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MATHEMATICS (647 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: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 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: 5)
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: 6)
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: 9)
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: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied 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: 18)
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: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 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: 17)
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: 12)
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: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
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]
  • 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)
  • 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
    • 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
    • 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)
  • Orientability for gauge theories on Calabi–Yau manifolds
    • Authors: Yalong Cao; Naichung Conan Leung
      Pages: 48 - 70
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Yalong Cao, Naichung Conan Leung
      We study orientability issues of moduli spaces from gauge theories on Calabi–Yau manifolds. Our results generalize and strengthen those for Donaldson–Thomas theory on Calabi–Yau manifolds of dimensions 3 and 4. We also prove a corresponding result in the relative situation which is relevant to the gluing formula in DT theory.

      PubDate: 2017-05-11T03:48:10Z
      DOI: 10.1016/j.aim.2017.04.030
      Issue No: Vol. 314 (2017)
  • Superconformal minimal models and admissible Jack polynomials
    • Authors: Olivier Blondeau-Fournier; Pierre Mathieu; David Ridout; Simon Wood
      Pages: 71 - 123
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Olivier Blondeau-Fournier, Pierre Mathieu, David Ridout, Simon Wood
      We give new proofs of the rationality of the N = 1 superconformal minimal model vertex operator superalgebras and of the classification of their modules in both the Neveu–Schwarz and Ramond sectors. For this, we combine the standard free field realisation with the theory of Jack symmetric functions. A key role is played by Jack symmetric polynomials with a certain negative parameter that are labelled by admissible partitions. These polynomials are shown to describe free fermion correlators, suitably dressed by a symmetrising factor. The classification proofs concentrate on explicitly identifying Zhu's algebra and its twisted analogue. Interestingly, these identifications do not use an explicit expression for the non-trivial vacuum singular vector. While the latter is known to be expressible in terms of an Uglov symmetric polynomial or a linear combination of Jack superpolynomials, it turns out that standard Jack polynomials (and functions) suffice to prove the classification.

      PubDate: 2017-05-11T03:48:10Z
      DOI: 10.1016/j.aim.2017.04.026
      Issue No: Vol. 314 (2017)
  • Uniform approximation of Bloch functions and the boundedness of the
           integration operator on H∞
    • Authors: Wayne Smith; Dmitriy M. Stolyarov; Alexander Volberg
      Pages: 185 - 202
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Wayne Smith, Dmitriy M. Stolyarov, Alexander Volberg
      We obtain a necessary and sufficient condition for the operator of integration to be bounded on H ∞ in a simply connected domain. The main ingredient of the proof is a new result on uniform approximation of Bloch functions.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.028
      Issue No: Vol. 314 (2017)
  • Higher rank partial and false theta functions and representation theory
    • Authors: Thomas Creutzig; Antun Milas
      Pages: 203 - 227
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Thomas Creutzig, Antun Milas
      We study higher rank Jacobi partial and false theta functions (generalizations of the classical partial and false theta functions) associated to positive definite rational lattices. In particular, we focus our attention on certain Kostant's partial theta functions coming from ADE root lattices, which are then linked to representation theory of W-algebras. We derive modular transformation properties of regularized higher rank partial and false theta functions as well as Kostant's version of these. Modulo conjectures in representation theory, as an application, we compute regularized quantum dimensions of atypical and typical modules of “narrow” logarithmic W-algebras associated to rescaled root lattices. This paper substantially generalize our previous work [19] pertaining to ( 1 , p ) -singlet W-algebras (the sl 2 case). Results in this paper are very general and are applicable in a variety of situations.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.027
      Issue No: Vol. 314 (2017)
  • Tensor triangular geometry for classical Lie superalgebras
    • Authors: Brian D. Boe; Jonathan R. Kujawa; Daniel K. Nakano
      Pages: 228 - 277
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Brian D. Boe, Jonathan R. Kujawa, Daniel K. Nakano
      Tensor triangular geometry as introduced by Balmer [3] is a powerful idea which can be used to extract the ambient geometry from a given tensor triangulated category. In this paper we provide a general setting for a compactly generated tensor triangulated category which enables one to classify thick tensor ideals and the Balmer spectrum. For the general linear Lie superalgebra g = g 0 ¯ ⊕ g 1 ¯ we construct a Zariski space from a detecting subalgebra of g and demonstrate that this topological space governs the tensor triangular geometry for the category of finite dimensional g -modules which are semisimple over g 0 ¯ .

