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  Subjects -> MATHEMATICS (Total: 879 journals)
    - APPLIED MATHEMATICS (71 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (651 journals)
    - MATHEMATICS (GENERAL) (42 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (77 journals)

MATHEMATICS (651 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 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: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
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: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 3)
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: 10)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 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: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied 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: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 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: 4)
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: 21)
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: 2)
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: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 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: 4)
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)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)

        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  [3042 journals]
  • Smooth duality in natural characteristic
    • Authors: Jan Kohlhaase
      Pages: 1 - 49
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Jan Kohlhaase
      We develop a duality theory for admissible smooth representations of p-adic Lie groups on vector spaces over fields of characteristic p. To this end we introduce certain higher smooth duality functors and relate our construction to the Auslander duality of completed group rings. We study the behavior of smooth duality under tensor products, inflation and induction, and discuss the dimension theory of smooth mod-p representations of a p-adic reductive group. Finally, we compute the higher smooth duals of the irreducible smooth representations of GL 2 ( Q p ) in characteristic p and relate our results to the contragredient operation of Colmez.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.06.038
      Issue No: Vol. 317 (2017)
       
  • Geometric representations of the formal affine Hecke algebra
    • Authors: Gufang Zhao; Changlong Zhong
      Pages: 50 - 90
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Gufang Zhao, Changlong Zhong
      For any formal group law, there is a formal affine Hecke algebra defined by Hoffnung–Malagón-López–Savage–Zainoulline. Coming from this formal group law, there is also an oriented cohomology theory. We identify the formal affine Hecke algebra with a convolution algebra coming from the oriented cohomology theory applied to the Steinberg variety. As a consequence, this algebra acts on the corresponding cohomology of the Springer fibers. This generalizes the action of classical affine Hecke algebra on the K-theory of the Springer fibers constructed by Lusztig. We also give a residue interpretation of the formal affine Hecke algebra, which generalizes the residue construction of Ginzburg–Kapranov–Vasserot when the formal group law comes from a 1-dimensional algebraic group.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.03.026
      Issue No: Vol. 317 (2017)
       
  • Injective subsets of l∞(I)
    • Authors: Dominic Descombes; Maël Pavón
      Pages: 91 - 107
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Dominic Descombes, Maël Pavón
      We prove an explicit characterization of all injective subsets of the model space l ∞ ( I ) of all bounded real-valued functions defined on a non-empty set I, endowed with the supremum norm. Since the class of all injective metric spaces coincides with the one of all absolute 1-Lipschitz retracts, the present work yields a characterization of all the subsets of l ∞ ( I ) that are absolute 1-Lipschitz retracts.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.06.025
      Issue No: Vol. 317 (2017)
       
  • Semiprojectivity and properly infinite projections in graph
           C⁎-algebras
    • Authors: Søren Eilers; Takeshi Katsura
      Pages: 108 - 156
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Søren Eilers, Takeshi Katsura
      We give a complete description of which unital graph C ⁎ -algebras are semiprojective, and use it to disprove two conjectures by Blackadar. To do so, we perform a detailed analysis of which projections are properly infinite in such C ⁎ -algebras.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.06.034
      Issue No: Vol. 317 (2017)
       
  • Spectral cluster bounds for orthonormal systems and oscillatory integral
           operators in Schatten spaces
    • Authors: Rupert L. Frank; Julien Sabin
      Pages: 157 - 192
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Rupert L. Frank, Julien Sabin
      We generalize the L p spectral cluster bounds of Sogge for the Laplace–Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. The optimality of these new bounds is also discussed. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.06.023
      Issue No: Vol. 317 (2017)
       
  • Free Stein kernels and an improvement of the free logarithmic Sobolev
           inequality
    • Authors: Max Fathi; Brent Nelson
      Pages: 193 - 223
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Max Fathi, Brent Nelson
      We introduce a free version of the Stein kernel, relative to a semicircular law. We use it to obtain a free counterpart of the HSI inequality of Ledoux, Peccatti and Nourdin, which is an improvement of the free logarithmic Sobolev inequality of Biane and Speicher, as well as a rate of convergence in the (multivariate) entropic free Central Limit Theorem. We also compute the free Stein kernels for several relevant families of self-adjoint operators.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.06.035
      Issue No: Vol. 317 (2017)
       
  • Part I, Free actions of compact Abelian groups on C⁎-algebras
    • Authors: Kay Schwieger; Stefan Wagner
      Pages: 224 - 266
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Kay Schwieger, Stefan Wagner
      We study free actions of compact groups on unital C⁎-algebras. In particular, we provide a complete classification theory of these actions for compact Abelian groups and explain its relation to the classification of classical principal bundles.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.06.036
      Issue No: Vol. 317 (2017)
       
