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  Subjects -> MATHEMATICS (Total: 864 journals)
    - APPLIED MATHEMATICS (68 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (643 journals)
    - MATHEMATICS (GENERAL) (40 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (75 journals)

MATHEMATICS (643 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 20)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 4)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 15)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access  
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Analysis & Computational Mathematics     Hybrid Journal   (Followers: 5)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 1)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 5)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Advances in Mathematics
  [SJR: 3.261]   [H-I: 65]   [10 followers]  Follow
    
   Full-text available via subscription Subscription journal  (Not entitled to full-text)
   ISSN (Print) 0001-8708 - ISSN (Online) 1090-2082
   Published by Elsevier Homepage  [3043 journals]
  • Subcritical approach to sharp Hardy–Littlewood–Sobolev type
           inequalities on the upper half space
    • Authors: Jingbo Dou; Qianqiao Guo; Meijun Zhu
      Pages: 1 - 45
      Abstract: Publication date: 25 May 2017
      Source:Advances in Mathematics, Volume 312
      Author(s): Jingbo Dou, Qianqiao Guo, Meijun Zhu
      In this paper we establish the reversed sharp Hardy–Littlewood–Sobolev (HLS for short) inequality on the upper half space and obtain a new HLS type integral inequality on the upper half space (extending an inequality found by Hang, Wang and Yan in [6]) by introducing a uniform approach. The extremal functions are classified via the method of moving spheres, and the best constants are computed. The new approach can also be applied to obtain the classical HLS inequality and other similar inequalities.

      PubDate: 2017-03-25T07:04:46Z
      DOI: 10.1016/j.aim.2017.03.007
      Issue No: Vol. 312 (2017)
       
  • Brill–Noether varieties of k-gonal curves
    • Authors: Nathan Pflueger
      Pages: 46 - 63
      Abstract: Publication date: 25 May 2017
      Source:Advances in Mathematics, Volume 312
      Author(s): Nathan Pflueger
      We consider a general curve of fixed gonality k and genus g. We propose an estimate ρ ‾ g , k ( d , r ) for the dimension of the variety W d r ( C ) of special linear series on C, by solving an analogous problem in tropical geometry. Using work of Coppens and Martens, we prove that this estimate is exactly correct if k ≥ 1 5 g + 2 , and is an upper bound in all other cases. We also completely characterize the cases in which W d r ( C ) has the same dimension as for a general curve of genus g.

      PubDate: 2017-03-25T07:04:46Z
      DOI: 10.1016/j.aim.2017.01.027
      Issue No: Vol. 312 (2017)
       
  • Crossed S-matrices and character sheaves on unipotent groups
    • Authors: Tanmay Deshpande
      Pages: 64 - 106
      Abstract: Publication date: 25 May 2017
      Source:Advances in Mathematics, Volume 312
      Author(s): Tanmay Deshpande
      Let k be the algebraic closure of a finite field F q of characteristic p. Let G be a connected unipotent group over k equipped with an F q -structure given by a Frobenius map F : G ⟶ G . We will denote the corresponding algebraic group defined over F q by G 0 . Character sheaves on G are certain special objects in the triangulated braided monoidal category D G ( G ) of bounded conjugation equivariant Q ‾ l -complexes (where l ≠ p is a prime number) on G. Boyarchenko has proved that the “trace of Frobenius” functions associated with F-stable character sheaves on G form an orthonormal basis of the space of class functions on G 0 ( F q ) and that the matrix relating this basis to the basis formed by the irreducible characters of G 0 ( F q ) is block diagonal with “small” blocks. In particular, there is a partition of the set of character sheaves as well as a partition of the set of irreducible characters of G 0 ( F q ) into “small” families known as L -packets. In this paper we describe these block matrices relating character sheaves and irreducible characters corresponding to each L -packet. We prove that these matrices can be described as certain “crossed S-matrices” associated with each L -packet. We will also derive a formula for the dimensions of the irreducible representations of G 0 ( F q ) in terms of certain modular categorical data associated with the corresponding L -packet. In fact we will formulate and prove more general results which hold for possibly disconnected groups G such that G ∘ is unipotent. To prove our results, we will establish a formula (which holds for any algebraic group G) which expresses the inner product of the “trace of Frobenius” function of any F-stable object of D G ( G ) with any character of G 0 ( F q ) (or of any of its pure inner forms) in terms of certain categorical operations.

      PubDate: 2017-03-25T07:04:46Z
      DOI: 10.1016/j.aim.2017.03.013
      Issue No: Vol. 312 (2017)
       
  • Essential bases and toric degenerations arising from birational sequences
    • Authors: Xin Fang; Ghislain Fourier; Peter Littelmann
      Pages: 107 - 149
      Abstract: Publication date: 25 May 2017
      Source:Advances in Mathematics, Volume 312
      Author(s): Xin Fang, Ghislain Fourier, Peter Littelmann
      We present a new approach to construct T-equivariant flat toric degenerations of flag varieties and spherical varieties, combining ideas coming from the theory of Newton–Okounkov bodies with ideas originally stemming from PBW-filtrations. For each pair ( S , > ) consisting of a birational sequence and a monomial order, we attach to the affine variety G / / U a monoid Γ = Γ ( S , > ) . As a side effect we get a vector space basis B Γ of C [ G / / U ] , the elements being indexed by Γ. The basis B Γ has multiplicative properties very similar to those of the dual canonical basis. This makes it possible to transfer the methods of Alexeev and Brion [1] to this more general setting, once one knows that the monoid Γ is finitely generated and saturated.

