for Journals by Title or ISSN
for Articles by Keywords
help
  Subjects -> MATHEMATICS (Total: 909 journals)
    - APPLIED MATHEMATICS (75 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (676 journals)
    - MATHEMATICS (GENERAL) (41 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (78 journals)

MATHEMATICS (676 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
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: 25)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
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: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
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: 5)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 11)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
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: 6)
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: 9)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
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: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
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: 3)
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: 11)
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: 8)
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: 5)
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 Network Science     Open Access   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
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: 21)
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: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 3)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
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: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
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: 1)
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: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 1)
CHANCE     Hybrid Journal   (Followers: 6)
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: 3)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
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: 6)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
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: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
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: 4)
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: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)

        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
   ISSN (Print) 0001-8708 - ISSN (Online) 1090-2082
   Published by Elsevier Homepage  [3118 journals]
  • The Goldman–Turaev Lie bialgebra in genus zero and the
           Kashiwara–Vergne problem
    • Authors: Anton Alekseev; Nariya Kawazumi; Yusuke Kuno; Florian Naef
      Pages: 1 - 53
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Anton Alekseev, Nariya Kawazumi, Yusuke Kuno, Florian Naef
      In this paper, we describe a surprising link between the theory of the Goldman–Turaev Lie bialgebra on surfaces of genus zero and the Kashiwara–Vergne (KV) problem in Lie theory. Let Σ be an oriented 2-dimensional manifold with non-empty boundary and K a field of characteristic zero. The Goldman–Turaev Lie bialgebra is defined by the Goldman bracket { − , − } and Turaev cobracket δ on the K -span of homotopy classes of free loops on Σ. Applying an expansion θ : K π → K 〈 x 1 , … , x n 〉 yields an algebraic description of the operations { − , − } and δ in terms of non-commutative variables x 1 , … , x n . If Σ is a surface of genus g = 0 the lowest degree parts { − , − } − 1 and δ − 1 are canonically defined (and independent of θ). They define a Lie bialgebra structure on the space of cyclic words which was introduced and studied by Schedler [31]. It was conjectured by the second and the third authors that one can define an expansion θ such that { − , − } = { − , − } − 1 and δ = δ − 1 . The main result of this paper states that for surfaces of genus zero constructing such an expansion is essentially equivalent to the KV problem. In [24], Massuyeau constructed such expansions using the Kontsevich integral. In order to prove this result, we show that the Turaev cobracket δ can be constructed in terms of the double bracket (upgrading the Goldman bracket) and the non-commutative divergence cocycle which plays the central role in the KV theory. Among other things, this observation gives a new topological interpretation of the KV problem and allows to extend it to surfaces with arbitrary number of boundary components (and of arbitrary genus, see [2]).

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.005
      Issue No: Vol. 326 (2017)
       
  • Local Sobolev constant estimate for integral Ricci curvature bounds
    • Authors: Xianzhe Dai; Guofang Wei; Zhenlei Zhang
      Pages: 1 - 33
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Xianzhe Dai, Guofang Wei, Zhenlei Zhang
      We obtain a local Sobolev constant estimate for integral Ricci curvature, which enables us to extend several important tools such as the maximal principle, the gradient estimate, the heat kernel estimate and the L 2 Hessian estimate to manifolds with integral Ricci lower bounds, without the non-collapsing conditions.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.024
      Issue No: Vol. 325 (2017)
       
  • Finite time blow up in the hyperbolic Boussinesq system
    • Authors: Alexander Kiselev; Changhui Tan
      Pages: 34 - 55
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Alexander Kiselev, Changhui Tan
      In recent work of Luo and Hou [10], a new scenario for finite time blow up in solutions of 3D Euler equation has been proposed. The scenario involves a ring of hyperbolic points of the flow located at the boundary of a cylinder. In this paper, we propose a two dimensional model that we call “hyperbolic Boussinesq system”. This model is designed to provide insight into the hyperbolic point blow up scenario. The model features an incompressible velocity vector field, a simplified Biot–Savart law, and a simplified term modeling buoyancy. We prove that finite time blow up happens for a natural class of initial data.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.019
      Issue No: Vol. 325 (2017)
       
  • Multiple elliptic gamma functions associated to cones
    • Authors: Jacob Winding
      Pages: 56 - 86
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Jacob Winding
      We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, associated to good rational cones. We explain how good cones are related to collections of S L r ( Z ) -elements and prove that the generalized multiple sine and multiple elliptic gamma functions enjoy infinite product representations and modular properties determined by the cone. This generalizes the modular properties of the elliptic gamma function studied by Felder and Varchenko, and the results about the usual multiple sine and elliptic gamma functions found by Narukawa.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.022
      Issue No: Vol. 325 (2017)
       