  • The Freidlin–Gärtner formula for general reaction terms
    • Authors: Luca Rossi
      Pages: 267 - 298
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Luca Rossi
      We devise a new geometric approach to study the propagation of disturbance – compactly supported data – in reaction–diffusion equations. The method builds a bridge between the propagation of disturbance and of almost planar solutions. It applies to very general reaction–diffusion equations. The main consequences we derive in this paper are: a new proof of the classical Freidlin–Gärtner formula for the asymptotic speed of spreading for periodic Fisher–KPP equations; extension of the formula to the monostable, combustion and bistable cases; existence of the asymptotic speed of spreading for equations with almost periodic temporal dependence; derivation of multi-tiered propagation for multistable equations.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.07.002
      Issue No: Vol. 317 (2017)
       
  • Comparing the commutative and non-commutative resolutions for
           determinantal varieties of skew symmetric and symmetric matrices
    • Authors: Špela Špenko; Michel Van den Bergh
      Pages: 350 - 370
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Špela Špenko, Michel Van den Bergh
      Let Y be the variety of (skew) symmetric n × n -matrices of rank ≤r. In paper we construct a full faithful embedding between the derived category of a non-commutative resolution of Y, constructed earlier by the authors, and the derived category of the classical Springer resolution of Y.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.06.004
      Issue No: Vol. 317 (2017)
       
  • Towards homological projective duality for S2P3 and S2P4
    • Authors: Shinobu Hosono; Hiromichi Takagi
      Pages: 371 - 409
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Shinobu Hosono, Hiromichi Takagi
      We provide homological foundations to establish conjectural homological projective dualities in two cases; 1) the duality between S 2 P 3 and the double cover of the projective 9-space branched along the symmetric determinantal quartic, and 2) the duality between S 2 P 4 and the double cover of the symmetric determinantal quintic in P 14 branched along the symmetric determinantal locus of rank at most 3.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.06.039
      Issue No: Vol. 317 (2017)
       
  • Wave breaking in the Whitham equation
    • Authors: Vera Mikyoung Hur
      Pages: 410 - 437
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Vera Mikyoung Hur
      We prove wave breaking — bounded solutions with unbounded derivatives — in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope of the initial datum is sufficiently negative, whereby we solve a Whitham's conjecture. We extend the result to equations of Korteweg–de Vries type for a range of fractional dispersion.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.07.006
      Issue No: Vol. 317 (2017)
       
  • Metric uniformization of morphisms of Berkovich curves
    • Authors: Michael Temkin
      Pages: 438 - 472
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Michael Temkin
      We show that the metric structure of morphisms f : Y → X between quasi-smooth compact Berkovich curves over an algebraically closed field admits a finite combinatorial description. In particular, for a large enough skeleton Γ = ( Γ Y , Γ X ) of f, the sets N f , ≥ n of points of Y of multiplicity at least n in the fiber are radial around Γ Y with the radius changing piecewise monomially along Γ Y . In this case, for any interval l = [ z , y ] ⊂ Y connecting a point z of type 1 to the skeleton, the restriction f l gives rise to a profile piecewise monomial function φ y : [ 0 , 1 ] → [ 0 , 1 ] that depends only on the type 2 point y ∈ Γ Y . In particular, the metric structure of f is determined by Γ and the family of the profile functions { φ y } with y ∈ Γ Y ( 2 ) . We prove that this family is piecewise monomial in y and naturally extends to the whole Y. In addition, we extend the classical theory of higher ramification groups to arbitrary real-valued fields and show that φ y coincides with the Herbrand function of H ( y ) / H ( f ( y ) ) . This gives a curious geometric interpretation of the Herbrand function, which also applies to non-normal and even inseparable extensions.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.07.010
      Issue No: Vol. 317 (2017)
       
  • Embeddedness of the solutions to the H-Plateau problem
    • Authors: Baris Coskunuzer
      Pages: 553 - 574
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Baris Coskunuzer
      We generalize Meeks and Yau's embeddedness result on the solutions of the Plateau problem to constant mean curvature disks. We show that any minimizing H-disk in an H 0 -convex domain is embedded for any H ∈ [ 0 , H 0 ) . In particular, for the unit ball B in R 3 , this implies that for any H ∈ [ 0 , 1 ] , any Jordan curve in ∂ B bounds an embedded H-disk in B.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.07.004
      Issue No: Vol. 317 (2017)
       
  • Batalin–Vilkovisky quantization and the algebraic index
    • Authors: Ryan E. Grady; Qin Li; Si Li
      Pages: 575 - 639
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Ryan E. Grady, Qin Li, Si Li
      Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic manifold X and the Batalin–Vilkovisky (BV) quantization of a one-dimensional sigma model with target X. This model is a quantum field theory of AKSZ type and is quantized rigorously using Costello's homotopic theory of effective renormalization. We show that Fedosov's Abelian connections on the Weyl bundle produce solutions to the effective quantum master equation. Moreover, BV integration produces a natural trace map on the deformation quantized algebra. This formulation allows us to exploit a (rigorous) localization argument in quantum field theory to deduce the algebraic index theorem via semi-classical analysis, i.e., one-loop Feynman diagram computations.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.07.007
      Issue No: Vol. 317 (2017)
       
  • A uniform estimate for general quaternionic Calabi problem (with appendix
           by Daniel Barlet)
    • Authors: Semyon Alesker; Egor Shelukhin
      Pages: 1 - 52
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Semyon Alesker, Egor Shelukhin
      We prove a C 0 a priori estimate on a solution of the quaternionic Calabi problem on an arbitrary compact connected HKT-manifold. This generalizes earlier results [9] and [7] where this result was proven under certain extra assumptions on the manifold.