      PubDate: 2017-03-25T07:04:46Z
      DOI: 10.1016/j.aim.2017.03.014
      Issue No: Vol. 312 (2017)
       
  • Rationally isomorphic hermitian forms and torsors of some non-reductive
           groups
    • Authors: Eva Bayer-Fluckiger; Uriya A. First
      Pages: 150 - 184
      Abstract: Publication date: 25 May 2017
      Source:Advances in Mathematics, Volume 312
      Author(s): Eva Bayer-Fluckiger, Uriya A. First
      Let R be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an R-algebra with involution, which are rationally isomorphic and have isomorphic semisimple coradicals, are in fact isomorphic. The same result is also obtained for quadratic forms equipped with an action of a finite group. The results have cohomological restatements that resemble the Grothendieck–Serre conjecture, except the group schemes involved are not reductive. We show that these group schemes are closely related to group schemes arising in Bruhat–Tits theory.

      PubDate: 2017-03-25T07:04:46Z
      DOI: 10.1016/j.aim.2017.03.012
      Issue No: Vol. 312 (2017)
       
  • Finite topology minimal surfaces in homogeneous three-manifolds
    • Authors: William H. Meeks; Joaquín Pérez
      Pages: 185 - 197
      Abstract: Publication date: 25 May 2017
      Source:Advances in Mathematics, Volume 312
      Author(s): William H. Meeks, Joaquín Pérez
      We prove that any complete, embedded minimal surface M with finite topology in a homogeneous three-manifold N has positive injectivity radius. When one relaxes the condition that N be homogeneous to that of being locally homogeneous, then we show that the closure of M has the structure of a minimal lamination of N. As an application of this general result we prove that any complete, embedded minimal surface with finite genus and a countable number of ends is compact when the ambient space is S 3 equipped with a homogeneous metric of nonnegative scalar curvature.

      PubDate: 2017-03-25T07:04:46Z
      DOI: 10.1016/j.aim.2017.03.015
      Issue No: Vol. 312 (2017)
       
  • A topological transformation group without non-trivial equivariant
           compactifications
    • Authors: Vladimir G. Pestov
      Pages: 1 - 17
      Abstract: Publication date: 30 April 2017
      Source:Advances in Mathematics, Volume 311
      Author(s): Vladimir G. Pestov
      There is a countable metrizable group acting continuously on the space of rationals in such a way that the only equivariant compactification of the space is a singleton. This is obtained by a recursive application of a construction due to Megrelishvili, which is a metric fan equipped with a certain group of homeomorphisms. The question of existence of a topological transformation group with the property in the title was asked by Yu.M. Smirnov in the 1980s.

      PubDate: 2017-03-05T13:58:42Z
      DOI: 10.1016/j.aim.2017.02.023
      Issue No: Vol. 311 (2017)
       
  • Linear stability of compressible vortex sheets in two-dimensional
           elastodynamics
    • Authors: Robin Ming Chen; Jilong Hu; Dehua Wang
      Pages: 18 - 60
      Abstract: Publication date: 30 April 2017
      Source:Advances in Mathematics, Volume 311
      Author(s): Robin Ming Chen, Jilong Hu, Dehua Wang
      The linear stability of rectilinear compressible vortex sheets is studied for two-dimensional isentropic elastic flows. This problem has a free boundary and the boundary is characteristic. A necessary and sufficient condition is obtained for the linear stability of the rectilinear vortex sheets. More precisely, it is shown that, besides the stable supersonic zone, the elasticity exerts an additional stable subsonic zone. We also find that there is a class of states in the interior of subsonic zone where the stability of such states is weaker than the stability of other states in the sense that there is an extra loss of tangential derivatives with respect to the source terms. This is a new feature that the Euler flow does not possess. One of the difficulties for the elastic flow is that the non-differentiable points of the eigenvalues may coincide with the roots of the Lopatinskii determinant. As a result, the Kreiss symmetrization cannot be applied directly. Instead, we perform an upper triangularization of the system to separate only the outgoing modes at all points in the frequency space, so that an exact estimate of the outgoing modes can be obtained. Moreover, all the outgoing modes are shown to be zero due to the L 2 -regularity of solutions. The estimates for the incoming modes can be derived directly from the Lopatinskii determinant. This new approach avoids the lengthy computation and estimates for the outgoing modes when Kreiss symmetrization is applied. This method can also be applied to the Euler flow and MHD flow.

      PubDate: 2017-03-05T13:58:42Z
      DOI: 10.1016/j.aim.2017.02.014
      Issue No: Vol. 311 (2017)
       
  • Semisimple Hopf algebras via geometric invariant theory
    • Authors: Ehud Meir
      Pages: 61 - 90
      Abstract: Publication date: 30 April 2017
      Source:Advances in Mathematics, Volume 311
      Author(s): Ehud Meir
      We study Hopf algebras via tools from geometric invariant theory. We show that all the invariants we get can be constructed using the integrals of the Hopf algebra and its dual together with the multiplication and the comultiplication, and that these invariants determine the isomorphism class of the Hopf algebra. We then define certain canonical subspaces I n v i , j of tensor powers of H and H ⁎ , and use the invariant theory to prove that these subspaces satisfy a certain non-degeneracy condition. Using this non-degeneracy condition together with results on symmetric monoidal categories, we prove that the spaces I n v i , j can also be described as ( H ⊗ i ⊗ ( H ⁎ ) ⊗ j ) A , where A is the group of Hopf automorphisms of H. As a result we prove that the number of possible Hopf orders of any semisimple Hopf algebra over a given number ring is finite. We give some examples of these invariants arising from the theory of Frobenius–Schur Indicators, and from Reshetikhin–Turaev invariants of three manifolds. We give a complete description of the invariants for a group algebra, proving that they all encode the number of homomorphisms from some finitely presented group to the group. We also show that if all the invariants are algebraic integers, then the Hopf algebra satisfies Kaplansky's sixth conjecture: the dimensions of the irreducible representations of H divide the dimension of H.