  • Rigorous effective bounds on the Hausdorff dimension of continued fraction
           Cantor sets: A hundred decimal digits for the dimension of E2
    • Authors: O. Jenkinson; M. Pollicott
      Pages: 87 - 115
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): O. Jenkinson, M. Pollicott
      We prove that the algorithm of [19] for approximating the Hausdorff dimension of dynamically defined Cantor sets, using periodic points of the underlying dynamical system, can be used to establish completely rigorous high accuracy bounds on the dimension. The effectiveness of these rigorous estimates is illustrated for Cantor sets consisting of continued fraction expansions with restricted digits. For example the Hausdorff dimension of the set E 2 (of those reals whose continued fraction expansion only contains digits 1 and 2) can be rigorously approximated, with an accuracy of over 100 decimal places, using points of period up to 25. The method for establishing rigorous dimension bounds involves the holomorphic extension of mappings associated to the allowed continued fraction digits, an appropriate disc which is contracted by these mappings, and an associated transfer operator acting on the Hilbert Hardy space of analytic functions on this disc. We introduce methods for rigorously bounding the approximation numbers for the transfer operators, showing that this leads to effective estimates on the Taylor coefficients of the associated determinant, and hence to explicit bounds on the Hausdorff dimension.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.028
      Issue No: Vol. 325 (2017)
       
  • Gap-labelling conjecture with nonzero magnetic field
    • Authors: Moulay Tahar Benameur; Varghese Mathai
      Pages: 116 - 164
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Moulay Tahar Benameur, Varghese Mathai
      Given a constant magnetic field on Euclidean space R p determined by a skew-symmetric ( p × p ) matrix Θ, and a Z p -invariant probability measure μ on the disorder set Σ which is by hypothesis a Cantor set, where the action is assumed to be minimal, the corresponding Integrated Density of States of any self-adjoint operator affiliated to the twisted crossed product algebra C ( Σ ) ⋊ σ Z p , where σ is the multiplier on Z p associated to Θ, takes on values on spectral gaps in the magnetic gap-labelling group. The magnetic frequency group is defined as an explicit countable subgroup of R involving Pfaffians of Θ and its sub-matrices. We conjecture that the magnetic gap labelling group is a subgroup of the magnetic frequency group. We give evidence for the validity of our conjecture in 2D, 3D, the Jordan block diagonal case and the periodic case in all dimensions.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.030
      Issue No: Vol. 325 (2017)
       
  • The limit of the Hermitian–Yang–Mills flow on reflexive
           sheaves
    • Authors: Jiayu Li; Chuanjing Zhang; Xi Zhang
      Pages: 165 - 214
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Jiayu Li, Chuanjing Zhang, Xi Zhang
      In this paper, we study the asymptotic behavior of the Hermitian–Yang–Mills flow on a reflexive sheaf. We prove that the limiting reflexive sheaf is isomorphic to the double dual of the graded sheaf associated to the Harder–Narasimhan–Seshadri filtration, this answers a question by Bando and Siu.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.029
      Issue No: Vol. 325 (2017)
       
  • A Lindelöf group with non-Lindelöf square
    • Authors: Yinhe Peng; Liuzhen Wu
      Pages: 215 - 242
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Yinhe Peng, Liuzhen Wu
      We show that the Lindelöf property of a topological group is not inherited by its square, thus solving an old problem from [2]. Our construction introduces a new method to this area of mathematics and is of independent interest as it may have some further applications. Our method builds on ideas of [11] and techniques from [20] and give us also an optimal result about the partition properties on ω 1 .

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.021
      Issue No: Vol. 325 (2017)
       
  • Building blocks of polarized endomorphisms of normal projective varieties
    • Authors: Sheng Meng; De-Qi Zhang
      Pages: 243 - 273
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Sheng Meng, De-Qi Zhang
      An endomorphism f of a projective variety X is polarized (resp. quasi-polarized) if f ⁎ H ∼ q H (linear equivalence) for some ample (resp. nef and big) Cartier divisor H and integer q > 1 . First, we use cone analysis to show that a quasi-polarized endomorphism is always polarized, and the polarized property descends via any equivariant dominant rational map. Next, we show that a suitable maximal rationally connected fibration (MRC) can be made f-equivariant using a construction of N. Nakayama, that f descends to a polarized endomorphism of the base Y of this MRC and that this Y is a Q-abelian variety (quasi-étale quotient of an abelian variety). Finally, we show that we can run the minimal model program (MMP) f-equivariantly for mildly singular X and reach either a Q-abelian variety or a Fano variety of Picard number one. As a consequence, the building blocks of polarized endomorphisms are those of Q-abelian varieties and those of Fano varieties of Picard number one. Along the way, we show that f always descends to a polarized endomorphism of the Albanese variety Alb ( X ) of X, and that the pullback of a power of f acts as a scalar multiplication on the Néron–Severi group of X (modulo torsion) when X is smooth and rationally connected. Partial answers about X being of Calabi–Yau type, or Fano type are also given with an extra primitivity assumption on f which seems necessary by an example.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.026
      Issue No: Vol. 325 (2017)
       
  • A vanishing theorem for Dirac cohomology of standard modules
    • Authors: Kei Yuen Chan
      Pages: 274 - 311
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Kei Yuen Chan
      This paper studies the Dirac cohomology of standard modules in the setting of graded Hecke algebras with geometric parameters. We prove that the Dirac cohomology of a standard module vanishes if and only if the module is not twisted-elliptic tempered. The proof makes use of two deep results. One is some structural information from the generalized Springer correspondence obtained by S. Kato and Lusztig. Another one is a computation of the Dirac cohomology of tempered modules by Barbasch–Ciubotaru–Trapa and Ciubotaru. We apply our result to compute the Dirac cohomology of ladder representations for type A n . For each of such representations with non-zero Dirac cohomology, we associate to a canonical Weyl group representation. We use the Dirac cohomology to conclude that such representations appear with multiplicity one.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.023
      Issue No: Vol. 325 (2017)
       