      PubDate: 2017-06-14T15:22:11Z
      DOI: 10.1016/j.aim.2017.05.023
      Issue No: Vol. 316 (2017)
       
  • Pointwise decay for the Maxwell field on black hole space–times
    • Authors: Jason Metcalfe; Daniel Tataru; Mihai Tohaneanu
      Pages: 53 - 93
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Jason Metcalfe, Daniel Tataru, Mihai Tohaneanu
      In this article we study the pointwise decay properties of solutions to the Maxwell system on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time, we establish peeling estimates, as well as a t − 4 rate of decay on compact regions for all the components of the Maxwell tensor.

      PubDate: 2017-06-26T15:45:29Z
      DOI: 10.1016/j.aim.2017.05.024
      Issue No: Vol. 316 (2017)
       
  • Non-compact Newton boundary and Whitney equisingularity for non-isolated
           singularities
    • Authors: Christophe Eyral; Mutsuo Oka
      Pages: 94 - 113
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Christophe Eyral, Mutsuo Oka
      In an unpublished lecture note, J. Briançon observed that if { f t } is a family of isolated complex hypersurface singularities such that the Newton boundary of f t is independent of t and f t is non-degenerate, then the corresponding family of hypersurfaces { f t − 1 ( 0 ) } is Whitney equisingular (and hence topologically equisingular). A first generalization of this assertion to families with non-isolated singularities was given by the second author under a rather technical condition. In the present paper, we give a new generalization under a simpler condition.

      PubDate: 2017-06-26T15:45:29Z
      DOI: 10.1016/j.aim.2017.06.003
      Issue No: Vol. 316 (2017)
       
  • C⁎-algebras associated to graphs of groups
    • Authors: Nathan Brownlowe; Alexander Mundey; David Pask; Jack Spielberg; Anne Thomas
      Pages: 114 - 186
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Nathan Brownlowe, Alexander Mundey, David Pask, Jack Spielberg, Anne Thomas
      To a large class of graphs of groups we associate a C ⁎ -algebra universal for generators and relations. We show that this C ⁎ -algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of groups on the boundary of its Bass–Serre tree. We characterise when this action is minimal, and find a sufficient condition under which it is locally contractive. In the case of generalised Baumslag–Solitar graphs of groups (graphs of groups in which every group is infinite cyclic) we also characterise topological freeness of this action. We are then able to establish a dichotomy for simple C ⁎ -algebras associated to generalised Baumslag–Solitar graphs of groups: they are either a Kirchberg algebra, or a stable Bunce–Deddens algebra.

      PubDate: 2017-06-26T15:45:29Z
      DOI: 10.1016/j.aim.2017.05.022
      Issue No: Vol. 316 (2017)
       
  • Generalized Kähler–Ricci flow and the classification of nondegenerate
           generalized Kähler surfaces
    • Authors: Jeffrey Streets
      Pages: 187 - 215
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Jeffrey Streets
      We study the generalized Kähler–Ricci flow on complex surfaces with nondegenerate Poisson structure, proving long time existence and convergence of the flow to a weak hyperKähler structure.

      PubDate: 2017-06-26T15:45:29Z
      DOI: 10.1016/j.aim.2017.06.002
      Issue No: Vol. 316 (2017)
       
  • Quantization and injective submodules of differential operator modules
    • Authors: Charles H. Conley; Dimitar Grantcharov
      Pages: 216 - 254
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Charles H. Conley, Dimitar Grantcharov
      The Lie algebra of vector fields on R m acts naturally on the spaces of differential operators between tensor field modules. Its projective subalgebra is isomorphic to sl m + 1 , and its affine subalgebra is a maximal parabolic subalgebra of the projective subalgebra with Levi factor gl m . We prove two results. First, we realize explicitly all injective objects of the parabolic category O g l m ( sl m + 1 ) of gl m -finite sl m + 1 -modules, as submodules of differential operator modules. Second, we study projective quantizations of differential operator modules, i.e., sl m + 1 -invariant splittings of their order filtrations. In the case of modules of differential operators from a tensor density module to an arbitrary tensor field module, we determine when there exists a unique projective quantization, when there exists no projective quantization, and when there exist multiple projective quantizations.

