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MATHEMATICS (656 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: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
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: 21)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 7)
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: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
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: 7)
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 Biostatistics     Open Access   (Followers: 9)
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: 9)
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 Network Science     Open Access  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
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: 19)
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: 2)
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: 5)
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: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
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: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (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: 3)
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: 14)
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: 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)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
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: 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)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
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)

        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  [3044 journals]
  • Euler class groups and the homology of elementary and special linear
    • Authors: Marco Schlichting
      Pages: 1 - 81
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Marco Schlichting
      We improve homology stability ranges for elementary and special linear groups over rings with many units. Our result implies stability for unstable Quillen K-groups and proves a conjecture of Bass. For commutative local rings with infinite residue fields, we show that the obstruction to further stability is given by Milnor–Witt K-theory. As an application we construct Euler classes of projective modules with values in the cohomology of the Milnor–Witt K-theory sheaf. For d-dimensional commutative noetherian rings with infinite residue fields we show that the vanishing of the Euler class is necessary and sufficient for an oriented projective module P of rank d to split off a rank 1 free direct summand. Along the way we obtain a new presentation of Milnor–Witt K-theory and of symplectic K 2 simplifying the classical Matsumoto–Moore presentation.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.034
      Issue No: Vol. 320 (2017)
  • Simplicial moves on balanced complexes
    • Authors: Ivan Izmestiev; Steven Klee; Isabella Novik
      Pages: 82 - 114
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Ivan Izmestiev, Steven Klee, Isabella Novik
      We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly ( d + 1 ) -colored) triangulation of a combinatorial d-manifold into another balanced triangulation. These moves form a natural analog of bistellar flips (also known as Pachner moves). Specifically, we establish the following theorem: any two balanced triangulations of a closed combinatorial d-manifold can be connected by a sequence of cross-flips. Along the way we prove that for every m ≥ d + 2 and any closed combinatorial d-manifold M, two m-colored triangulations of M can be connected by a sequence of bistellar flips that preserve the vertex colorings.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.036
      Issue No: Vol. 320 (2017)
  • Degeneracy loci classes in K-theory — determinantal and Pfaffian
    • Authors: Thomas Hudson; Takeshi Ikeda; Tomoo Matsumura; Hiroshi Naruse
      Pages: 115 - 156
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Thomas Hudson, Takeshi Ikeda, Tomoo Matsumura, Hiroshi Naruse
      We prove a determinantal formula that describes the K-theoretic degeneracy loci classes for Grassmann bundles. We further prove Pfaffian formulas for symplectic and odd orthogonal Grassmann bundles. The former generalizes Damon–Kempf–Laksov's determinantal formula, and the latter generalize Pragacz–Kazarian's formulas for the Chow ring.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.038
      Issue No: Vol. 320 (2017)
  • Sheets and associated varieties of affine vertex algebras
    • Authors: Tomoyuki Arakawa; Anne Moreau
      Pages: 157 - 209
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Tomoyuki Arakawa, Anne Moreau
      We show that sheet closures appear as associated varieties of affine vertex algebras. Further, we give new examples of non-admissible affine vertex algebras whose associated variety is contained in the nilpotent cone. We also prove some conjectures from our previous paper and give new examples of lisse affine W-algebras.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.039
      Issue No: Vol. 320 (2017)
  • Log canonical models of elliptic surfaces
    • Authors: Kenneth Ascher; Dori Bejleri
      Pages: 210 - 243
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Kenneth Ascher, Dori Bejleri
      We classify the log canonical models of elliptic surface pairs ( f : X → C , S + F A ) where f : X → C is an elliptic fibration, S is a section, and F A is a weighted sum of marked fibers. In particular, we show how the log canonical models depend on the choice of the weights. We describe a wall and chamber decomposition of the space of weights based on how the log canonical model changes. In addition, we give a generalized formula for the canonical bundle of an elliptic surface with section and marked fibers. This is the first step in constructing compactifications of moduli spaces of elliptic surfaces using the minimal model program.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.035
      Issue No: Vol. 320 (2017)
  • Finite versus infinite: An insufficient shift
    • Authors: Yann Pequignot
      Pages: 244 - 249
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Yann Pequignot
      The shift graph G S is defined on the space of infinite subsets of natural numbers by letting two sets be adjacent if one can be obtained from the other by removing its least element. We show that this graph is not a minimum among the graphs of the form G f defined on some Polish space X, where two distinct points are adjacent if one can be obtained from the other by a given Borel function f : X → X . This answers the primary outstanding question from [8].