  • Quantales and Fell bundles
    • Authors: Pedro Resende
      Pages: 312 - 374
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Pedro Resende
      We study Fell bundles on groupoids from the viewpoint of quantale theory. Given any saturated upper semicontinuous Fell bundle π : E → G on an étale groupoid G with G 0 locally compact Hausdorff, equipped with a suitable completion C*-algebra A of its convolution algebra, we obtain a map of involutive quantales p : Max A → Ω ( G ) , where Max A consists of the closed linear subspaces of A and Ω ( G ) is the topology of G. We study various properties of p which mimick, to various degrees, those of open maps of topological spaces. These are closely related to properties of G, π, and A, such as G being Hausdorff, principal, or topological principal, or π being a line bundle. Under suitable conditions, which include G being Hausdorff, but without requiring saturation of the Fell bundle, A is an algebra of sections of the bundle if and only if it is the reduced C*-algebra C r ⁎ ( G , E ) . We also prove that Max A is stably Gelfand. This implies the existence of a pseudogroup I B and of an étale groupoid B associated canonically to any sub-C*-algebra B ⊂ A . We study a correspondence between Fell bundles and sub-C*-algebras based on these constructions, and compare it to the construction of Weyl groupoids from Cartan subalgebras.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.12.001
      Issue No: Vol. 325 (2017)
       
  • Cyclotomic root systems and bad primes
    • Authors: Michel Broué; Ruth Corran; Jean Michel
      Pages: 375 - 458
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Michel Broué, Ruth Corran, Jean Michel
      We generalize the definition and properties of root systems to complex reflection groups — roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root systems over the field of definition k of the reflection representation. In the case of spetsial reflection groups, we generalize as well the definition and properties of bad primes.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.020
      Issue No: Vol. 325 (2017)
       
  • On polytopes with congruent projections or sections
    • Authors: Sergii Myroshnychenko; Dmitry Ryabogin
      Pages: 482 - 504
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Sergii Myroshnychenko, Dmitry Ryabogin
      Let 2 ≤ k ≤ d − 1 and let P and Q be two convex polytopes in E d . Assume that their projections, P H , Q H , onto every k-dimensional subspace H, are congruent. In this paper we show that P and Q or P and −Q are translates of each other. We also prove an analogous result for sections by showing that P = Q or P = − Q , provided the polytopes contain the origin in their interior and their sections, P ∩ H , Q ∩ H , by every k-dimensional subspace H, are congruent.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.12.003
      Issue No: Vol. 325 (2017)
       
  • On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a
           variation of Ramanujan's ω(q)
    • Authors: Kathrin Bringmann; Chris Jennings-Shaffer; Karl Mahlburg
      Pages: 505 - 532
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg
      We analyze the mock modular behavior of P ¯ ω ( q ) , a partition function introduced by Andrews, Dixit, Schultz, and Yee. This function arose in a study of smallest parts functions related to classical third order mock theta functions, one of which is ω ( q ) . We find that the modular completion of P ¯ ω ( q ) is not simply a harmonic Maass form, but is instead the derivative of a linear combination of products of various harmonic Maass forms and theta functions. We precisely describe its behavior under modular transformations and find that the image under the Maass lowering operator lies in a relatively simpler space.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.12.002
      Issue No: Vol. 325 (2017)
       
  • On the dynamics of finite temperature trapped Bose gases
    • Authors: Avy Soffer; Minh-Binh Tran
      Pages: 533 - 607
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Avy Soffer, Minh-Binh Tran
      The system that describes the dynamics of a Bose–Einstein Condensate (BEC) and the thermal cloud at finite temperature consists of a nonlinear Schrodinger (NLS) and a quantum Boltzmann (QB) equations. In such a system of trapped Bose gases at finite temperature, the QB equation corresponds to the evolution of the density distribution function of the thermal cloud and the NLS is the equation of the condensate. The quantum Boltzmann collision operator in this temperature regime is the sum of two operators C 12 and C 22 , which describe collisions of the condensate and the non-condensate atoms and collisions between non-condensate atoms. Above the BEC critical temperature, the system is reduced to an equation containing only a collision operator similar to C 22 , which possesses a blow-up positive radial solution with respect to the L ∞ norm (cf. [29]). On the other hand, at the very low temperature regime (only a portion of the transition temperature T B E C ), the system can be simplified into an equation of C 12 , with a different (much higher order) transition probability, which has a unique global classical positive radial solution with weighted L 1 norm (cf. [3]). In our model, we first decouple the QB, which contains C 12 + C 22 , and the NLS equations, then show a global existence and uniqueness result for classical positive radial solutions to the spatially homogeneous kinetic system. Different from the case considered in [29], due to the presence of the BEC, the collision integrals are associated to sophisticated energy manifolds rather than spheres, since the particle energy is approximated by the Bogoliubov dispersion law. Moreover, the mass of the full system is not conserved while it is conserved for the case considered in [29]. A new theory is then supplied.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.007
      Issue No: Vol. 325 (2017)
       
