note we establish a \emph{slow divergence} counterpart of their result: $W(\psi)$ has full measure, provided\eqref{dsccond} holds and additionally there exists some $c>0$ such that $$ \sum_{n=2^{2^h}+1}^{2^{2^{h+1}}} \frac{\psi(n) \varphi(n)}{n} \leq \frac{c}{h} \qquad \textrm{for all \quad $h \geq 1$.} $$