      PubDate: 2017-06-26T15:45:29Z
      DOI: 10.1016/j.aim.2017.06.001
      Issue No: Vol. 316 (2017)
       
  • Endpoint estimates for one-dimensional oscillator integral operators
    • Authors: Lechao Xiao
      Pages: 255 - 291
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Lechao Xiao
      The one-dimensional oscillatory integral operator associated to a real analytic phase S is given by T λ f ( x ) = ∫ − ∞ ∞ e i λ S ( x , y ) χ ( x , y ) f ( y ) d y . In their fundamental work, Phong and Stein established sharp L 2 estimates for T λ . The goal of this paper is to extend their results to all endpoints. In particular, we obtain a complete characterization for the mapping properties for T λ on L p ( R ) . More precisely, we show that ‖ T λ f ‖ p ≲ λ − α ‖ f ‖ p holds for some α > 0 if and only if ( 1 α p , 1 α p ′ ) lies in the reduced Newton polygon of S.

      PubDate: 2017-06-26T15:45:29Z
      DOI: 10.1016/j.aim.2017.06.007
      Issue No: Vol. 316 (2017)
       
  • Global entropy solutions to weakly nonlinear gas dynamics
    • Authors: Peng Qu; Zhouping Xin
      Pages: 292 - 355
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Peng Qu, Zhouping Xin
      Entropy weak solutions with bounded periodic initial data are considered for the system of weakly nonlinear gas dynamics. Through a modified Glimm scheme, an approximate solution sequence is constructed, and then a priori estimates are provided with the methods of approximate characteristics and approximate conservation laws, which gives not only the existence and uniqueness but also the uniform total variation bounds for the entropy solutions.

      PubDate: 2017-06-26T15:45:29Z
      DOI: 10.1016/j.aim.2017.06.006
      Issue No: Vol. 316 (2017)
       
  • The resolution of the Yang–Mills Plateau problem in super-critical
           dimensions
    • Authors: Mircea Petrache; Tristan Rivière
      Pages: 469 - 540
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Mircea Petrache, Tristan Rivière
      We study the minimization problem for the Yang–Mills energy under fixed boundary connection in supercritical dimension n ≥ 5 . We define the natural function space A G in which to formulate this problem in analogy to the space of integral currents used for the classical Plateau problem. The space A G can be also interpreted as a space of weak connections on a “real measure theoretic version” of reflexive sheaves from complex geometry. We prove the existence of weak solutions to the Yang–Mills Plateau problem in the space A G . We then prove the optimal regularity result for solutions of this Plateau problem. On the way to prove this result we establish a Coulomb gauge extraction theorem for weak curvatures with small Yang–Mills density. This generalizes to the general framework of weak L 2 curvatures previous works of Meyer–Rivière and Tao–Tian in which respectively a strong approximability property and an admissibility property were assumed in addition.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.06.012
      Issue No: Vol. 316 (2017)
       
  • Lefschetz theorems for torsion algebraic cycles in codimension 2
    • Authors: Deepam Patel; G.V. Ravindra
      Pages: 554 - 575
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Deepam Patel, G.V. Ravindra
      Let Y be a smooth projective variety over C , and X be a smooth hypersurface in Y. We prove that the natural restriction map on Chow groups of codimension two cycles is an isomorphism when restricted to the torsion subgroups provided dim ⁡ Y ≥ 5 . We prove an analogous statement for a very general hypersurface X ⊂ P 4 of degree ≥5. In the more general setting of a very general hypersurface X of sufficiently high degree in a fixed smooth projective four-fold Y, under some additional hypothesis, we prove that the restriction map is an isomorphism on ℓ-primary torsion for almost all primes ℓ. As a consequence, we obtain a weak Lefschetz theorem for torsion in the Griffiths groups of codimension 2 cycles, and prove the injectivity of the Abel–Jacobi map when restricted to torsion in this Griffiths group, thereby providing a partial answer to a question of Nori.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.05.018
      Issue No: Vol. 316 (2017)
       
  • Tannaka duality revisited
    • Authors: Bhargav Bhatt; Daniel Halpern-Leistner
      Pages: 576 - 612
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Bhargav Bhatt, Daniel Halpern-Leistner
      We establish several strengthened versions of Lurie's Tannaka duality theorem for certain classes of spectral algebraic stacks. Our most general version of Tannaka duality identifies maps between stacks with exact symmetric monoidal functors between ∞-categories of quasi-coherent complexes which preserve connective and pseudo-coherent complexes.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2016.08.040
      Issue No: Vol. 316 (2017)
       
  • Universality limits for generalized Jacobi measures
    • Authors: Tivadar Danka
      Pages: 613 - 666
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Tivadar Danka
      In this paper universality limits are studied in connection with measures which exhibit power-type singular behavior somewhere in their support. We extend the results of Lubinsky for Jacobi measures supported on [ − 1 , 1 ] to generalized Jacobi measures supported on a compact subset of the real line, where the singularity can be located in the interior or at an endpoint of the support. The analysis is based upon the Riemann–Hilbert method, Christoffel functions, the polynomial inverse image method of Totik and the normal family approach of Lubinsky.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.06.026
      Issue No: Vol. 316 (2017)
       