  • The necessity of nowhere equivalence
    • Authors: Wei He; Yeneng Sun
      Pages: 608 - 639
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Wei He, Yeneng Sun
      We prove some regularity properties (convexity, closedness, compactness and preservation of upper hemicontinuity) for distribution and regular conditional distribution of correspondences under the nowhere equivalence condition. We show the necessity of such a condition for any of these properties to hold. As an application, we demonstrate that the nowhere equivalence condition is satisfied on the underlying agent space if and only if pure-strategy Nash equilibria exist in general large games with any fixed uncountable compact action space.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.11.032
      Issue No: Vol. 325 (2017)
       
  • Projections of planar Mandelbrot random measures
    • Authors: Julien Barral; De-Jun Feng
      Pages: 640 - 718
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Julien Barral, De-Jun Feng
      Let μ be a planar Mandelbrot measure and π ⁎ μ its orthogonal projection on one of the principal axes. We study the thermodynamic and geometric properties of π ⁎ μ . We first show that π ⁎ μ is exact dimensional, with dim ⁡ ( π ⁎ μ ) = min ⁡ ( dim ⁡ ( μ ) , dim ⁡ ( ν ) ) , where ν is the Bernoulli product measure obtained as the expectation of π ⁎ μ . We also prove that π ⁎ μ is absolutely continuous with respect to ν if and only if dim ⁡ ( μ ) > dim ⁡ ( ν ) . Our results provides a new proof of Dekking–Grimmett–Falconer formula for the Hausdorff and box dimension of the topological support of π ⁎ μ , as well as a new variational interpretation. We obtain the free energy function τ π ⁎ μ of π ⁎ μ on a wide subinterval [ 0 , q c ) of R + . For q ∈ [ 0 , 1 ] , it is given by a variational formula which sometimes yields phase transitions of order larger than 1. For q > 1 , it is given by min ⁡ ( τ ν , τ μ ) , which can exhibit first order phase transitions. This is in contrast with the analyticity of τ μ over [ 0 , q c ) . Also, we prove the validity of the multifractal formalism for π ⁎ μ at each α ∈ ( τ π ⁎ μ ′ ( q c − ) , τ π ⁎ μ ′ ( 0 + ) ] .

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.008
      Issue No: Vol. 325 (2017)
       
  • Long term regularity of the one-fluid Euler–Maxwell system in 3D
           with vorticity
    • Authors: Alexandru D. Ionescu; Victor Lie
      Pages: 719 - 769
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Alexandru D. Ionescu, Victor Lie
      A basic model for describing plasma dynamics is given by the “one-fluid” Euler–Maxwell system, in which a compressible electron fluid interacts with its own self-consistent electromagnetic field. In this paper we prove long-term regularity of solutions of this system in 3 spatial dimensions, in the case of small initial data with nontrivial vorticity. Our main conclusion is that the time of existence of solutions depends only on the size of the vorticity of the initial data, as long as the initial data is sufficiently close to a constant stationary solution.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.11.027
      Issue No: Vol. 325 (2017)
       
  • Heisenberg uniqueness pairs corresponding to a finite number of parallel
           lines
    • Authors: Sayan Bagchi
      Pages: 814 - 823
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Sayan Bagchi
      In this paper, we study the Heisenberg uniqueness pairs corresponding to a finite number of parallel lines Γ. We give a necessary condition and a sufficient condition for a subset Λ of R 2 so that ( Γ , Λ ) becomes a HUP.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.012
      Issue No: Vol. 325 (2017)
       
  • Brunn–Minkowski inequalities in product metric measure spaces
    • Authors: Manuel Ritoré; Jesús Yepes Nicolás
      Pages: 824 - 863
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Manuel Ritoré, Jesús Yepes Nicolás
      Given one metric measure space X satisfying a linear Brunn–Minkowski inequality, and a second one Y satisfying a Brunn–Minkowski inequality with exponent p ≥ − 1 , we prove that the product X × Y with the standard product distance and measure satisfies a Brunn–Minkowski inequality of order 1 / ( 1 + p − 1 ) under mild conditions on the measures and the assumption that the distances are strictly intrinsic. The same result holds when we consider restricted classes of sets. We also prove that a linear Brunn–Minkowski inequality is obtained in X × Y when Y satisfies a Prékopa–Leindler inequality. In particular, we show that the classical Brunn–Minkowski inequality holds for any pair of weakly unconditional sets in R n (i.e., those containing the projection of every point in the set onto every coordinate subspace) when we consider the standard distance and the product measure of n one-dimensional real measures with positively decreasing densities. This yields an improvement of the class of sets satisfying the Gaussian Brunn–Minkowski inequality. Furthermore, associated isoperimetric inequalities as well as recently obtained Brunn–Minkowski's inequalities are derived from our results.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.010
      Issue No: Vol. 325 (2017)
       
  • Floer homology and fractional Dehn twists
    • Authors: Matthew Hedden; Thomas E. Mark
      Pages: 1 - 39
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Matthew Hedden, Thomas E. Mark
      We establish a relationship between Heegaard Floer homology and the fractional Dehn twist coefficient of surface automorphisms. Specifically, we show that the rank of the Heegaard Floer homology of a 3-manifold bounds the absolute value of the fractional Dehn twist coefficient of the monodromy of any of its open book decompositions with connected binding. We prove this by showing that the rank of Floer homology gives bounds for the number of boundary parallel right or left Dehn twists necessary to add to a surface automorphism to guarantee that the associated contact manifold is tight or overtwisted, respectively. By examining branched double covers, we also show that the rank of the Khovanov homology of a link bounds the fractional Dehn twist coefficient of its odd-stranded braid representatives.