      PubDate: 2017-03-05T13:58:42Z
      DOI: 10.1016/j.aim.2017.02.020
      Issue No: Vol. 311 (2017)
       
  • Dimensional homotopy t-structures in motivic homotopy theory
    • Authors: Mikhail Bondarko; Frédéric Déglise
      Pages: 91 - 189
      Abstract: Publication date: 30 April 2017
      Source:Advances in Mathematics, Volume 311
      Author(s): Mikhail Bondarko, Frédéric Déglise
      The aim of this work is to construct certain homotopy t-structures on various categories of motivic homotopy theory, extending works of Voevodsky, Morel, Déglise and Ayoub. We prove these t-structures possess many good properties, some analogous to those of the perverse t-structure of Beilinson, Bernstein and Deligne. We compute the homology of certain motives, notably in the case of relative curves. We also show that the hearts of these t-structures provide convenient extensions of the theory of homotopy invariant sheaves with transfers, extending some of the main results of Voevodsky. These t-structures are closely related to Gersten weight structures as defined by Bondarko.

      PubDate: 2017-03-05T13:58:42Z
      DOI: 10.1016/j.aim.2017.02.003
      Issue No: Vol. 311 (2017)
       
  • Differentiability of Lq-spectrum and multifractal decomposition by using
           infinite graph-directed IFSs
    • Authors: Guotai Deng; Sze-Man Ngai
      Pages: 190 - 237
      Abstract: Publication date: 30 April 2017
      Source:Advances in Mathematics, Volume 311
      Author(s): Guotai Deng, Sze-Man Ngai
      By constructing an infinite graph-directed iterated function system associated with a finite iterated function system, we develop a new approach for proving the differentiability of the L q -spectrum and establishing the multifractal formalism of certain self-similar measures with overlaps, especially those defined by similitudes with different contraction ratios. We apply our technique to a well-known class of self-similar measures of generalized finite type.

      PubDate: 2017-03-05T13:58:42Z
      DOI: 10.1016/j.aim.2017.02.021
      Issue No: Vol. 311 (2017)
       
  • On Fujita's spectrum conjecture
    • Authors: Gabriele Di Cerbo
      Pages: 238 - 248
      Abstract: Publication date: 30 April 2017
      Source:Advances in Mathematics, Volume 311
      Author(s): Gabriele Di Cerbo
      We prove Fujita's spectrum conjecture on the discreteness of pseudo-effective thresholds for polarized varieties.

      PubDate: 2017-03-10T14:10:08Z
      DOI: 10.1016/j.aim.2017.02.018
      Issue No: Vol. 311 (2017)
       
  • Möbius curvature, Laguerre curvature and Dupin hypersurface
    • Authors: Tongzhu Li; Jie Qing; Changping Wang
      Pages: 249 - 294
      Abstract: Publication date: 30 April 2017
      Source:Advances in Mathematics, Volume 311
      Author(s): Tongzhu Li, Jie Qing, Changping Wang
      In this paper we show that a Dupin hypersurface with constant Möbius curvatures is Möbius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere. We also show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre equivalent to a flat Laguerre isoparametric hypersurface. These results solve the major issues related to the conjectures of Cecil et al. on the classification of Dupin hypersurfaces.

      PubDate: 2017-03-10T14:10:08Z
      DOI: 10.1016/j.aim.2017.02.024
      Issue No: Vol. 311 (2017)
       
  • Non-unitary fusion categories and their doubles via endomorphisms
    • Authors: David E. Evans; Terry Gannon
      Pages: 1 - 43
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): David E. Evans, Terry Gannon
      We realise non-unitary fusion categories using subfactor-like methods, and compute their quantum doubles and modular data. For concreteness we focus on generalising the Haagerup–Izumi family of Q-systems. For example, we construct endomorphism realisations of the (non-unitary) Yang–Lee model, and non-unitary analogues of one of the even subsystems of the Haagerup subfactor and of the Grossman–Snyder system. We supplement Izumi's equations for identifying the half-braidings, which were incomplete even in his Q-system setting. We conjecture a remarkably simple form for the modular S and T matrices of the doubles of these fusion categories. We would expect all of these doubles to be realised as the category of modules of a rational VOA and conformal net of factors. We expect our approach will also suffice to realise the non-semisimple tensor categories arising in logarithmic conformal field theories.

      PubDate: 2017-02-07T01:49:43Z
      DOI: 10.1016/j.aim.2017.01.015
      Issue No: Vol. 310 (2017)
       
  • Polynomial degree bounds for matrix semi-invariants
    • Authors: Harm Derksen; Visu Makam
      Pages: 44 - 63
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Harm Derksen, Visu Makam
      We study the left–right action of SL n × SL n on m-tuples of n × n matrices with entries in an infinite field K. We show that invariants of degree n 2 − n define the null cone. Consequently, invariants of degree ≤ n 6 generate the ring of invariants if char ( K ) = 0 . We also prove that for m ≫ 0 , invariants of degree at least n ⌊ n + 1 ⌋ are required to define the null cone. We generalize our results to matrix invariants of m-tuples of p × q matrices, and to rings of semi-invariants for quivers. For the proofs, we use new techniques such as the regularity lemma by Ivanyos, Qiao and Subrahmanyam, and the concavity property of the tensor blow-ups of matrix spaces. We will discuss several applications to algebraic complexity theory, such as a deterministic polynomial time algorithm for non-commutative rational identity testing, and the existence of small division-free formulas for non-commutative polynomials.

      PubDate: 2017-02-07T01:49:43Z
      DOI: 10.1016/j.aim.2017.01.018
      Issue No: Vol. 310 (2017)
       
  • Fundamental group functors in descent-exact homological categories
    • Authors: Mathieu Duckerts-Antoine
      Pages: 64 - 120
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Mathieu Duckerts-Antoine
      We study the notion of a fundamental group in the framework of descent-exact homological categories. This setting is sufficiently large to include several categories of “algebraic” nature such as almost abelian categories, semi-abelian categories, and categories of topological semi-abelian algebras. For many adjunctions in this context, we describe the fundamental groups by generalised Brown–Ellis–Hopf formulae for the integral homology of groups.