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.044
      Issue No: Vol. 320 (2017)
  • Duality structures and discrete conformal variations of piecewise constant
           curvature surfaces
    • Authors: David Glickenstein; Joseph Thomas
      Pages: 250 - 278
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): David Glickenstein, Joseph Thomas
      A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating the simplex has an isometric embedding into a constant curvature background geometry (Euclidean, hyperbolic, or spherical) with the specified edge lengths. Additional geometric structure leads to a notion of discrete conformal structure, generalizing circle packings and their generalizations as studied by Thurston and others. We analyze discrete conformal variations of piecewise constant curvature 2-manifolds, giving particular attention to the variation of angles. Formulas are derived for the derivatives of angles in each background geometry, which yield formulas for the derivatives of curvatures and to curvature functionals. Finally, we provide a complete classification of possible definitions of discrete conformal structures in each of the background geometries.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.043
      Issue No: Vol. 320 (2017)
  • The twisted inverse image pseudofunctor over commutative DG rings and
           perfect base change
    • Authors: Liran Shaul
      Pages: 279 - 328
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Liran Shaul
      Let K be a Gorenstein noetherian ring of finite Krull dimension, and consider the category of cohomologically noetherian commutative differential graded rings A over K , such that H 0 ( A ) is essentially of finite type over K , and A has finite flat dimension over K . We extend Grothendieck's twisted inverse image pseudofunctor to this category by generalizing the theory of rigid dualizing complexes to this setup. We prove functoriality results with respect to cohomologically finite and cohomologically essentially smooth maps, and prove a perfect base change result for f ! in this setting. As application, we deduce a perfect derived base change result for the twisted inverse image of a map between ordinary commutative noetherian rings. Our results generalize and solve some recent conjectures of Yekutieli.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.041
      Issue No: Vol. 320 (2017)
  • The slice method for G-torsors
    • Authors: Roland Lötscher; Mark MacDonald
      Pages: 329 - 360
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Roland Lötscher, Mark MacDonald
      The notion of a ( G , N ) -slice of a G-variety was introduced by P.I. Katsylo in the early 80's for an algebraically closed base field of characteristic 0. Slices (also known under the name of relative sections) have ever since provided a fundamental tool in invariant theory, allowing reduction of rational or regular invariants of an algebraic group G to invariants of a “simpler” group. We refine this notion for a G-scheme over an arbitrary field, and use it to get reduction of structure group results for G-torsors. Namely we show that any ( G , N ) -slice of a versal G-scheme gives surjective maps H 1 ( L , N ) → H 1 ( L , G ) in fppf-cohomology for infinite fields L containing F. We show that every stabilizer in general position H for a geometrically irreducible G-variety V gives rise to a ( G , N G ( H ) ) -slice in our sense. The combination of these two results is applied in particular to obtain a striking new upper bound on the essential dimension of the simply connected split algebraic group of type E 7 .