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.022
      Issue No: Vol. 314 (2017)
  • Closed Willmore minimal hypersurfaces with constant scalar curvature in
           S5(1) are isoparametric
    • Authors: Qintao Deng; Huiling Gu; Qiaoyu Wei
      Pages: 278 - 305
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Qintao Deng, Huiling Gu, Qiaoyu Wei
      In this paper, we will prove that any closed minimal Willmore hypersurface M 4 of S 5 with constant scalar curvature must be isoparametric. To be precise, M 4 is either an equatorial 4 sphere, a product of sphere S 2 ( 2 2 ) × S 2 ( 2 2 ) or a Cartan's minimal hypersurface. In particular, the value of the second fundamental form S can only be 0, 4, 12. This result strongly supports Chern's Conjecture.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.05.002
      Issue No: Vol. 314 (2017)
  • The structure of the inverse system of Gorenstein k-algebras
    • Authors: J. Elias; M.E. Rossi
      Pages: 306 - 327
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): J. Elias, M.E. Rossi
      Macaulay's Inverse System gives an effective method to construct Artinian Gorenstein k-algebras. To date a general structure for Gorenstein k-algebras of any dimension (and codimension) is not understood. In this paper we extend Macaulay's correspondence characterizing the submodules of the divided power ring in one-to-one correspondence with Gorenstein d-dimensional k-algebras. We discuss effective methods for constructing Gorenstein graded rings. Several examples illustrating our results are given.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.025
      Issue No: Vol. 314 (2017)
  • The porous medium equation on Riemannian manifolds with negative
           curvature. The large-time behaviour
    • Authors: Gabriele Grillo; Matteo Muratori; Juan Luis Vázquez
      Pages: 328 - 377
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Gabriele Grillo, Matteo Muratori, Juan Luis Vázquez
      We consider nonnegative solutions of the porous medium equation (PME) on Cartan–Hadamard manifolds whose negative curvature can be unbounded. We take compactly supported initial data because we are also interested in free boundaries. We classify the geometrical cases we study into quasi-hyperbolic, quasi-Euclidean and critical cases, depending on the growth rate of the curvature at infinity. We prove sharp upper and lower bounds on the long-time behaviour of the solutions in terms of corresponding bounds on the curvature. In particular we estimate the location of the free boundary. A global Harnack principle follows. We also present a change of variables that allows to transform radially symmetric solutions of the PME on model manifolds into radially symmetric solutions of a corresponding weighted PME on Euclidean space and back. This equivalence turns out to be an important tool of the theory.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.023
      Issue No: Vol. 314 (2017)
  • Configuration spaces and polyhedral products
    • Authors: Piotr Beben; Jelena Grbić
      Pages: 378 - 425
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Piotr Beben, Jelena Grbić
      This paper aims to find the most general combinatorial conditions under which a moment–angle complex ( D 2 , S 1 ) K is a co-H-space, thus splitting unstably in terms of its full subcomplexes. In this way we study to which extent the conjecture holds that a moment–angle complex over a Golod simplicial complex is a co-H-space. Our main tool is a certain generalisation of the theory of labelled configuration spaces.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.05.001
      Issue No: Vol. 314 (2017)
  • Supports of representations of the rational Cherednik algebra of type A
    • Authors: Stewart Wilcox
      Pages: 426 - 492
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Stewart Wilcox
      We first consider the rational Cherednik algebra corresponding to the action of a finite group on a complex variety, as defined by Etingof. We define a category of representations of this algebra which is analogous to “category O ” for the rational Cherednik algebra of a vector space. We generalise to this setting Bezrukavnikov and Etingof's results about the possible support sets of such representations. Then we focus on the case of S n acting on C n , determining which irreducible modules in this category have which support sets. We also show that the category of representations with a given support, modulo those with smaller support, is equivalent to the category of finite dimensional representations of a certain Hecke algebra.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.031
      Issue No: Vol. 314 (2017)
  • Stability of transonic shocks in steady supersonic flow past
           multidimensional wedges
    • Authors: Gui-Qiang Chen; Beixiang Fang
      Pages: 493 - 539
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Gui-Qiang Chen, Beixiang Fang
      We are concerned with the stability of multidimensional (M-D) transonic shocks in steady supersonic flow past multidimensional wedges. One of our motivations is that the global stability issue for the M-D case is much more sensitive than that for the 2-D case, which requires more careful rigorous mathematical analysis. In this paper, we develop a nonlinear approach and employ it to establish the stability of weak shock solutions containing a transonic shock-front for potential flow with respect to the M-D perturbation of the wedge boundary in appropriate function spaces. To achieve this, we first formulate the stability problem as a free boundary problem for nonlinear elliptic equations. Then we introduce the partial hodograph transformation to reduce the free boundary problem into a fixed boundary value problem near a background solution with fully nonlinear boundary conditions for second-order nonlinear elliptic equations in an unbounded domain. To solve this reduced problem, we linearize the nonlinear problem on the background shock solution and then, after solving this linearized elliptic problem, develop a nonlinear iteration scheme that is proved to be contractive.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.019