      PubDate: 2017-02-13T09:31:38Z
      DOI: 10.1016/j.aim.2017.02.001
      Issue No: Vol. 310 (2017)
       
  • Convergence criteria for FIW-algebras and polynomial statistics on maximal
           tori in type B/C
    • Authors: Rita Jiménez Rolland; Jennifer C.H. Wilson
      Pages: 121 - 158
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Rita Jiménez Rolland, Jennifer C.H. Wilson
      A result of Lehrer describes a beautiful relationship between topological and combinatorial data on certain families of varieties with actions of finite reflection groups. His formula relates the cohomology of complex varieties to point counts on associated varieties over finite fields. Church, Ellenberg, and Farb use their representation stability results on the cohomology of flag manifolds, together with classical results on the cohomology rings, to prove asymptotic stability for “polynomial” statistics on associated varieties over finite fields. In this paper we investigate the underlying algebraic structure of these families' cohomology rings that makes the formulas convergent. We prove that asymptotic stability holds in general for subquotients of FI W -algebras finitely generated in degree at most one, a result that is in a sense sharp. As a consequence, we obtain convergence results for polynomial statistics on the set of maximal tori in Sp 2 n ( F q ‾ ) and SO 2 n + 1 ( F q ‾ ) that are invariant under the Frobenius morphism. Our results also give a new proof of the stability theorem for invariant maximal tori in GL n ( F q ‾ ) due to Church–Ellenberg–Farb.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.01.029
      Issue No: Vol. 310 (2017)
       
  • Foliations, orders, representations, L-spaces and graph manifolds
    • Authors: Steven Boyer; Adam Clay
      Pages: 159 - 234
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Steven Boyer, Adam Clay
      We show that the properties of admitting a co-oriented taut foliation and having a left-orderable fundamental group are equivalent for rational homology 3-sphere graph manifolds and relate them to the property of not being a Heegaard–Floer L-space. This is accomplished in several steps. First we show how to detect families of slopes on the boundary of a Seifert fibred manifold in four different fashions—using representations, using left-orders, using foliations, and using Heegaard–Floer homology. Then we show that each method of detection determines the same family of detected slopes. Next we provide necessary and sufficient conditions for the existence of a co-oriented taut foliation on a graph manifold rational homology 3-sphere, respectively a left-order on its fundamental group, which depend solely on families of detected slopes on the boundaries of its pieces. The fact that Heegaard–Floer methods can be used to detect families of slopes on the boundary of a Seifert fibred manifold combines with certain conjectures in the literature to suggest an L-space gluing theorem for rational homology 3-sphere graph manifolds as well as other interesting problems in Heegaard–Floer theory.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.01.026
      Issue No: Vol. 310 (2017)
       
  • Automorphisms of smooth canonically polarized surfaces in positive
           characteristic
    • Authors: Nikolaos Tziolas
      Pages: 235 - 289
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Nikolaos Tziolas
      This paper investigates the geometry of a smooth canonically polarized surface X defined over an algebraically closed field of characteristic p > 0 in the case when the automorphism scheme of X is not smooth. In particular, it is shown that a smooth canonically polarized surface X with 1 ≤ K X 2 ≤ 2 and non-smooth automorphism scheme tends to be uniruled and simply connected and is the purely inseparable quotient of a ruled or rational surface by a rational vector field. Moreover, restrictions on certain numerical invariants of X are obtained in order for Aut ( X ) to be smooth.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.002
      Issue No: Vol. 310 (2017)
       
  • Connection coefficients for classical orthogonal polynomials of several
           variables
    • Authors: Plamen Iliev; Yuan Xu
      Pages: 290 - 326
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Plamen Iliev, Yuan Xu
      Connection coefficients between different orthonormal bases satisfy two discrete orthogonal relations themselves. For classical orthogonal polynomials whose weights are invariant under the action of the symmetric group, connection coefficients between a basis consisting of products of hypergeometric functions and another basis obtained from the first one by applying a permutation are studied. For the Jacobi polynomials on the simplex, it is shown that the connection coefficients can be expressed in terms of Tratnik's multivariable Racah polynomials and their weights. This gives, in particular, a new interpretation of the hidden duality between the variables and the degree indices of the Racah polynomials, which lies at the heart of their bispectral properties. These techniques also lead to explicit formulas for connection coefficients of Hahn and Krawtchouk polynomials of several variables, as well as for orthogonal polynomials on balls and spheres.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.01.028
      Issue No: Vol. 310 (2017)
       
  • Stokes geometry of higher order linear ordinary differential equations and
           middle convolution
    • Authors: Takahiro Moteki; Yoshitsugu Takei
      Pages: 327 - 376
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Takahiro Moteki, Yoshitsugu Takei
      The middle convolution, introduced by Katz and developed by Dettweiler–Reiter, Oshima and others, defines an operation of reduction of linear ordinary differential equations with polynomial coefficients. In this paper, employing an idea of the exact steepest descent method proposed by Aoki–Kawai–Takei, we study how to determine the complete Stokes geometry and how to obtain the Borel summability of WKB solutions of a higher order linear ordinary differential equation with a large parameter when it is reduced to a second order equation via middle convolution. To show the practical usefulness of the method, we also investigate some concrete examples numerically.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.006
      Issue No: Vol. 310 (2017)
       