  • Interpolation and extrapolation of strictly singular operators between Lp
           spaces
    • Authors: Francisco L. Hernández; Evgeny M. Semenov; Pedro Tradacete
      Pages: 667 - 690
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Francisco L. Hernández, Evgeny M. Semenov, Pedro Tradacete
      We study the interpolation and extrapolation properties of strictly singular operators between different L p spaces. To this end, the structure of strictly singular non-compact operators between L p − L q spaces is analyzed. Among other things, we clarify the relation between strict singularity and the L-characteristic set of an operator. In particular, Krasnoselskii's interpolation theorem for compact operators is extended to the class of strictly singular operators.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.06.028
      Issue No: Vol. 316 (2017)
       
  • The structure of the free boundary in the fully nonlinear thin obstacle
           problem
    • Authors: Xavier Ros-Oton; Joaquim Serra
      Pages: 710 - 747
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Xavier Ros-Oton, Joaquim Serra
      We study the regularity of the free boundary in the fully nonlinear thin obstacle problem. Our main result establishes that the free boundary is C 1 near any regular point. This extends to the fully nonlinear setting the celebrated result of Athanasopoulos–Caffarelli–Salsa [1]. The proofs we present here are completely independent from those in [1], and do not rely on any monotonicity formula. Furthermore, an interesting and novel feature of our proofs is that we establish the regularity of the free boundary without classifying blow-ups, a priori they could be non-homogeneous and/or non-unique. We do not classify blow-ups but only prove that they are 1D on { x n = 0 } .

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.06.032
      Issue No: Vol. 316 (2017)
       
  • Cartan subalgebras and the UCT problem
    • Authors: Selçuk Barlak; Xin Li
      Pages: 748 - 769
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Selçuk Barlak, Xin Li
      We show that a separable, nuclear C*-algebra satisfies the UCT if it has a Cartan subalgebra. Furthermore, we prove that the UCT is closed under crossed products by group actions which respect Cartan subalgebras. This observation allows us to deduce, among other things, that a crossed product O 2 ⋊ α Z p satisfies the UCT if there is some automorphism γ of O 2 with the property that γ ( D 2 ) ⊆ O 2 ⋊ α Z p is regular, where D 2 denotes the canonical masa of O 2 . We prove that this condition is automatic if γ ( D 2 ) ⊆ O 2 ⋊ α Z p is not a masa or α ( γ ( D 2 ) ) is inner conjugate to γ ( D 2 ) . Finally, we relate the UCT problem for separable, nuclear, M 2 ∞ -absorbing C*-algebras to Cartan subalgebras and order two automorphisms of O 2 .

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.06.024
      Issue No: Vol. 316 (2017)
       
  • Relative Chow stability and extremal metrics
    • Authors: Reza Seyyedali
      Pages: 770 - 805
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Reza Seyyedali
      We prove that the existence of extremal metrics implies asymptotically relative Chow stability. An application of this is the uniqueness, up to automorphisms, of extremal metrics in any polarization.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.06.031
      Issue No: Vol. 316 (2017)
       
  • Centro-affine tensor valuations
    • Authors: Christoph Haberl; Lukas Parapatits
      Pages: 806 - 865
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Christoph Haberl, Lukas Parapatits
      All measurable SL ( n ) -covariant symmetric tensor valuations on convex polytopes containing the origin in their interiors are completely classified. It is shown that essentially the only examples of such valuations are the moment tensor and a tensor derived from L p surface area measures. This generalizes and unifies earlier results for the scalar, vector and matrix valued case.

      PubDate: 2017-07-07T14:44:21Z
      DOI: 10.1016/j.aim.2017.06.030
      Issue No: Vol. 316 (2017)
       
  • Fourier quasicrystals and discreteness of the diffraction spectrum
    • Authors: Nir Lev; Alexander Olevskii
      Pages: 1 - 26
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): Nir Lev, Alexander Olevskii
      We prove that a positive-definite measure in R n with uniformly discrete support and discrete closed spectrum, is representable as a finite linear combination of Dirac combs, translated and modulated. This extends our recent results where we proved this under the assumption that also the spectrum is uniformly discrete. As an application we obtain that Hof's quasicrystals with uniformly discrete diffraction spectra must have a periodic diffraction structure.