      PubDate: 2017-11-18T16:22:33Z
      DOI: 10.1016/j.aim.2017.11.008
      Issue No: Vol. 324 (2017)
       
  • Norms of random matrices: Local and global problems
    • Authors: Elizaveta Rebrova; Roman Vershynin
      Pages: 40 - 83
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Elizaveta Rebrova, Roman Vershynin
      Can the behavior of a random matrix be improved by modifying a small fraction of its entries' Consider a random matrix A with i.i.d. entries. We show that the operator norm of A can be reduced to the optimal order O ( n ) by zeroing out a small submatrix of A if and only if the entries have zero mean and finite variance. Moreover, we obtain an almost optimal dependence between the size of the removed submatrix and the resulting operator norm. Our approach utilizes the cut norm and Grothendieck–Pietsch factorization for matrices, and it combines the methods developed recently by C. Le and R. Vershynin and by E. Rebrova and K. Tikhomirov.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.001
      Issue No: Vol. 324 (2017)
       
  • Ramsey properties of nonlinear Diophantine equations
    • Authors: Mauro Di Nasso; Lorenzo Luperi Baglini
      Pages: 84 - 117
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Mauro Di Nasso, Lorenzo Luperi Baglini
      We present general sufficient and necessary conditions for the partition regularity of Diophantine equations, which extend the classic Rado's Theorem by covering large classes of nonlinear equations. The goal is to contribute to an overall theory of Ramsey properties of (nonlinear) Diophantine equations that encompasses the known results in this area under a unified framework. Sufficient conditions are obtained by exploiting algebraic properties in the space of ultrafilters β N , grounding on combinatorial properties of positive density sets and IP sets. Necessary conditions are proved by a new technique in nonstandard analysis, based on the use of the relation of u-equivalence for the hypernatural numbers N ⁎ .

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.003
      Issue No: Vol. 324 (2017)
       
  • Badly approximable points on planar curves and winning
    • Authors: Jinpeng An; Victor Beresnevich; Sanju Velani
      Pages: 148 - 202
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Jinpeng An, Victor Beresnevich, Sanju Velani
      For any i , j > 0 with i + j = 1 , let Bad ( i , j ) denote the set of points ( x , y ) ∈ R 2 such that max ⁡ { ‖ q x ‖ 1 / i , ‖ q y ‖ 1 / j } > c / q for some positive constant c = c ( x , y ) and all q ∈ N . We show that Bad ( i , j ) ∩ C is winning in the sense of Schmidt games for a large class of planar curves C , namely, everywhere non-degenerate planar curves and straight lines satisfying a natural Diophantine condition. This strengthens recent results solving a problem of Davenport from the sixties. In short, within the context of Davenport's problem, the winning statement is best possible. Furthermore, we obtain the inhomogeneous generalisations of the winning results for planar curves and lines and also show that the inhomogeneous form of Bad ( i , j ) is winning for two dimensional Schmidt games.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.009
      Issue No: Vol. 324 (2017)
       
  • Cells with many facets in a Poisson hyperplane tessellation
    • Authors: Gilles Bonnet; Pierre Calka; Matthias Reitzner
      Pages: 203 - 240
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Gilles Bonnet, Pierre Calka, Matthias Reitzner
      Let Z be the typical cell of a stationary Poisson hyperplane tessellation in R d . The distribution of the number of facets f ( Z ) of the typical cell is investigated. It is shown, that under a well-spread condition on the directional distribution, the quantity n 2 d − 1 P ( f ( Z ) = n ) n is bounded from above and from below. When f ( Z ) is large, the isoperimetric ratio of Z is bounded away from zero with high probability. These results rely on one hand on the Complementary Theorem which provides a precise decomposition of the distribution of Z and on the other hand on several geometric estimates related to the approximation of polytopes by polytopes with fewer facets. From the asymptotics of the distribution of f ( Z ) , tail estimates for the so-called Φ content of Z are derived as well as results on the conditional distribution of Z when its Φ content is large.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.016
      Issue No: Vol. 324 (2017)
       
  • Tilting modules of affine quasi-hereditary algebras
    • Authors: Ryo Fujita
      Pages: 241 - 266
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Ryo Fujita
      We discuss tilting modules of affine quasi-hereditary algebras. We present an existence theorem of indecomposable tilting modules when the algebra has a large center and use it to deduce a criterion for an exact functor between two affine highest weight categories to give an equivalence. As an application, we prove that the Arakawa–Suzuki functor (Arakawa–Suzuki, 1998) gives a fully faithful embedding of a block of the deformed BGG category of gl m into the module category of a suitable completion of degenerate affine Hecke algebra of G L n .