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.042
      Issue No: Vol. 320 (2017)
  • Irregular varieties with geometric genus one, theta divisors, and fake
    • Authors: Jungkai Chen; Zhi Jiang; Zhiyu Tian
      Pages: 361 - 390
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Jungkai Chen, Zhi Jiang, Zhiyu Tian
      We study the Albanese image of a compact Kähler manifold whose geometric genus is one. In particular, we prove that if the Albanese map is not surjective, then the manifold maps surjectively onto an ample divisor in some abelian variety, and in many cases the ample divisor is a theta divisor. With a further natural assumption on the topology of the manifold, we prove that the manifold is an algebraic fiber space over a genus two curve. Finally we apply these results to study the geometry of a compact Kähler manifold which has the same Hodge numbers as those of an abelian variety of the same dimension.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.09.004
      Issue No: Vol. 320 (2017)
  • Fourier integral operators on Lie groupoids
    • Authors: Jean-Marie Lescure; Stéphane Vassout
      Pages: 391 - 450
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Jean-Marie Lescure, Stéphane Vassout
      As announced in [36], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study Lagrangian conic submanifolds of the symplectic groupoid T ⁎ G . This includes their product, transposition and inversion. We also study the relationship between these Lagrangian submanifolds and the equivariant families of Lagrangian submanifolds of T ⁎ G x × T ⁎ G x parametrized by the units x ∈ G ( 0 ) of G. This allows us to select a subclass of Lagrangian distributions on any Lie groupoid G that deserve the name of Fourier integral G-operators (G-FIOs). By construction, the class of G-FIOs contains the class of equivariant families of ordinary Fourier integral operators on the manifolds G x , x ∈ G ( 0 ) . We then develop for G-FIOs the first stages of the calculus in the spirit of Hormander's work. Finally, we illustrate this calculus in the case of manifolds with boundary.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.027
      Issue No: Vol. 320 (2017)
  • Solvability of Dirac type equations
    • Authors: Qingchun Ji; Ke Zhu
      Pages: 451 - 474
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Qingchun Ji, Ke Zhu
      This paper develops a weighted L 2 -method for the (half) Dirac equation. For Dirac bundles over closed Riemann surfaces, we give a sufficient condition for the solvability of the (half) Dirac equation in terms of a curvature integral. Applying this to the Dolbeault–Dirac operator, we establish an automatic transversality criteria for holomorphic curves in Kähler manifolds. On compact Riemannian manifolds, we give a new perspective on some well-known results about the first eigenvalue of the Dirac operator, and improve the estimates when the Dirac bundle has a Z 2 -grading. On Riemannian manifolds with cylindrical ends, we obtain solvability in the L 2 -spaces with suitable exponential weights while allowing mild negativity of the curvature.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.040
      Issue No: Vol. 320 (2017)
  • Heegaard Floer homology of Matsumoto's manifolds
    • Authors: Motoo Tange
      Pages: 475 - 499
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Motoo Tange
      We consider a homology sphere M n ( K 1 , K 2 ) presented by two knots K 1 , K 2 with linking number 1 and framing ( 0 , n ) . We call the manifold Matsumoto's manifold. We show that M n ( T 2 , 3 , K 2 ) never bounds any contractible 4-manifold if n < 2 τ ( K 2 ) holds. We also give a formula of Ozsváth–Szabó's τ-invariant as the total sum of the Euler numbers of the reduced filtration. We compute the δ-invariants of the twisted Whitehead doubles of torus knots and correction terms of the branched covers of the Whitehead doubles. By using Owens and Strle's obstruction we show that the 12-twisted Whitehead double of the ( 2 , 7 ) -torus knot and the 20-twisted Whitehead double of the ( 3 , 7 ) -torus knot are not slice but the double branched covers bound rational homology 4-balls. These are new examples having a gap between what a knot is slice and what a double branched cover bounds a rational homology 4-ball.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.013
      Issue No: Vol. 320 (2017)
  • On the effective cone of M‾g,n
    • Authors: Scott Mullane
      Pages: 500 - 519
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Scott Mullane
      For every g ≥ 2 and n ≥ g + 1 we exhibit infinitely many extremal effective divisors in M ‾ g , n coming from the strata of abelian differentials.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.09.005
      Issue No: Vol. 320 (2017)
  • Convex hulls of random walks: Expected number of faces and face
    • Authors: Zakhar Kabluchko; Vladislav Vysotsky; Dmitry Zaporozhets
      Pages: 595 - 629
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Zakhar Kabluchko, Vladislav Vysotsky, Dmitry Zaporozhets
      Consider a sequence of partial sums S i = ξ 1 + … + ξ i , 1 ≤ i ≤ n , starting at S 0 = 0 , whose increments ξ 1 , … , ξ n are random vectors in R d , d ≤ n . We are interested in the properties of the convex hull C n : = Conv ( S 0 , S 1 , … , S n ) . Assuming that the tuple ( ξ 1 , … , ξ n ) is exchangeable and a certain general position condition holds, we prove that the expected number of k-dimensional faces of C n is given by the formula E [ f k ( C n ) ] = 2 ⋅ k ! n ! ∑ l = 0 ∞ [ n + 1 d − 2 l ] { d − 2 l k + 1 } , for all 0 ≤ k ≤ d − 1 , where [ n m ] and { n m } are Stirling numbers of the first and second kind, respectively. Further, we compute explicitly the probability that for given indices 0 ≤ i 1 < … < i k + 1 ≤ n , the points S i 1 , … , S i k + 1 form a k-dimensional face of Conv ( S 0 , S 1 , … , S n ) . This is done in two different settings: for random walks with symmetrically exchangeable increments and for random bridges with exchangeable increments. These results generalize the classical one-dimensional discrete arcsine law for the position of the maximum due to E. Sparre Andersen. All our formulae are distribution-free, that is do not depend on the distribution of the increments
      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.09.002
      Issue No: Vol. 320 (2017)
  • Factorization and non-factorization theorems for pseudocontinuable
    • Authors: Konstantin M. Dyakonov
      Pages: 630 - 651
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Konstantin M. Dyakonov
      Let θ be an inner function on the unit disk, and let K θ p : = H p ∩ θ H 0 p ‾ be the associated star-invariant subspace of the Hardy space H p , with p ≥ 1 . While a nontrivial function f ∈ K θ p is never divisible by θ, it may have a factor h which is ‘‘not too different” from θ in the sense that the ratio h / θ (or just the anti-analytic part thereof) is smooth on the circle. In this case, f is shown to have additional integrability and/or smoothness properties, much in the spirit of the Hardy–Littlewood–Sobolev embedding theorem. The appropriate norm estimates are established, and their sharpness is discussed.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.09.001
      Issue No: Vol. 320 (2017)
  • Finite topology self-translating surfaces for the mean curvature flow in
    • Authors: Juan Dávila; Manuel del Pino; Xuan Hien Nguyen
      Pages: 674 - 729
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Juan Dávila, Manuel del Pino, Xuan Hien Nguyen
      Finite topology self-translating surfaces for the mean curvature flow constitute a key element in the analysis of Type II singularities from a compact surface because they arise as limits after suitable blow-up scalings around the singularity. We prove the existence of such a surface M ⊂ R 3 that is orientable, embedded, complete, and with three ends asymptotically paraboloidal. The fact that M is self-translating means that the moving surface S ( t ) = M + t e z evolves by mean curvature flow, or equivalently, that M satisfies the equation H M = ν ⋅ e z where H M denotes mean curvature, ν is a choice of unit normal to M, and e z is a unit vector along the z-axis. This surface M is in correspondence with the classical three-end Costa–Hoffman–Meeks minimal surface with large genus, which has two asymptotically catenoidal ends and one planar end, and a long array of small tunnels in the intersection region resembling a periodic Scherk surface. This example is the first non-trivial one of its kind, and it suggests a strong connection between this problem and the theory of embedded complete minimal surfaces with finite total curvature.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.09.014
      Issue No: Vol. 320 (2017)
  • Moment map flows and the Hecke correspondence for quivers
    • Authors: Graeme Wilkin
      Pages: 730 - 794
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Graeme Wilkin
      In this paper we investigate the convergence properties of the upwards gradient flow of the norm-square of a moment map on the space of representations of a quiver. The first main result gives a necessary and sufficient algebraic criterion for a complex group orbit to intersect the unstable set of a given critical point. Therefore we can classify all of the isomorphism classes which contain an initial condition that flows up to a given critical point. As an application, we then show that Nakajima's Hecke correspondence for quivers has a Morse-theoretic interpretation as pairs of critical points connected by flow lines for the norm-square of a moment map. The results are valid in the general setting of finite quivers with relations.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.09.011
      Issue No: Vol. 320 (2017)
  • A K-theoretic interpretation of real Deligne cohomology
    • Authors: J.P. Pridham
      Pages: 795 - 826
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): J.P. Pridham
      We show that real Deligne cohomology of a complex manifold X arises locally as a topological vector space completion of the analytic Lie groupoid of holomorphic vector bundles. Thus Beilinson's regulator arises naturally as a comparison map between K-theory groups of different types.