  • Goldilocks domains, a weak notion of visibility, and applications
    • Authors: Gautam Bharali; Andrew Zimmer
      Pages: 377 - 425
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Gautam Bharali, Andrew Zimmer
      In this paper we introduce a new class of domains in complex Euclidean space, called Goldilocks domains, and study their complex geometry. These domains are defined in terms of a lower bound on how fast the Kobayashi metric grows and an upper bound on how fast the Kobayashi distance grows as one approaches the boundary. Strongly pseudoconvex domains and weakly pseudoconvex domains of finite type always satisfy this Goldilocks condition, but we also present families of Goldilocks domains that have low boundary regularity or have boundary points of infinite type. We will show that the Kobayashi metric on these domains behaves, in some sense, like a negatively curved Riemannian metric. In particular, it satisfies a visibility condition in the sense of Eberlein and O'Neill. This behavior allows us to prove a variety of results concerning boundary extension of maps and to establish Wolff–Denjoy theorems for a wide collection of domains.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.005
      Issue No: Vol. 310 (2017)
       
  • Invertibility of sparse non-Hermitian matrices
    • Authors: Anirban Basak; Mark Rudelson
      Pages: 426 - 483
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Anirban Basak, Mark Rudelson
      We consider a class of sparse random matrices of the form A n = ( ξ i , j δ i , j ) i , j = 1 n , where { ξ i , j } are i.i.d. centered random variables, and { δ i , j } are i.i.d. Bernoulli random variables taking value 1 with probability p n , and prove a quantitative estimate on the smallest singular value for p n = Ω ( log ⁡ n n ) , under a suitable assumption on the spectral norm of the matrices. This establishes the invertibility of a large class of sparse matrices. For p n = Ω ( n − α ) with some α ∈ ( 0 , 1 ) , we deduce that the condition number of A n is of order n with probability tending to one under the optimal moment assumption on { ξ i , j } . This in particular, extends a conjecture of von Neumann about the condition number to sparse random matrices with heavy-tailed entries. In the case that the random variables { ξ i , j } are i.i.d. sub-Gaussian, we further show that a sparse random matrix is singular with probability at most exp ⁡ ( − c n p n ) whenever p n is above the critical threshold p n = Ω ( log ⁡ n n ) . The results also extend to the case when { ξ i , j } have a non-zero mean. We further find quantitative estimates on the smallest singular value of the adjacency matrix of a directed Erdős–Réyni graph whenever its edge connectivity probability is above the critical threshold Ω ( log ⁡ n n ) .

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.009
      Issue No: Vol. 310 (2017)
       
  • Subnormality of unbounded composition operators over one-circuit directed
           graphs: Exotic examples
    • Authors: Piotr Budzyński; Zenon Jan Jabłoński; Il Bong Jung; Jan Stochel
      Pages: 484 - 556
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Piotr Budzyński, Zenon Jan Jabłoński, Il Bong Jung, Jan Stochel
      A recent example of a non-hyponormal injective composition operator in an L 2 -space generating Stieltjes moment sequences, invented by three of the present authors, was built over a non-locally finite directed tree. The main goal of this paper is to solve the problem of whether there exists such an operator over a locally finite directed graph and, in the affirmative case, to find the simplest possible graph with these properties (simplicity refers to local valency). The problem is solved affirmatively for the locally finite directed graph G 2 , 0 , which consists of two branches and one loop. The only simpler directed graph for which the problem remains unsolved consists of one branch and one loop. The consistency condition, the only efficient tool for verifying subnormality of unbounded composition operators, is intensively studied in the context of G 2 , 0 , which leads to a constructive method of solving the problem. The method itself is partly based on transforming the Krein and the Friedrichs measures coming either from shifted Al-Salam–Carlitz q-polynomials or from a quartic birth and death process.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.004
      Issue No: Vol. 310 (2017)
       
  • Cartesian modules over representations of small categories
    • Authors: Sergio Estrada; Simone Virili
      Pages: 557 - 609
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Sergio Estrada, Simone Virili
      We introduce the new concept of cartesian module over a pseudofunctor R from a small category to the category of small preadditive categories. Already the case when R is a (strict) functor taking values in the category of commutative rings is sufficient to cover the classical construction of quasi-coherent sheaves of modules over a scheme. On the other hand, our general setting allows for a good theory of contravariant additive locally flat functors, providing a geometrically meaningful extension of a classical Representation Theorem of Makkai and Paré. As an application, we relate and extend some previous constructions of the pure derived category of a scheme.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.01.030
      Issue No: Vol. 310 (2017)
       
  • A refined version of Grothendieck's birational anabelian conjecture for
           curves over finite fields
    • Authors: Mohamed Saïdi; Akio Tamagawa
      Pages: 610 - 662
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Mohamed Saïdi, Akio Tamagawa
      In this paper we prove a refined version of Uchida's theorem on isomorphisms between absolute Galois groups of global fields in positive characteristics, where one “ignores” the information provided by a “small” set of primes.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.010
      Issue No: Vol. 310 (2017)
       
  • Surfaces of minimal degree of tame representation type and mutations of
           Cohen–Macaulay modules
    • Authors: Daniele Faenzi; Francesco Malaspina
      Pages: 663 - 695
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Daniele Faenzi, Francesco Malaspina
      We provide two examples of smooth projective surfaces of tame CM type, by showing that the parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in P 5 is either a single point or a projective line. These turn out to be the only smooth projective ACM varieties of tame CM type besides elliptic curves, [1]. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For F 0 and F 1 , embedded as quintic or sextic scrolls, a complete classification of rigid ACM bundles is given.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.007
      Issue No: Vol. 310 (2017)
       
  • Global small solutions to the compressible 2D magnetohydrodynamic system
           without magnetic diffusion
    • Authors: Jiahong Wu; Yifei Wu
      Pages: 759 - 888
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Jiahong Wu, Yifei Wu
      This paper establishes the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state. In addition, explicit large-time decay rates for various Sobolev norms of the solutions are also obtained. These results are achieved through a new approach of diagonalizing a system of coupled linearized equations. The standard method of diagonalization via the eigenvalues and eigenvectors of the matrix symbol is very difficult to implement here. This new process allows us to obtain an integral representation of the full system through explicit kernels. In addition, in order to overcome various difficulties such as the anisotropicity and criticality, we fully exploit the structure of the integral representation and employ extremely delicate Fourier analysis and associated estimates.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.013
      Issue No: Vol. 310 (2017)
       