      PubDate: 2017-05-31T04:59:10Z
      DOI: 10.1016/j.aim.2017.05.015
      Issue No: Vol. 315 (2017)
       
  • Variations of Hodge structure and orbits in flag varieties
    • Authors: Matt Kerr; Colleen Robles
      Pages: 27 - 87
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): Matt Kerr, Colleen Robles
      Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford–Tate domains, arise as open G R -orbits in flag varieties G / P . We investigate Hodge-theoretic aspects of the geometry and representation theory associated with these flag varieties. In particular, we relate the Griffiths–Yukawa coupling to the variety of lines on G / P (under a minimal homogeneous embedding), construct a large class of polarized G R -orbits in G / P , and compute the associated Hodge-theoretic boundary components. An emphasis is placed throughout on adjoint flag varieties and the corresponding families of Hodge structures of levels two and four.

      PubDate: 2017-05-31T04:59:10Z
      DOI: 10.1016/j.aim.2017.05.013
      Issue No: Vol. 315 (2017)
       
  • Representations of the parafermion vertex operator algebras
    • Authors: Chongying Dong; Li Ren
      Pages: 88 - 101
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): Chongying Dong, Li Ren
      The rationality of the parafermion vertex operator algebra K ( g , k ) associated to any finite dimensional simple Lie algebra g and any nonnegative integer k is established and the irreducible modules are determined.

      PubDate: 2017-06-05T14:48:41Z
      DOI: 10.1016/j.aim.2017.05.016
      Issue No: Vol. 315 (2017)
       
  • Finite reflection groups and graph norms
    • Authors: David Conlon; Joonkyung Lee
      Pages: 130 - 165
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): David Conlon, Joonkyung Lee
      Given a graph H on vertex set { 1 , 2 , ⋯ , n } and a function f : [ 0 , 1 ] 2 → R , define ‖ f ‖ H : = ∫ ∏ i j ∈ E ( H ) f ( x i , x j ) d μ V ( H ) 1 / E ( H ) , where μ is the Lebesgue measure on [ 0 , 1 ] . We say that H is norming if ‖ ⋅ ‖ H is a semi-norm. A similar notion ‖ ⋅ ‖ r ( H ) is defined by ‖ f ‖ r ( H ) : = ‖ f ‖ H and H is said to be weakly norming if ‖ ⋅ ‖ r ( H ) is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. We demonstrate that any graph whose edges percolate in an appropriate way under the action of a certain natural family of automorphisms is weakly norming. This result includes all previously known examples of weakly norming graphs, but also allows us to identify a much broader class arising from finite reflection groups. We include several applications of our results. In particular, we define and compare a number of generalisations of Gowers' octahedral norms and we prove some new instances of Sidorenko's conjecture.

      PubDate: 2017-06-14T15:22:11Z
      DOI: 10.1016/j.aim.2017.05.009
      Issue No: Vol. 315 (2017)
       
  • The spectral estimates for the Neumann–Laplace operator in space
           domains
    • Authors: V. Gol'dshtein; A. Ukhlov
      Pages: 166 - 193
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): V. Gol'dshtein, A. Ukhlov
      In this paper we prove discreteness of the spectrum of the Neumann–Laplacian (the free membrane problem) in a large class of non-convex space domains. The lower estimates of the first non-trivial Neumann eigenvalue are obtained in terms of geometric characteristics of Sobolev mappings. The suggested approach is based on Sobolev–Poincaré inequalities that are obtained with the help of a geometric theory of composition operators on Sobolev spaces. These composition operators are induced by generalizations of conformal mappings that are called as mappings of bounded 2-distortion (weak 2-quasiconformal mappings).

      PubDate: 2017-06-14T15:22:11Z
      DOI: 10.1016/j.aim.2017.05.005
      Issue No: Vol. 315 (2017)
       
  • All SL2-tilings come from infinite triangulations
    • Authors: Christine Bessenrodt; Thorsten Holm; Peter Jørgensen
      Pages: 194 - 245
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): Christine Bessenrodt, Thorsten Holm, Peter Jørgensen
      An SL 2 -tiling is a bi-infinite matrix of positive integers such that each adjacent 2 × 2 -submatrix has determinant 1. Such tilings are infinite analogues of Conway–Coxeter friezes, and they have strong links to cluster algebras, combinatorics, mathematical physics, and representation theory. We show that, by means of so-called Conway–Coxeter counting, every SL 2 -tiling arises from a triangulation of the disc with two, three or four accumulation points. This improves earlier results which only discovered SL 2 -tilings with infinitely many entries equal to 1. Indeed, our methods show that there are large classes of tilings with only finitely many entries equal to 1, including a class of tilings with no 1's at all. In the latter case, we show that the minimal entry of a tiling is unique.