      Issue No: Vol. 314 (2017)
  • Existence and construction of resonances for atoms coupled to the
           quantized radiation field
    • Authors: Volker Bach; Miguel Ballesteros; Alessandro Pizzo
      Pages: 540 - 572
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Volker Bach, Miguel Ballesteros, Alessandro Pizzo
      The processes of emission and absorption of photons by atoms can be rigorously understood in the low-energy limit if we neglect the creation and annihilation of electrons. They are related to eigenvalues of the atomic Hamiltonian that are embedded in the continuous spectrum of the free Hamiltonian of the electromagnetic field. The mathematical analysis of the perturbation of these eigenvalues due to the electromagnetic interaction relies on a complex deformation technique relating the original Hamiltonian to a non-selfadjoint operator. We develop a new technique to analyze the spectrum of operators used in non-relativistic quantum electrodynamics. Our method can be applied to prove most of the results that previously required an involved renormalization group construction. We use analytic perturbation theory of operators in Hilbert spaces instead. More precisely, we extend the multi-scale analysis introduced by one of us in 2003 [15], which was used so far only for the study of selfadjoint operators, to non-selfadjoint operators. Compared to the selfadjoint case (see, for example, [3]) the analysis of these non-selfadjoint operators is more difficult, because we cannot make use of the functional calculus (spectral theorem) and the min–max principle in some crucial estimates.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.029
      Issue No: Vol. 314 (2017)
  • Divergent series and Serre's intersection formula for graded rings
    • Authors: Daniel Erman
      Pages: 573 - 582
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Daniel Erman
      On a smooth variety, Serre's intersection formula computes intersection multiplicities via an alternating sum of the lengths of Tor groups. When the variety is singular, the corresponding sum can be a divergent series. But there are alternate geometric approaches for assigning (often fractional) intersection multiplicities in some singular settings. Our motivating question comes from Fulton, who asks whether an analytic continuation of the divergent series from Serre's formula can be related to these fractional multiplicities. We apply work of Avramov and Buchweitz to answer Fulton's question in the context of graded rings.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.05.010
      Issue No: Vol. 314 (2017)
  • Optimal boundary gradient estimates for Lamé systems with partially
           infinite coefficients
    • Authors: Jiguang Bao; Hongjie Ju; Haigang Li
      Pages: 583 - 629
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Jiguang Bao, Hongjie Ju, Haigang Li
      In this paper, we derive the pointwise upper bounds and lower bounds on the gradients of solutions to the Lamé systems with partially infinite coefficients as the surface of discontinuity of the coefficients of the system is located very close to the boundary. When the distance tends to zero, the optimal blow-up rates of the gradients are established for inclusions with arbitrary shapes and in all dimensions.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.05.004
      Issue No: Vol. 314 (2017)
  • Waring loci and the Strassen conjecture
    • Authors: Enrico Carlini; Maria Virginia Catalisano; Alessandro Oneto
      Pages: 630 - 662
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Enrico Carlini, Maria Virginia Catalisano, Alessandro Oneto
      The Waring locus of a form F is the collection of the degree one forms appearing in some minimal sum of powers decomposition of F. In this paper, we give a complete description of Waring loci for several families of forms, such as quadrics, monomials, binary forms and plane cubics. We also introduce a Waring loci version of Strassen's Conjecture, which implies the original conjecture, and we prove it in many cases.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.05.008
      Issue No: Vol. 314 (2017)
  • Logarithmic étale cohomology, II
    • Authors: Chikara Nakayama
      Pages: 663 - 725
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Chikara Nakayama
      We introduce the log étale cohomology in the second (full log étale) sense after K. Kato and prove several fundamental results including base change theorems. To prove them, we use some corresponding results in the log étale cohomology in the first (kummer log étale) sense. Conversely, they are used to show some new results in the kummer log étale cohomology.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.05.006
      Issue No: Vol. 314 (2017)
  • Finiteness theorems on hypersurfaces in partial differential-algebraic
    • Authors: James Freitag; Rahim Moosa
      Pages: 726 - 755
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): James Freitag, Rahim Moosa
      Hrushovski's generalization and application of Jouanolou (1978) [9] is here refined and extended to the partial differential setting with possibly nonconstant coefficient fields. In particular, it is shown that if X is a differential-algebraic variety over a partial differential field F that is finitely generated over its constant field F 0 , then there exists a dominant differential-rational map from X to the constant points of an algebraic variety V over F 0 , such that all but finitely many codimension one subvarieties of X over F arise as pull-backs of algebraic subvarieties of V over F 0 . As an application, it is shown that the algebraic solutions to a first order algebraic differential equation over C ( t ) are of bounded height, answering a question of Eremenko. Two expected model-theoretic applications to DCF 0 , m are also given: 1) Lascar rank and Morley rank agree in dimension two, and 2) dimension one strongly minimal sets orthogonal to the constants are ℵ 0 -categorical. A detailed exposition of Hrushovski's original (unpublished) theorem is included, influenced by Ghys (2000) [5].