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.09.018
      Issue No: Vol. 320 (2017)
  • Hole probability for nodal sets of the cut-off Gaussian Free Field
    • Authors: Alejandro Rivera
      Pages: 1 - 39
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Alejandro Rivera
      Let ( Σ , g ) be a closed connected surface equipped with a riemannian metric. Let ( λ n ) n ∈ N and ( ψ n ) n ∈ N be the increasing sequence of eigenvalues and the sequence of corresponding L 2 -normalized eigenfunctions of the laplacian on Σ. For each L > 0 , we consider ϕ L = ∑ 0 < λ n ≤ L ξ n λ n ψ n where the ξ n are i.i.d centered gaussians with variance 1. As L → ∞ , ϕ L converges a.s. to the Gaussian Free Field on Σ in the sense of distributions. We first compute the asymptotic behavior of the covariance function for this family of fields as L → ∞ . We then use this result to obtain the asymptotics of the probability that ϕ L is positive on a given open proper subset with smooth boundary. In doing so, we also prove the concentration of the supremum of ϕ L around 1 2 π ln ⁡ L .

      PubDate: 2017-08-28T04:47:53Z
      DOI: 10.1016/j.aim.2017.08.002
      Issue No: Vol. 319 (2017)
  • Rectangular Kronecker coefficients and plethysms in geometric complexity
    • Authors: Christian Ikenmeyer; Greta Panova
      Pages: 40 - 66
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Christian Ikenmeyer, Greta Panova
      We prove that in the geometric complexity theory program the vanishing of rectangular Kronecker coefficients cannot be used to prove superpolynomial determinantal complexity lower bounds for the permanent polynomial. Moreover, we prove the positivity of rectangular Kronecker coefficients for a large class of partitions where the side lengths of the rectangle are at least quadratic in the length of the partition. We also compare rectangular Kronecker coefficients with their corresponding plethysm coefficients, which leads to a new lower bound for rectangular Kronecker coefficients. Moreover, we prove that the saturation of the rectangular Kronecker semigroup is trivial, we show that the rectangular Kronecker positivity stretching factor is 2 for a long first row, and we completely classify the positivity of rectangular limit Kronecker coefficients that were introduced by Manivel in 2011.

      PubDate: 2017-08-28T04:47:53Z
      DOI: 10.1016/j.aim.2017.08.024
      Issue No: Vol. 319 (2017)
  • A note on Willmore minimizing Klein bottles in Euclidean space
    • Authors: Jonas Hirsch; Elena Mäder-Baumdicker
      Pages: 67 - 75
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Jonas Hirsch, Elena Mäder-Baumdicker
      We show that φ ∘ τ ˜ 3 , 1 : K → R 4 × { 0 } n − 4 is the unique minimizer among immersed Klein bottles in its conformal class, where φ : S 4 → R 4 is a stereographic projection and τ ˜ 3 , 1 is the bipolar surface of Lawson's τ 3 , 1 -surface [11]. We conjecture that φ ∘ τ ˜ 3 , 1 is the unique minimizer among immersed Klein bottles into R n , n ≥ 4 , whose existence the authors and P. Breuning proved in [2].