      PubDate: 2017-06-14T15:22:11Z
      DOI: 10.1016/j.aim.2017.05.019
      Issue No: Vol. 315 (2017)
       
  • Local equations for equivariant evolutionary models
    • Authors: Marta Casanellas; Jesús Fernández-Sánchez; Mateusz Michałek
      Pages: 285 - 323
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): Marta Casanellas, Jesús Fernández-Sánchez, Mateusz Michałek
      Phylogenetic varieties related to equivariant substitution models have been studied largely in the last years. One of the main objectives has been finding a set of generators of the ideal of these varieties, but this has not yet been achieved in some cases (for example, for the general Markov model this involves the open “salmon conjecture”, see [2]) and it is not clear how to use all generators in practice. Motivated by applications in biology, we tackle the problem from another point of view. The elements of the ideal that could be useful for applications in phylogenetics only need to describe the variety around certain points of no evolution (see [13]). We produce a collection of explicit equations that describe the variety on a Zariski open neighborhood of these points (see Theorem 5.4). Namely, for any tree T on any number of leaves (and any degrees at the interior nodes) and for any equivariant model on any set of states κ, we compute the codimension of the corresponding phylogenetic variety. We prove that this variety is smooth at general points of no evolution and, if a mild technical condition is satisfied (“d-claw tree hypothesis”), we provide an algorithm to produce a complete intersection that describes the variety around these points.

      PubDate: 2017-06-14T15:22:11Z
      DOI: 10.1016/j.aim.2017.05.003
      Issue No: Vol. 315 (2017)
       
  • Diagonally and antidiagonally symmetric alternating sign matrices of odd
           order
    • Authors: Roger E. Behrend; Ilse Fischer; Matjaž Konvalinka
      Pages: 324 - 365
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): Roger E. Behrend, Ilse Fischer, Matjaž Konvalinka
      We study the enumeration of diagonally and antidiagonally symmetric alternating sign matrices (DASASMs) of fixed odd order by introducing a case of the six-vertex model whose configurations are in bijection with such matrices. The model involves a grid graph on a triangle, with bulk and boundary weights which satisfy the Yang–Baxter and reflection equations. We obtain a general expression for the partition function of this model as a sum of two determinantal terms, and show that at a certain point each of these terms reduces to a Schur function. We are then able to prove a conjecture of Robbins from the mid 1980's that the total number of ( 2 n + 1 ) × ( 2 n + 1 ) DASASMs is ∏ i = 0 n ( 3 i ) ! ( n + i ) ! , and a conjecture of Stroganov from 2008 that the ratio between the numbers of ( 2 n + 1 ) × ( 2 n + 1 ) DASASMs with central entry −1 and 1 is n / ( n + 1 ) . Among the several product formulae for the enumeration of symmetric alternating sign matrices which were conjectured in the 1980's, that for odd-order DASASMs is the last to have been proved.

      PubDate: 2017-06-14T15:22:11Z
      DOI: 10.1016/j.aim.2017.05.014
      Issue No: Vol. 315 (2017)
       
  • Concordance homomorphisms from knot Floer homology
    • Authors: Peter S. Ozsváth; András I. Stipsicz; Zoltán Szabó
      Pages: 366 - 426
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): Peter S. Ozsváth, András I. Stipsicz, Zoltán Szabó
      We modify the construction of knot Floer homology to produce a one-parameter family of homologies tHFK for knots in S 3 . These invariants can be used to give homomorphisms from the smooth concordance group C to Z , giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.

      PubDate: 2017-06-14T15:22:11Z
      DOI: 10.1016/j.aim.2017.05.017
      Issue No: Vol. 315 (2017)
       
  • Holonomy limits of complex projective structures
    • Authors: David Dumas
      Pages: 427 - 473
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): David Dumas
      We study the limits of holonomy representations of complex projective structures on a compact Riemann surface in the Morgan–Shalen compactification of the character variety. We show that the dual R -trees of the quadratic differentials associated to a divergent sequence of projective structures determine the Morgan–Shalen limit points up to a natural folding operation. For quadratic differentials with simple zeros, no folding is possible and the limit of holonomy representations is isometric to the dual tree. We also derive an estimate for the growth rate of the holonomy map in terms of a norm on the space of quadratic differentials.

      PubDate: 2017-06-14T15:22:11Z
      DOI: 10.1016/j.aim.2017.05.021
      Issue No: Vol. 315 (2017)
       
  • Harish-Chandra bimodules over rational Cherednik algebras
    • Authors: Simental
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): José Simental
      We study Harish-Chandra bimodules over the rational Cherednik algebra H c ( W ) associated to a complex reflection group W with parameter c. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We classify those pairs of parameters ( c , c ′ ) for which there exist fully supported Harish-Chandra bimodules, and give a description of the category of all Harish-Chandra bimodules modulo those without full support. When W is a symmetric group we are able to classify all irreducible Harish-Chandra bimodules. Our proofs are based on localization techniques, the action of the Namikawa–Weyl group on the set of parameters, and the study of partial KZ functors.