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.013
      Issue No: Vol. 324 (2017)
       
  • ⁎-isomorphism of Leavitt path algebras over Z
    • Authors: Toke Meier Carlsen
      Pages: 326 - 335
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Toke Meier Carlsen
      We characterise when the Leavitt path algebras over Z of two arbitrary countable directed graphs are ⁎-isomorphic by showing that two Leavitt path algebras over Z are ⁎-isomorphic if and only if the corresponding graph groupoids are isomorphic (if and only if there is a diagonal preserving isomorphism between the corresponding graph C ⁎ -algebras). We also prove that any ⁎-homomorphism between two Leavitt path algebras over Z maps the diagonal to the diagonal. Both results hold for more general subrings of C than just Z .

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.018
      Issue No: Vol. 324 (2017)
       
  • On the gonality and the slope of a fibered surface
    • Authors: Xin Lu; Kang Zuo
      Pages: 336 - 354
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Xin Lu, Kang Zuo
      Let f : X → B be a locally non-trivial relatively minimal fibration of curves of genus g ≥ 2 . We obtain a lower bound of the slope λ ( f ) increasing with the gonality of the general fiber of f. In particular, we show that λ ( f ) ≥ 4 provided that f is non-hyperelliptic and g ≥ 16 .

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.014
      Issue No: Vol. 324 (2017)
       
  • Exceptional collections on Dolgachev surfaces associated with
           degenerations
    • Authors: Yonghwa Cho; Yongnam Lee
      Pages: 394 - 436
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Yonghwa Cho, Yongnam Lee
      Dolgachev surfaces are simply connected minimal elliptic surfaces with p g = q = 0 and of Kodaira dimension 1. These surfaces are constructed by logarithmic transformations of rational elliptic surfaces. In this paper, we explain the construction of Dolgachev surfaces via Q -Gorenstein smoothing of singular rational surfaces with two cyclic quotient singularities. This construction is based on the paper [25]. Also, some exceptional bundles on Dolgachev surfaces associated with Q -Gorenstein smoothing have been constructed based on the idea of Hacking [12]. In the case if Dolgachev surfaces were of type ( 2 , 3 ) , we describe the Picard group and present an exceptional collection of maximal length. Finally, we prove that the presented exceptional collection is not full, hence there exists a nontrivial phantom category in the derived category.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.012
      Issue No: Vol. 324 (2017)
       
  • Finite orbits in multivalued maps and Bernoulli convolutions
    • Authors: Christoph Bandt
      Pages: 437 - 485
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Christoph Bandt
      Bernoulli convolutions are certain measures on the unit interval depending on a parameter β between 1 and 2. In spite of their simple definition, they are not yet well understood. We study their two-dimensional density which exists by a theorem of Solomyak. To each Bernoulli convolution, there is an interval D called the overlap region, and a map which assigns two values to each point of D and one value to all other points of [ 0 , 1 ] . There are two types of finite orbits of these multivalued maps which correspond to zeros and potential singularities of the density, respectively. Orbits which do not meet D belong to an ordinary map called β-transformation and exist for all β > 1.6182 . They were studied by Erdös, Jóo, Komornik, Sidorov, de Vries and others as points with unique addresses, and by Jordan, Shmerkin and Solomyak as points with maximal local dimension. In the two-dimensional view, these orbits form address curves related to the Milnor–Thurston itineraries in one-dimensional dynamics. The curves depend smoothly on the parameter and represent quantiles of all corresponding Bernoulli convolutions. Finite orbits which intersect D have a network-like structure and can exist only at Perron parameters β. Their points are intersections of extended address curves, and can have finite or countable number of addresses, as found by Sidorov. For an uncountable number of parameters, the central point 1 2 has only two addresses. The intersection of periodic address curves can lead to singularities of the measures. We give examples which are not Pisot or Salem parameters.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.011
      Issue No: Vol. 324 (2017)
       
  • Modular characteristic classes for representations over finite fields
    • Authors: Anssi Lahtinen; David Sprehn
      Pages: 1 - 37
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Anssi Lahtinen, David Sprehn
      The cohomology of the degree-n general linear group over a finite field of characteristic p, with coefficients also in characteristic p, remains poorly understood. For example, the lowest degree previously known to contain nontrivial elements is exponential in n. In this paper, we introduce a new system of characteristic classes for representations over finite fields, and use it to construct a wealth of explicit nontrivial elements in these cohomology groups. In particular we obtain nontrivial elements in degrees linear in n. We also construct nontrivial elements in the mod p homology and cohomology of the automorphism groups of free groups, and the general linear groups over the integers. These elements reside in the unstable range where the homology and cohomology remain mysterious.

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.029
      Issue No: Vol. 323 (2017)
       
  • Connecting toric manifolds by conical Kähler–Einstein metrics
    • Authors: Ved Datar; Bin Guo; Jian Song; Xiaowei Wang
      Pages: 38 - 83
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Ved Datar, Bin Guo, Jian Song, Xiaowei Wang
      We give criterions for the existence of toric conical Kähler–Einstein and Kähler–Ricci soliton metrics on any toric manifold in relation to the greatest Ricci and Bakry–Emery–Ricci lower bound. We also show that any two toric manifolds with the same dimension can be joined by a continuous path of toric manifolds with conical Kähler–Einstein metrics in the Gromov–Hausdorff topology.