      PubDate: 2017-08-28T04:47:53Z
      DOI: 10.1016/j.aim.2017.08.021
      Issue No: Vol. 319 (2017)
  • Tensor valuations on lattice polytopes
    • Authors: Monika Ludwig; Laura Silverstein
      Pages: 76 - 110
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Monika Ludwig, Laura Silverstein
      The Ehrhart polynomial and the reciprocity theorems by Ehrhart & Macdonald are extended to tensor valuations on lattice polytopes. A complete classification is established of tensor valuations of rank up to eight that are equivariant with respect to the special linear group over the integers and translation covariant. Every such valuation is a linear combination of the Ehrhart tensors which is shown to no longer hold true for rank nine.

      PubDate: 2017-08-28T04:47:53Z
      DOI: 10.1016/j.aim.2017.08.015
      Issue No: Vol. 319 (2017)
  • On pointwise and weighted estimates for commutators of
           Calderón–Zygmund operators
    • Authors: Andrei K. Lerner; Sheldy Ombrosi; Israel P. Rivera-Ríos
      Pages: 153 - 181
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Andrei K. Lerner, Sheldy Ombrosi, Israel P. Rivera-Ríos
      In recent years, it has been well understood that a Calderón–Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar pointwise estimate for the commutator [ b , T ] with a locally integrable function b. This result is applied into two directions. If b ∈ B M O , we improve several weighted weak type bounds for [ b , T ] . If b belongs to the weighted BMO, we obtain a quantitative form of the two-weighted bound for [ b , T ] due to Bloom–Holmes–Lacey–Wick.

      PubDate: 2017-08-28T04:47:53Z
      DOI: 10.1016/j.aim.2017.08.022
      Issue No: Vol. 319 (2017)
  • Maximal green sequences for quivers of finite mutation type
    • Authors: Matthew R. Mills
      Pages: 182 - 210
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Matthew R. Mills
      In general, the existence of a maximal green sequence is not mutation invariant. In this paper we show that it is in fact mutation invariant for cluster quivers of finite mutation type. In particular, we show that a mutation finite cluster quiver has a maximal green sequence unless it arises from a once-punctured closed marked surface, or one of the two quivers in the mutation class of X 7 . We develop a procedure to explicitly find maximal green sequences for cluster quivers associated to arbitrary triangulations of closed marked surfaces with at least two punctures. As a corollary, it follows that any triangulation of a marked surface with boundary has a maximal green sequence. We also compute explicit maximal green sequences for exceptional quivers of finite mutation type.

      PubDate: 2017-08-28T04:47:53Z
      DOI: 10.1016/j.aim.2017.08.019
      Issue No: Vol. 319 (2017)
  • Bantay's trace in unitary modular tensor categories
    • Authors: Luca Giorgetti; Karl-Henning Rehren
      Pages: 211 - 223
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Luca Giorgetti, Karl-Henning Rehren
      We give a proof of a formula for the trace of self-braidings (in an arbitrary channel) in UMTCs which first appeared in the context of rational conformal field theories (CFTs) [2]. The trace is another invariant for UMTCs which depends only on modular data, and contains the expression of the Frobenius–Schur indicator [21] as a special case. Furthermore, we discuss some applications of the trace formula to the realizability problem of modular data and to the classification of UMTCs.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.018
      Issue No: Vol. 319 (2017)
  • Full measure reducibility and localization for quasiperiodic Jacobi
           operators: A topological criterion
    • Authors: Rui Han; Svetlana Jitomirskaya
      Pages: 224 - 250
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Rui Han, Svetlana Jitomirskaya
      We establish a topological criterion for connection between reducibility to constant rotations and dual localization, for the general family of analytic quasiperiodic Jacobi operators. As a corollary, we obtain the sharp arithmetic phase transition for the extended Harper's model in the positive Lyapunov exponent region.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.026
      Issue No: Vol. 319 (2017)
  • Convergence rate for spectral distribution of addition of random matrices
    • Authors: Zhigang Bao; László Erdős; Kevin Schnelli
      Pages: 251 - 291
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Zhigang Bao, László Erdős, Kevin Schnelli
      Let A and B be two N by N deterministic Hermitian matrices and let U be an N by N Haar distributed unitary matrix. It is well known that the spectral distribution of the sum H = A + U B U ⁎ converges weakly to the free additive convolution of the spectral distributions of A and B, as N tends to infinity. We establish the optimal convergence rate 1 N in the bulk of the spectrum.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.028
      Issue No: Vol. 319 (2017)
  • Resilience for the Littlewood–Offord problem
    • Authors: Afonso S. Bandeira; Asaf Ferber; Matthew Kwan
      Pages: 292 - 312
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Afonso S. Bandeira, Asaf Ferber, Matthew Kwan
      Consider the sum X ( ξ ) = ∑ i = 1 n a i ξ i , where a = ( a i ) i = 1 n is a sequence of non-zero reals and ξ = ( ξ i ) i = 1 n is a sequence of i.i.d. Rademacher random variables (that is, Pr ⁡ [ ξ i = 1 ] = Pr ⁡ [ ξ i = − 1 ] = 1 / 2 ). The classical Littlewood–Offord problem asks for the best possible upper bound on the concentration probabilities Pr ⁡ [ X = x ] . In this paper we study a resilience version of the Littlewood–Offord problem: how many of the ξ i is an adversary typically allowed to change without being able to force concentration on a particular value' We solve this problem asymptotically, and present a few interesting open problems.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.031
      Issue No: Vol. 319 (2017)
  • Upper tails and independence polynomials in random graphs
    • Authors: Bhaswar B. Bhattacharya; Shirshendu Ganguly; Eyal Lubetzky; Yufei Zhao
      Pages: 313 - 347
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Bhaswar B. Bhattacharya, Shirshendu Ganguly, Eyal Lubetzky, Yufei Zhao
      The upper tail problem in the Erdős–Rényi random graph G ∼ G n , p asks to estimate the probability that the number of copies of a graph H in G exceeds its expectation by a factor 1 + δ . Chatterjee and Dembo showed that in the sparse regime of p → 0 as n → ∞ with p ≥ n − α for an explicit α = α H > 0 , this problem reduces to a natural variational problem on weighted graphs, which was thereafter asymptotically solved by two of the authors in the case where H is a clique. Here we extend the latter work to any fixed graph H and determine a function c H ( δ ) such that, for p as above and any fixed δ > 0 , the upper tail probability is exp ⁡ [ − ( c H ( δ ) + o ( 1 ) ) n 2 p Δ log ⁡ ( 1 / p ) ] , where Δ is the maximum degree of H. As it turns out, the leading order constant in the large deviation rate function, c H ( δ ) , is governed by the independence polynomial of H, defined as P H ( x ) = ∑ i H ( k ) x k where i H ( k ) is the number of independent sets of size k in H. For instance, if H is a regular graph on m vertices, then c H ( δ ) is the minimum between 1 2 δ 2 / m and the unique positive solution of P H ( x ) = 1 + δ .