      PubDate: 2017-07-21T02:31:05Z
       
  • Copies of the random graph
    • Authors: Stevo
      Abstract: Publication date: 7 September 2017
      Source:Advances in Mathematics, Volume 317
      Author(s): Miloš S. Kurilić, Stevo Todorčević
      Let 〈 R , ∼ 〉 be the Rado graph, Emb ( R ) the monoid of its self-embeddings, P ( R ) = { f ( R ) : f ∈ Emb ( R ) } the set of copies of R contained in R, and I R the ideal of subsets of R which do not contain a copy of R. We consider the poset 〈 P ( R ) , ⊂ 〉 , the algebra P ( R ) / I R , and the inverse of the right Green's preorder on Emb ( R ) , and show that these preorders are forcing equivalent to a two step iteration of the form P ⁎ π , where the poset P is similar to the Sacks perfect set forcing: adds a generic real, has the ℵ 0 -covering property and, hence, preserves ω 1 , has the Sacks property and does not produce splitting reals, while π codes an ω-distributive forcing. Consequently, the Boolean completions of these four posets are isomorphic and the same holds for each countable graph containing a copy of the Rado graph.

      PubDate: 2017-07-21T02:31:05Z
       
  • A stratification related to characteristic polynomials
    • Authors: James Arthur
      Abstract: Publication date: Available online 10 July 2017
      Source:Advances in Mathematics
      Author(s): James Arthur
      We shall describe two problems in Beyond Endoscopy, the strategy advanced by Langlands for bringing the trace formula to bear on the general principle of functoriality. One is to be able to apply the Poisson summation formula to the regular elliptic part of the trace formula for a general linear group GL ( n + 1 ) . The other is to be able to recognize the spectral contribution of the nontempered discrete spectrum to the resulting geometric expansion.

      PubDate: 2017-07-21T02:31:05Z
      DOI: 10.1016/j.aim.2017.06.020
       
  • A proof of the Cp′-regularity conjecture in the plane
    • Authors: Eduardo Teixeira; Miguel Urbano
      Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): Damião J. Araújo, Eduardo V. Teixeira, José Miguel Urbano
      We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C p ′ = C 1 , 1 p − 1 ; this regularity is optimal.

      PubDate: 2017-07-07T14:44:21Z
       
  • Sets of large dimension not containing polynomial configurations
    • Abstract: Publication date: 20 August 2017
      Source:Advances in Mathematics, Volume 316
      Author(s): András Máthé
      The main result of this paper is the following. Given countably many multivariate polynomials with rational coefficients and maximum degree d, we construct a compact set E ⊂ R n of Hausdorff dimension n / d which does not contain finite point configurations corresponding to the zero sets of the given polynomials. Given a set E ⊂ R n , we study the angles determined by three-point subsets of E. The main result implies the existence of a compact set in R n of Hausdorff dimension n / 2 which does not contain the angle π / 2 . (This is known to be sharp if n is even.) We show that there is a compact set of Hausdorff dimension n / 8 which does not contain an angle in any given countable set. We also construct a compact set E ⊂ R n of Hausdorff dimension n / 6 for which the set of angles determined by E is Lebesgue null. In the other direction, we present a result that every set of sufficiently large dimension contains an angle ε close to any given angle. The main result can also be applied to distance sets. As a corollary we obtain a compact set E ⊂ R n ( n ≥ 2 ) of Hausdorff dimension n / 2 which does not contain rational distances nor collinear points, for which the distance set is Lebesgue null, moreover, every distance and direction is realised only at most once by E.

      PubDate: 2017-07-07T14:44:21Z
       
  • Inverse anisotropic mean curvature flow and a Minkowski type inequality
    • Authors: Chao Xia
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): Chao Xia
      In this paper, we show that the inverse anisotropic mean curvature flow in R n + 1 , initiating from a star-shaped, strictly F-mean convex hypersurface, exists for all time and after rescaling the flow converges exponentially fast to a rescaled Wulff shape in the C ∞ topology. As an application, we prove a Minkowski type inequality for star-shaped, F-mean convex hypersurfaces.

      PubDate: 2017-06-14T15:22:11Z
       
  • On the set of wild points of attracting surfaces in R3
    • Authors: J.J.
      Abstract: Publication date: 31 July 2017
      Source:Advances in Mathematics, Volume 315
      Author(s): J.J. Sánchez-Gabites
      Suppose that a closed surface S ⊆ R 3 is an attractor, not necessarily global, for a discrete dynamical system. Assuming that its set of wild points W is totally disconnected, we prove that (up to an ambient homeomorphism) it has to be contained in a straight line. As a corollary we show that there exist uncountably many different 2-spheres in R 3 none of which can be realized as an attractor for a homeomorphism. Our techniques hinge on a quantity r ( K ) that can be defined for any compact set K ⊆ R 3 and is related to “how wildly” it sits in R 3 . We establish the topological results that (i) r ( W ) ≤ r ( S ) and (ii) any totally disconnected set having a finite r must be contained in a straight line (up to an ambient homeomorphism). The main result follows from these and the fact that attractors have a finite r.

      PubDate: 2017-06-14T15:22:11Z
       
 
 
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