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.035
      Issue No: Vol. 323 (2017)
       
  • Filtrations, 1-parameter subgroups, and rational injectivity
    • Authors: Eric M. Friedlander
      Pages: 84 - 113
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Eric M. Friedlander
      We investigate rational G-modules M for a linear algebraic group G over an algebraically closed field k of characteristic p > 0 using filtrations by sub-coalgebras of the coordinate algebra k [ G ] of G. Even in the special case of the additive group G a , interesting structures and examples are revealed. The “degree” filtration we consider for unipotent algebraic groups leads to a “filtration by exponential degree” applicable to rational G modules for any linear algebraic group G of exponential type; this filtration is defined in terms of 1-parameter subgroups and is related to support varieties introduced recently by the author for such rational G-modules. We formulate in terms of this filtration a necessary and sufficient condition for rational injectivity for rational G-modules. Our investigation leads to the consideration of two new classes of rational G-modules: those that are “mock injective” and those that are “mock trivial”.

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.023
      Issue No: Vol. 323 (2017)
       
  • Necessary subspace concentration conditions for the even dual Minkowski
           problem
    • Authors: Martin Henk; Hannes Pollehn
      Pages: 114 - 141
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Martin Henk, Hannes Pollehn
      We prove tight subspace concentration inequalities for the dual curvature measures C ˜ q ( K , ⋅ ) of an n-dimensional origin-symmetric convex body for q ≥ n + 1 . This supplements former results obtained in the range q ≤ n .

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.037
      Issue No: Vol. 323 (2017)
       
  • Algebraic geometry over hyperrings
    • Authors: Jaiung Jun
      Pages: 142 - 192
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Jaiung Jun
      We develop basic notions and methods of algebraic geometry over the algebraic objects called hyperrings. Roughly speaking, hyperrings generalize rings in such a way that an addition is ‘multi-valued’. This paper largely consists of two parts; algebraic aspects and geometric aspects of hyperrings. We first investigate several technical algebraic properties of a hyperring. In the second part, we begin by giving another interpretation of a tropical variety as an algebraic set over the hyperfield which canonically arises from a totally ordered semifield. Then we define a notion of an integral hyperring scheme ( X , O X ) and prove that Γ ( X , O X ) ≃ R for any integral affine hyperring scheme X = Spec R .

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.043
      Issue No: Vol. 323 (2017)
       
  • Periodic distributions and periodic elements in modulation spaces
    • Authors: Joachim Toft; Elmira Nabizadeh
      Pages: 193 - 225
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Joachim Toft, Elmira Nabizadeh
      We characterize periodic elements in Gevrey classes, Gelfand–Shilov distribution spaces and modulation spaces, in terms of estimates of involved Fourier coefficients, and by estimates of their short-time Fourier transforms. If q ∈ [ 1 , ∞ ) , ω is a suitable weight and ( E 0 E ) ′ is the set of all E-periodic elements, then we prove that the dual of M ( ω ) ∞ , q ∩ ( E 0 E ) ′ equals M ( 1 / ω ) ∞ , q ′ ∩ ( E 0 E ) ′ by suitable extensions of Bessel's identity.

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.040
      Issue No: Vol. 323 (2017)
       
  • Canonical tilting relative generators
    • Authors: Agnieszka Bodzenta; Alexey Bondal
      Pages: 226 - 278
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Agnieszka Bodzenta, Alexey Bondal
      Given a relatively projective birational morphism f : X → Y of smooth algebraic spaces with dimension of fibers bounded by 1, we construct tilting relative (over Y) generators T X , f and S X , f in D b ( X ) . We develop a piece of general theory of strict admissible lattice filtrations in triangulated categories and show that D b ( X ) has such a filtration L where the lattice is the set of all birational decompositions f : X → g Z → h Y with smooth Z. The t-structures related to T X , f and S X , f are proved to be glued via filtrations left and right dual to L . We realise all such Z as the fine moduli spaces of simple quotients of O X in the heart of the t-structure for which S X , g is a relative projective generator over Y. This implements the program of interpreting relevant smooth contractions of X in terms of a suitable system of t-structures on D b ( X ) .

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.016
      Issue No: Vol. 323 (2017)
       
  • Green tensor of the Stokes system and asymptotics of stationary
           Navier–Stokes flows in the half space
    • Authors: Kyungkeun Kang; Hideyuki Miura; Tai-Peng Tsai
      Pages: 326 - 366
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
      We derive refined estimates of the Green tensor of the stationary Stokes system in the half space. We then investigate the spatial asymptotics of stationary solutions of the incompressible Navier–Stokes equations in the half space. We also discuss the asymptotics of fast decaying flows in the whole space and exterior domains. In the Appendix we consider axisymmetric self-similar solutions.