  • The degenerate special Lagrangian equation
    • Authors: Yanir A. Rubinstein; Jake P. Solomon
      Pages: 889 - 939
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Yanir A. Rubinstein, Jake P. Solomon
      This article introduces the degenerate special Lagrangian equation (DSL) and develops the basic analytic tools to construct and study its solutions. The DSL governs geodesics in the space of positive graph Lagrangians in C n . Existence of geodesics in the space of positive Lagrangians is an important step in a program for proving existence and uniqueness of special Lagrangians. Moreover, it would imply certain cases of the strong Arnold conjecture from Hamiltonian dynamics. We show the DSL is degenerate elliptic. We introduce a space–time Lagrangian angle for one-parameter families of graph Lagrangians, and construct its regularized lift. The superlevel sets of the regularized lift define subequations for the DSL in the sense of Harvey–Lawson. We extend the existence theory of Harvey–Lawson for subequations to the setting of domains with corners, and thus obtain solutions to the Dirichlet problem for the DSL in all branches. Moreover, we introduce the calibration measure, which plays a rôle similar to that of the Monge–Ampère measure in convex and complex geometry. The existence of this measure and regularity estimates allow us to prove that the solutions we obtain in the outer branches of the DSL have a well-defined length in the space of positive Lagrangians.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.008
      Issue No: Vol. 310 (2017)
       
  • On Pillay's conjecture in the general case
    • Authors: Mário J. Edmundo; Marcello Mamino; Luca Prelli; Janak Ramakrishnan; Giuseppina Terzo
      Pages: 940 - 992
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Mário J. Edmundo, Marcello Mamino, Luca Prelli, Janak Ramakrishnan, Giuseppina Terzo
      Let M be an arbitrary o-minimal structure. Let G be a definably compact, definably connected, abelian definable group of dimension n. Here we compute: (i) the new intrinsic o-minimal fundamental group of G; (ii) for each k > 0 , the k-torsion subgroups of G; (iii) the o-minimal cohomology algebra over Q of G. As a corollary we obtain a new uniform proof of Pillay's conjecture, an o-minimal analogue of Hilbert's fifth problem, relating definably compact groups to compact real Lie groups, extending the proof already known in o-minimal expansions of ordered fields.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.015
      Issue No: Vol. 310 (2017)
       
  • Heisenberg uniqueness pairs for some algebraic curves in the plane
    • Authors: Deb Kumar Giri; R.K. Srivastava
      Pages: 993 - 1016
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Deb Kumar Giri, R.K. Srivastava
      A Heisenberg uniqueness pair is a pair ( Γ , Λ ) , where Γ is a curve and Λ is a set in R 2 such that whenever a finite Borel measure μ having support on Γ which is absolutely continuous with respect to the arc length on Γ satisfies μ ˆ Λ = 0 , then it is identically 0. In this article, we investigate the Heisenberg uniqueness pairs corresponding to the spiral, hyperbola, circle and certain exponential curves. Further, we work out a characterization of the Heisenberg uniqueness pairs corresponding to four parallel lines. In the latter case, we observe a phenomenon of interlacing of three trigonometric polynomials.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.019
      Issue No: Vol. 310 (2017)
       
  • Normalizers of primitive permutation groups
    • Authors: Robert M. Guralnick; Attila Maróti; László Pyber
      Pages: 1017 - 1063
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Robert M. Guralnick, Attila Maróti, László Pyber
      Let G be a transitive normal subgroup of a permutation group A of finite degree n. The factor group A / G can be considered as a certain Galois group and one would like to bound its size. One of the results of the paper is that A / G < n if G is primitive unless n = 3 4 , 54, 38, 58, or 316. This bound is sharp when n is prime. In fact, when G is primitive, Out ( G ) < n unless G is a member of a given infinite sequence of primitive groups and n is different from the previously listed integers. Many other results of this flavor are established not only for permutation groups but also for linear groups and Galois groups.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.012
      Issue No: Vol. 310 (2017)
       
  • Cluster algebras, invariant theory, and Kronecker coefficients I
    • Authors: Jiarui Fei
      Pages: 1064 - 1112
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): Jiarui Fei
      We relate the m-truncated Kronecker products of symmetric functions to the semi-invariant rings of a family of quiver representations. We find cluster algebra structures for these semi-invariant rings when m = 2 . Each g -vector cone G ◇ l of these cluster algebras controls the 2-truncated Kronecker products for all symmetric functions of degree no greater than l. As a consequence, each relevant Kronecker coefficient is the difference of the number of the lattice points inside two rational polytopes. We also give explicit description of all G ◇ l 's. As an application, we compute some invariant rings.

      PubDate: 2017-03-18T06:03:05Z
      DOI: 10.1016/j.aim.2017.02.016
      Issue No: Vol. 310 (2017)
       
  • Higher equivariant excision
    • Authors: Emanuele Dotto
      Pages: 1 - 96
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Emanuele Dotto
      We develop a theory of Goodwillie calculus for functors between G-equivariant homotopy theories, where G is a finite group. We construct J-excisive approximations for any finite G-set J. These combine into a poset, the Goodwillie tree, that extends the classical Goodwillie tower. We prove convergence results for the tree of a functor on pointed G-spaces that commutes with fixed-points, and we reinterpret the Tom Dieck-splitting as an instance of a more general splitting phenomenon that occurs for the fixed-points of the equivariant derivatives of these functors. As our main example we describe the layers of the tree of the identity functor in terms of the equivariant Spanier–Whitehead duals of the partition complexes.