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.003
      Issue No: Vol. 319 (2017)
  • Diffusive wave in the low Mach limit for compressible Navier–Stokes
    • Authors: Feimin Huang; Tian-Yi Wang; Yong Wang
      Pages: 348 - 395
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Feimin Huang, Tian-Yi Wang, Yong Wang
      The low Mach limit for 1D non-isentropic compressible Navier–Stokes flow, whose density and temperature have different asymptotic states at infinity, is rigorously justified. The problems are considered on both well-prepared and ill-prepared data. For the well-prepared data, the solutions of compressible Navier–Stokes equations are shown to converge to a nonlinear diffusion wave solution globally in time as Mach number goes to zero when the difference between the states at ±∞ is suitably small. In particular, the velocity of diffusion wave is only driven by the variation of temperature. It is further shown that the solution of compressible Navier–Stokes system also has the same property when Mach number is small, which has never been observed before. The convergence rates on both Mach number and time are also obtained for the well-prepared data. For the ill-prepared data, the limit relies on the uniform estimates including weighted time derivatives and an extended convergence lemma. And the difference between the states at ±∞ can be arbitrary large in this case.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.004
      Issue No: Vol. 319 (2017)
  • Heat kernel and curvature bounds in Ricci flows with bounded scalar
    • Authors: Richard H. Bamler; Qi S. Zhang
      Pages: 396 - 450
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Richard H. Bamler, Qi S. Zhang
      In this paper we analyze Ricci flows on which the scalar curvature is globally or locally bounded from above by a uniform or time-dependent constant. On such Ricci flows we establish a new time-derivative bound for solutions to the heat equation. Based on this bound, we solve several open problems: 1. distance distortion estimates, 2. the existence of a cutoff function, 3. Gaussian bounds for heat kernels, and, 4. a backward pseudolocality theorem, which states that a curvature bound at a later time implies a curvature bound at a slightly earlier time. Using the backward pseudolocality theorem, we next establish a uniform L 2 curvature bound in dimension 4 and we show that the flow in dimension 4 converges to an orbifold at a singularity. We also obtain a stronger ε-regularity theorem for Ricci flows. This result is particularly useful in the study of Kähler Ricci flows on Fano manifolds, where it can be used to derive certain convergence results.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.025
      Issue No: Vol. 319 (2017)
  • The set of all orthogonal complex structures on the flat 6-tori
    • Authors: Gabriel Khan; Bo Yang; Fangyang Zheng
      Pages: 451 - 471
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Gabriel Khan, Bo Yang, Fangyang Zheng
      In [2], Borisov, Salamon and Viaclovsky constructed non-standard orthogonal complex structures on flat tori T R 2 n for any n ≥ 3 . We will call these examples BSV-tori. In this note, we show that on a flat 6-torus, all the orthogonal complex structures are either the complex tori or the BSV-tori. This solves the classification problem for compact Hermitian manifolds with flat Riemannian connection in the case of complex dimension three.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.037
      Issue No: Vol. 319 (2017)
  • Finite and infinite dimensional Lie group structures on Riordan groups
    • Authors: Gi-Sang Cheon; Ana Luzón; Manuel A. Morón; L. Felipe Prieto-Martinez; Minho Song
      Pages: 522 - 566
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Gi-Sang Cheon, Ana Luzón, Manuel A. Morón, L. Felipe Prieto-Martinez, Minho Song
      We introduce a Frechet Lie group structure on the Riordan group. We give a description of the corresponding Lie algebra as a vector space of infinite lower triangular matrices. We describe a natural linear action induced on the Frechet space K N by any element in the Lie algebra. We relate this to a certain family of bivariate linear partial differential equations. We obtain the solutions of such equations using one-parameter groups in the Riordan group. We show how a particular semidirect product decomposition in the Riordan group is reflected in the Lie algebra. We study the stabilizer of a formal power series under the action induced by Riordan matrices. We get stabilizers in the fraction field K ( ( x ) ) using bi-infinite representations. We provide some examples. The main tool to get our results is the paper [18] where the Riordan group was described using inverse sequences of groups of finite matrices.