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.031
      Issue No: Vol. 323 (2017)
       
  • Ramanujan coverings of graphs
    • Authors: Chris Hall; Doron Puder; William F. Sawin
      Pages: 367 - 410
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Chris Hall, Doron Puder, William F. Sawin
      Let G be a finite connected graph, and let ρ be the spectral radius of its universal cover. For example, if G is k-regular then ρ = 2 k − 1 . We show that for every r, there is an r-covering (a.k.a. an r-lift) of G where all the new eigenvalues are bounded from above by ρ. It follows that a bipartite Ramanujan graph has a Ramanujan r-covering for every r. This generalizes the r = 2 case due to Marcus, Spielman and Srivastava [26]. Every r-covering of G corresponds to a labeling of the edges of G by elements of the symmetric group S r . We generalize this notion to labeling the edges by elements of various groups and present a broader scenario where Ramanujan coverings are guaranteed to exist. In particular, this shows the existence of richer families of bipartite Ramanujan graphs than was known before. Inspired by [26], a crucial component of our proof is the existence of interlacing families of polynomials for complex reflection groups. The core argument of this component is taken from [27]. Another important ingredient of our proof is a new generalization of the matching polynomial of a graph. We define the r-th matching polynomial of G to be the average matching polynomial of all r-coverings of G. We show this polynomial shares many properties with the original matching polynomial. For example, it is real rooted with all its roots inside [ − ρ , ρ ] .

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.042
      Issue No: Vol. 323 (2017)
       
  • Drinfeld center of enriched monoidal categories
    • Authors: Liang Kong; Hao Zheng
      Pages: 411 - 426
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Liang Kong, Hao Zheng
      We define the Drinfeld center of a monoidal category enriched over a braided monoidal category, and show that every modular tensor category can be realized in a canonical way as the Drinfeld center of a self-enriched monoidal category. We also give a generalization of this result for important applications in physics.

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.038
      Issue No: Vol. 323 (2017)
       
  • Bressoud's conjecture
    • Authors: Sun Kim
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Sun Kim
      In 1980, D. M. Bressoud obtained an analytic generalization of the Rogers–Ramanujan–Gordon identities. He then tried to establish a combinatorial interpretation of his identity, which specializes to many well-known Rogers–Ramanujan type identities. He proved that a certain partition identity follows from his identity in a very restrictive case and conjectured that the partition identity holds true in general. In this paper, we prove Bressoud's conjecture for the general case by providing bijective proofs.

      PubDate: 2017-12-27T05:35:23Z
       
  • Sharp logarithmic estimates for positive dyadic shifts
    • Authors: Adam
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Adam Osękowski
      The paper contains the study of sharp logarithmic estimates for positive dyadic shifts A given on probability spaces ( X , μ ) equipped with a tree-like structure. For any K > 0 we determine the smallest constant L = L ( K ) such that ∫ E A f d μ ≤ K ∫ R Ψ ( f ) d μ + L ( K ) ⋅ μ ( E ) , where Ψ ( t ) = ( t + 1 ) log ⁡ ( t + 1 ) − t , E is an arbitrary measurable subset of X and f is an integrable function on X. The proof exploits Bellman function method: we extract the above estimate from the existence of an appropriate special function, enjoying certain size and concavity-type conditions. As a corollary, a dual exponential bound is obtained.

      PubDate: 2017-12-13T02:41:29Z
       
  • Bokstein homomorphism as a universal object
    • Authors: Kaledin
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): D. Kaledin
      We give a simple construction of the correspondence between square-zero extensions R ′ of a ring R by an R-bimodule M and second MacLane cohomology classes of R with coefficients in M (the simplest non-trivial case of the construction is R = M = Z / p , R ′ = Z / p 2 , thus the Bokstein homomorphism of the title). Following Jibladze and Pirashvili, we treat MacLane cohomology as cohomology of non-additive endofunctors of the category of projective R-modules. We explain how to describe liftings of R-modules and complexes of R-modules to R ′ in terms of data purely over R. We show that if R is commutative, then commutative square-zero extensions R ′ correspond to multiplicative extensions of endofunctors. We then explore in detail one particular multiplicative non-additive endofunctor constructed from cyclic powers of a module V over a commutative ring R annihilated by a prime p. In this case, R ′ is the second Witt vectors ring W 2 ( R ) considered as a square-zero extension of R by the Frobenius twist R ( 1 ) .

      PubDate: 2017-12-13T02:41:29Z
       
  • L(R,μ) is unique
    • Authors: Daniel Nam; Trang
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Daniel Rodríguez, Nam Trang
      Under various appropriate hypotheses it is shown that there is only one determinacy model of the form L ( R , μ ) in which μ is a supercompact measure on P ω 1 ( R ) . In particular, this gives a positive answer to a question asked by W.H. Woodin in 1983.

      PubDate: 2017-12-13T02:41:29Z
       
  • Equivariant split generation and mirror symmetry of special isogenous tori
    • Authors: Weiwei
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Weiwei Wu
      We prove a version of equivariant split generation of Fukaya category when a symplectic manifold admits a free action of a finite group G. Combining this with some generalizations of Seidel's algebraic frameworks from [35], we obtain new cases of homological mirror symmetry for some symplectic tori with non-split symplectic forms, which we call special isogenous tori. This extends the work of Abouzaid–Smith [2]. We also show that derived Fukaya categories are complete invariants of special isogenous tori.

      PubDate: 2017-11-12T02:49:38Z
       
 
 
JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327
 
Home (Search)
Subjects A-Z
Publishers A-Z
Customise
APIs
Your IP address: 54.234.65.78
 
About JournalTOCs
API
Help
News (blog, publications)
JournalTOCs on Twitter   JournalTOCs on Facebook

JournalTOCs © 2009-2016