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2017.01.004
      Issue No: Vol. 309 (2017)
       
  • Higher traces, noncommutative motives, and the categorified Chern
           character
    • Authors: Marc Hoyois; Sarah Scherotzke; Nicolò Sibilla
      Pages: 97 - 154
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Marc Hoyois, Sarah Scherotzke, Nicolò Sibilla
      We propose a categorification of the Chern character that refines earlier work of Toën and Vezzosi and of Ganter and Kapranov. If X is an algebraic stack, our categorified Chern character is a symmetric monoidal functor from a category of mixed noncommutative motives over X, which we introduce, to S 1 -equivariant perfect complexes on the derived free loop stack L X . As an application of the theory, we show that Toën and Vezzosi's secondary Chern character factors through secondary K-theory. Our techniques depend on a careful investigation of the functoriality of traces in symmetric monoidal ( ∞ , n ) -categories, which is of independent interest.

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2017.01.008
      Issue No: Vol. 309 (2017)
       
  • Nonintersecting Brownian bridges between reflecting or absorbing walls
    • Authors: Karl Liechty; Dong Wang
      Pages: 155 - 208
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Karl Liechty, Dong Wang
      We study a model of nonintersecting Brownian bridges on an interval with either absorbing or reflecting walls at the boundaries, focusing on the point in space-time at which the particles meet the wall. These processes are determinantal, and in different scaling limits when the particles approach the reflecting (resp. absorbing) walls we obtain hard-edge limiting kernels which are the even (resp. odd) parts of the Pearcey and tacnode kernels. We also show that in the single time case, our hard-edge tacnode kernels are equivalent to the ones studied by Delvaux [16], defined in terms of a 4 × 4 Lax pair for the inhomogeneous Painlevé II equation (PII). As a technical ingredient in the proof, we construct a Schlesinger transform for the 4 × 4 Lax pair in [16] which preserves the Hastings–McLeod solutions to PII.

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2016.10.024
      Issue No: Vol. 309 (2017)
       
  • An improvement to the Hasse–Weil bound and applications to character
           sums, cryptography and coding
    • Authors: Ronald Cramer; Chaoping Xing
      Pages: 238 - 253
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Ronald Cramer, Chaoping Xing
      The Hasse–Weil bound is a deep result in mathematics and has found wide applications in mathematics, theoretical computer science, information theory etc. In general, the bound is tight and cannot be improved. However, for some special families of curves the bound could be improved substantially. In this paper, we focus on the Hasse–Weil bound for the curve defined by y p − y = f ( x ) over the finite field F q , where p is the characteristic of F q . In 1993, Moreno–Moreno [7] gave an improvement to the Hasse–Weil bound for this family of curves. Recently, Kaufman and Lovett [4, FOCS2011] showed that the Hasse–Weil bound can be improved for this family of curves with f ( x ) = g ( x ) + h ( x ) , where g ( x ) is a polynomial of degree ≪ q and h ( x ) is a sparse polynomial of arbitrary degree but bounded weight degree. The other recent improvement by Rojas-Leon and Wan [9, Math. Ann. 2011] shows that an extra p can be removed for this family of curves if p is very large compared with polynomial degree of f ( x ) and log p ⁡ q . In this paper, we focus on the most interesting case for applications, namely p = 2 . We show that the Hasse–Weil bound for this special family of curves can be improved if q = 2 n with odd n ⩾ 3 which is the same case where Serre [10] improved the Hasse–Weil bound. However, our improvement is greater than Serre's and Moreno–Morenao's improvements for this special family of curves. Furthermore, our improvement works for p = 2 compared with the requirement of large p by Rojas-Leon and Wan. In addition, our improvement finds interesting applications to character sums, cryptography and coding theory. The key idea behind is that this curve has the Hasse–Witt invariant 0 and we show that the Hasse–Weil bound can be improved for any curves with the Hasse–Witt invariant 0. The main tool used in our proof involves Newton polygon and some results in algebraic geometry.

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2017.01.011
      Issue No: Vol. 309 (2017)
       
  • On the scattering operators for ACHE metrics of Bergman type on strictly
           pseudoconvex domains
    • Authors: Fang Wang
      Pages: 306 - 333
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Fang Wang
      The scattering operators associated to an ACHE metric of Bergman type on a strictly pseudoconvex domain are a one-parameter family of CR-conformally invariant pseudo-differential operators of Heisenberg class with respect to the induced CR structure on the boundary. In this paper, we mainly show that if the boundary Webster scalar curvature is positive, then for γ ∈ ( 0 , 1 ) the renormalised scattering operator P 2 γ has positive spectrum and satisfies the maximum principal; moreover, the fractional curvature Q 2 γ is also positive. This is parallel to the result of Guillarmou–Qing [16] for the real case. We also give two energy extension formulae for P 2 γ , which are parallel to the energy extension given by Chang–Case [2] for the real case.

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2017.01.020
      Issue No: Vol. 309 (2017)
       
  • KMS weights on graph C⁎-algebras
    • Authors: Klaus Thomsen
      Pages: 334 - 391
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Klaus Thomsen
      The paper contains a study of the gauge invariant KMS weights for a generalized gauge action on a graph C ⁎ -algebra. When the graph is irreducible and has the property that there are at most countably many roads to infinity in the graph, a complete description is given of the structure of KMS weights for the gauge action. The structure is very rich and is identical with the structure of KMS states for the restriction of the action to any corner defined by a projection in the fixed point algebra.

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2017.01.024
      Issue No: Vol. 309 (2017)
       
  • The derived category of complex periodic K-theory localized at an odd
           prime
    • Authors: Irakli Patchkoria
      Pages: 392 - 435
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Irakli Patchkoria
      We prove that for an odd prime p, the derived category D ( K U ( p ) ) of the p-local complex periodic K-theory spectrum K U ( p ) is triangulated equivalent to the derived category of its homotopy ring π ⁎ K U ( p ) . This implies that if p is an odd prime, the triangulated category D ( K U ( p ) ) is algebraic.