      PubDate: 2017-09-06T12:22:15Z
      DOI: 10.1016/j.aim.2017.08.033
      Issue No: Vol. 319 (2017)
  • On polynomially integrable convex bodies
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Alexander Koldobsky, Alexander S. Merkurjev, Vladyslav Yaskin
      An infinitely smooth convex body in R n is called polynomially integrable of degree N if its parallel section functions are polynomials of degree N. We prove that the only smooth convex bodies with this property in odd dimensions are ellipsoids, if N ≥ n − 1 . This is in contrast with the case of even dimensions and the case of odd dimensions with N < n − 1 , where such bodies do not exist, as it was recently shown by Agranovsky.

      PubDate: 2017-09-23T12:05:01Z
  • Cuspidal characters and automorphisms
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Gunter Malle
      We investigate the action of outer automorphisms of finite groups of Lie type on their irreducible characters. We obtain a definite result for cuspidal characters. As an application we verify the inductive McKay condition for some further infinite families of simple groups at certain primes.

      PubDate: 2017-09-23T12:05:01Z
  • Compressible Navier–Stokes system: Large solutions and
           incompressible limit
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Raphaël Danchin, Piotr Bogusław Mucha
      Here we prove the existence of global in time regular solutions to the two-dimensional compressible Navier–Stokes equations supplemented with arbitrary large initial velocity v 0 and almost constant density ϱ 0 , for large volume (bulk) viscosity. The result is generalized to the higher dimensional case under the additional assumption that the strong solution of the classical incompressible Navier–Stokes equations supplemented with the divergence-free projection of v 0 , is global. The systems are examined in R d with d ≥ 2 , in the critical B ˙ 2 , 1 s Besov spaces framework.

      PubDate: 2017-09-23T12:05:01Z
  • Two-end solutions to the Allen–Cahn equation in R3
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Changfeng Gui, Yong Liu, Juncheng Wei
      In this paper, we study axially symmetric solutions of Allen–Cahn equation in the three dimensional Euclidean space. Using a sophisticated continuation method, we show the existence of a complete family of axially symmetric solutions with a range of logarithmic growth rates, which may be regarded as the analogue of the family of catenoids and hence called two-end solutions. Nonexistence of two-end solution with a small growth rate is also shown, which differs from the theory of minimal surfaces.

      PubDate: 2017-09-23T12:05:01Z
  • On the distribution of Rudin–Shapiro polynomials and lacunary walks
           on SU(2)
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Brad Rodgers
      We characterize the limiting distribution of Rudin–Shapiro polynomials, showing that, normalized, their values become uniformly distributed in the disc. This resolves conjectures of Saffari and Montgomery. Our proof proceeds by relating the polynomials' distribution to that of a product of weakly dependent random matrices, which we analyze using the representation theory of S U ( 2 ) . Our approach leads us to a non-commutative analogue of the classical central limit theorem of Salem and Zygmund, which may be of independent interest.

      PubDate: 2017-09-23T12:05:01Z
  • Multilinear Schur multipliers and Schatten properties of operator Taylor
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Denis Potapov, Anna Skripka, Fedor Sukochev, Anna Tomskova
      We establish sharp conditions on scalar functions and perturbations that guarantee Schatten summability of nth order operator Taylor remainders. In the special case of dimension one, our estimates of these remainders deliver well known classical estimates of scalar Taylor remainders. We prove that if a scalar function f is in the set C n and a perturbation is in the pth Schatten class S p , p > n , then the respective nth order operator Taylor remainder is an element of S p / n and has an estimate like the one in [16]. We construct examples of f ∈ C n and perturbations in S n such that the nth order Taylor remainder of the respective operator function is not in S 1 . Our construction relies, in particular, on novel dimension dependent estimates for Schatten norms of multilinear Schur multipliers from below that are of interest in their own right. Our results apply to both self-adjoint and unitary operators.