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2017.01.023
      Issue No: Vol. 309 (2017)
       
  • On the Andrews–Zagier asymptotics for partitions without sequences
    • Authors: Kathrin Bringmann; Ben Kane; Daniel Parry; Robert Rhoades
      Pages: 436 - 451
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Kathrin Bringmann, Ben Kane, Daniel Parry, Robert Rhoades
      In this paper, we establish asymptotics of radial limits for certain functions of Wright. These functions appear in bootstrap percolation and the generating function for partitions without sequences of k consecutive part sizes. We specifically establish asymptotics numerically obtained by Zagier in the case k = 3 .

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2017.01.012
      Issue No: Vol. 309 (2017)
       
  • Vortex reconnection in the three dimensional Navier–Stokes equations
    • Authors: Alberto Enciso; Renato Lucà; Daniel Peralta-Salas
      Pages: 452 - 486
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Alberto Enciso, Renato Lucà, Daniel Peralta-Salas
      We prove that the vortex structures of solutions to the 3D Navier–Stokes equations can change their topology without any loss of regularity. More precisely, we construct smooth high-frequency solutions to the Navier–Stokes equations where vortex lines and vortex tubes of arbitrarily complicated topologies are created and destroyed in arbitrarily small times. This instance of vortex reconnection is structurally stable and in perfect agreement with the existing computer simulations and experiments. We also provide a (non-structurally stable) scenario where the destruction of vortex structures is instantaneous.

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2017.01.025
      Issue No: Vol. 309 (2017)
       
  • The polynomial part of the codimension growth of affine PI algebras
    • Authors: Eli Aljadeff; Geoffrey Janssens; Yakov Karasik
      Pages: 487 - 511
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Eli Aljadeff, Geoffrey Janssens, Yakov Karasik
      Let F be a field of characteristic zero and W an associative affine F-algebra satisfying a polynomial identity (PI). The codimension sequence { c n ( W ) } associated to W is known to be of the form Θ ( n t d n ) , where d is the well known PI-exponent of W. In this paper we establish an algebraic interpretation of the polynomial part (the constant t) by means of Kemer's theory. In particular, we show that in case W is a basic algebra (hence finite dimensional), t = q − d 2 + s , where q is the number of simple component in W / J ( W ) and s + 1 is the nilpotency degree of J ( W ) (the Jacobson radical of W). Thus proving a conjecture of Giambruno.

      PubDate: 2017-02-19T03:29:00Z
      DOI: 10.1016/j.aim.2017.01.022
      Issue No: Vol. 309 (2017)
       
  • Tukey classification of some ideals on ω and the lattices of weakly
           compact sets in Banach spaces
    • Authors: Plebanek
      Abstract: Publication date: 13 April 2017
      Source:Advances in Mathematics, Volume 310
      Author(s): A. Avilés, G. Plebanek, J. Rodríguez
      We study the lattice structure of the family of weakly compact subsets of the unit ball B X of a separable Banach space X, equipped with the inclusion relation (this structure is denoted by K ( B X ) ) and also with the parametrized family of “almost inclusion” relations K ⊆ L + ε B X , where ε > 0 (this structure is denoted by AK ( B X ) ). Tukey equivalence between partially ordered sets and a suitable extension to deal with AK ( B X ) are used. Assuming the axiom of analytic determinacy, we prove that separable Banach spaces fall into four categories, namely: K ( B X ) is equivalent either to a singleton, or to ω ω , or to the family K ( Q ) of compact subsets of the rational numbers, or to the family [ c ] < ω of all finite subsets of the continuum. Also under the axiom of analytic determinacy, a similar classification of AK ( B X ) is obtained. For separable Banach spaces not containing ℓ 1 , we prove in ZFC that K ( B X ) ∼ AK ( B X ) are equivalent to either {0}, ω ω , K ( Q ) or [ c ] < ω . The lattice structure of the family of all weakly null subsequences of an unconditional basis is also studied.

      PubDate: 2017-03-18T06:03:05Z
       
  • Equivariant Moore spaces and the Dade group
    • Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Ergün Yalçın
      Let G be a finite p-group and k be a field of characteristic p. A topological space X is called an n-Moore space if its reduced homology is nonzero only in dimension n. We call a G-CW-complex X an n _ -Moore G-space over k if for every subgroup H of G, the fixed point set X H is an n _ ( H ) -Moore space with coefficients in k, where n _ ( H ) is a function of H. We show that if X is a finite n _ -Moore G-space, then the reduced homology module of X is an endo-permutation kG-module generated by relative syzygies. A kG-module M is an endo-permutation module if End k ( M ) = M ⊗ k M ⁎ is a permutation kG-module. We consider the Grothendieck group of finite Moore G-spaces M ( G ) , with addition given by the join operation, and relate this group to the Dade group generated by relative syzygies.

      PubDate: 2017-02-19T03:29:00Z
       
  • Arc-wise analytic stratification, Whitney fibering conjecture and Zariski
           equisingularity
    • Authors: Adam
      Abstract: Publication date: 17 March 2017
      Source:Advances in Mathematics, Volume 309
      Author(s): Adam Parusiński, Laurenţiu Păunescu
      In this paper we show Whitney's fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivialization arc-wise analytic and we show that it can be constructed under the classical Zariski algebro-geometric equisingularity assumptions. Using a slightly stronger version of the Zariski equisingularity, we show the existence of Whitney's stratified fibration, satisfying the conditions (b) of Whitney and (w) of Verdier. Our construction is based on the Puiseux with parameter theorem and a generalization of Whitney's interpolation. For algebraic sets our construction gives a global stratification. We also present several applications of the arc-wise analytic trivialization, mainly to the stratification theory and the equisingularity of analytic set and function germs. In the real algebraic case, for an algebraic family of projective varieties, we show that the Zariski equisingularity implies local constancy of the associated weight filtration.

      PubDate: 2017-02-19T03:29:00Z
       
 
 
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