      PubDate: 2017-09-23T12:05:01Z
  • Random walks and induced Dirichlet forms on self-similar sets
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Shi-Lei Kong, Ka-Sing Lau, Ting-Kam Leonard Wong
      Let K be a self-similar set satisfying the open set condition. Following Kaimanovich's elegant idea [25], it has been proved that on the symbolic space X of K a natural augmented tree structure E exists; it is hyperbolic, and the hyperbolic boundary ∂ H X with the Gromov metric is Hölder equivalent to K. In this paper we consider certain reversible random walks with return ratio 0 < λ < 1 on ( X , E ) . We show that the Martin boundary M can be identified with ∂ H X and K. With this setup and a device of Silverstein [41], we obtain precise estimates of the Martin kernel and the Naïm kernel in terms of the Gromov product. Moreover, the Naïm kernel turns out to be a jump kernel satisfying the estimate Θ ( ξ , η ) ≍ ξ − η − ( α + β ) , where α is the Hausdorff dimension of K and β depends on λ. For suitable β, the kernel defines a regular non-local Dirichlet form on K. This extends the results of Kigami [27] concerning random walks on certain trees with Cantor-type sets as boundaries (see also [5]).

      PubDate: 2017-09-23T12:05:01Z
  • Existence of HKT metrics on hypercomplex manifolds of real dimension 8
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Gueo Grantcharov, Mehdi Lejmi, Misha Verbitsky
      A hypercomplex manifold M is a manifold equipped with three complex structures I , J , K satisfying quaternionic relations. Such a manifold admits a canonical torsion-free connection preserving the quaternion action, called the Obata connection. A quaternionic Hermitian metric is a Riemannian metric which is invariant with respect to unitary quaternions. Such a metric is called hyperkähler with torsion (HKT for short) if it is locally obtained as the Hessian of a function averaged with quaternions. An HKT metric is a natural analogue of a Kähler metric on a complex manifold. We push this analogy further, proving a quaternionic analogue of the result of Buchdahl and of Lamari that a compact complex surface M admits a Kähler structure if and only if b 1 ( M ) is even. We show that a hypercomplex manifold M with the Obata holonomy contained in S L ( 2 , H ) admits an HKT structure if and only if H 1 ( O ( M , I ) ) is even-dimensional.

      PubDate: 2017-09-23T12:05:01Z
  • Residues for flags of holomorphic foliations
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Jean-Paul Brasselet, Maurício Corrêa, Fernando Lourenço
      In this work we prove a Baum–Bott type residue theorem for flags of holomorphic foliations. We prove some relations between the residues of the flag and the residues of their correspondent foliations. We define the Nash residue for flags and we give a partial answer to the Baum–Bott type rationality conjecture in this context.

      PubDate: 2017-09-23T12:05:01Z
  • The distribution of zeros of ζ′(s) and gaps between zeros of
    • Authors: Fan
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Fan Ge
      Assume the Riemann Hypothesis. We establish a local structure theorem for zeros of the Riemann zeta-function ζ ( s ) and its derivative ζ ′ ( s ) . As an application, we prove a stronger form of half of a conjecture of Radziwiłł [18] concerning the global statistics of these zeros. Roughly speaking, we show that on the Riemann Hypothesis, if there occurs a small gap between consecutive zeta zeros, then there is exactly one zero of ζ ′ ( s ) lying not only very close to the critical line but also between that pair of zeta zeros. This refines a result of Zhang [22]. Some related results are also shown. For example, we prove a weak form of a conjecture of Soundararajan, and suggest a repulsion phenomena for zeros of ζ ′ ( s ) .

      PubDate: 2017-09-17T11:43:03Z
  • Affine strict polynomial functors and formality
    • Authors: Marcin
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Marcin Chałupnik
      We introduce the notion of an affine strict polynomial functor. We show how this concept helps to understand homological behavior of the operation of Frobenius twist in the category of strict polynomial functors over a field of positive characteristic. We also point out for an analogy between our category and the category of representations of the group of algebraic loops on G L n .

      PubDate: 2017-09-17T11:43:03Z
  • 12, 24 and beyond
    • Authors: Leonor Godinho; Frederik von Heymann Silvia Sabatini
      Abstract: Publication date: 15 October 2017
      Source:Advances in Mathematics, Volume 319
      Author(s): Leonor Godinho, Frederik von Heymann, Silvia Sabatini
      We generalize the well-known “12 and 24” theorems for reflexive polytopes of dimension 2 and 3 to any smooth reflexive polytope. Our methods apply to a wider category of objects, here called reflexive GKM graphs, that are associated with certain monotone symplectic manifolds which do not necessarily admit a toric action. As an application, we provide bounds on the Betti numbers for certain monotone Hamiltonian spaces which depend on the minimal Chern number of the manifold.

      PubDate: 2017-09-06T12:22:15Z
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