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.008
      Issue No: Vol. 314 (2017)
  • Isoparametric hypersurfaces in complex hyperbolic spaces
    • Authors: José Carlos Díaz-Ramos; Miguel Domínguez-Vázquez; Víctor Sanmartín-López
      Pages: 756 - 805
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): José Carlos Díaz-Ramos, Miguel Domínguez-Vázquez, Víctor Sanmartín-López
      We classify isoparametric hypersurfaces in complex hyperbolic spaces.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.05.012
      Issue No: Vol. 314 (2017)
  • Expanders and box spaces
    • Authors: Ana Khukhro; Alain Valette
      Pages: 806 - 834
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Ana Khukhro, Alain Valette
      We consider box spaces of finitely generated, residually finite groups G, and try to distinguish them up to coarse equivalence. We show that, for n ≥ 2 , the group S L n ( Z ) has a continuum of box spaces which are pairwise non-coarsely equivalent expanders. Moreover, varying the integer n ≥ 3 , expanders given as box spaces of S L n ( Z ) are pairwise not coarsely equivalent; similarly, varying the prime p, expanders given as box spaces of S L 2 ( Z [ p ] ) are pairwise not coarsely equivalent. We also show that, for prime p, the family of finite groups ( P S L 2 ( Z / p n Z ) ) n ≥ 1 can be turned in infinitely many ways (up to coarse equivalence) into a 6-regular expander. A strong form of non-expansion for a box space is the existence of α ∈ ] 0 , 1 ] such that the diameter of each component X n satisfies d i a m ( X n ) = Ω ( X n α ) . By [2], the existence of such a box space implies that G virtually maps onto Z : we establish the converse. For the lamplighter group ( Z / 2 Z ) ≀ Z and for a semi-direct product Z 2 ⋊ Z , such box spaces are explicitly constructed using specific congruence subgroups. We finally introduce the full box space of G, i.e. the metric disjoint union of all finite quotients of G. We prove that the full box space of a group mapping onto the free group F 2 is not coarsely equivalent to the full box space of an S-arithmetic group satisfying the Congruence Subgroup Property.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.05.007
      Issue No: Vol. 314 (2017)
  • A free boundary problem for the parabolic Poisson kernel
    • Authors: Max Engelstein
      Pages: 835 - 947
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Max Engelstein
      We study parabolic chord arc domains, introduced by Hofmann, Lewis and Nyström [14], and prove a free boundary regularity result below the continuous threshold. More precisely, we show that a Reifenberg flat, parabolic chord arc domain whose Poisson kernel has logarithm in VMO must in fact be a vanishing chord arc domain (i.e. satisfies a vanishing Carleson measure condition). This generalizes, to the parabolic setting, a result of Kenig and Toro [26] and answers in the affirmative a question left open in the aforementioned paper of Hofmann et al. A key step in this proof is a classification of “flat” blowups for the parabolic problem.

      PubDate: 2017-06-09T14:58:03Z
      DOI: 10.1016/j.aim.2017.04.032
      Issue No: Vol. 314 (2017)
  • Extensions in Jacobian algebras and cluster categories of marked surfaces
    • Authors: Ilke Canakci; Sibylle Schroll
      Pages: 1 - 49
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Ilke Canakci, Sibylle Schroll
      In the context of representation theory of finite dimensional algebras, string algebras have been extensively studied and most aspects of their representation theory are well-understood. One exception to this is the classification of extensions between indecomposable modules. In this paper we explicitly describe such extensions for a class of string algebras, namely gentle algebras associated to surface triangulations. These algebras arise as Jacobian algebras of unpunctured surfaces. We relate the extension spaces of indecomposable modules to crossings of generalised arcs in the surface and give explicit bases of the extension spaces for indecomposable modules in almost all cases. We show that the dimensions of these extension spaces are given in terms of crossing arcs in the surface. Our approach is new and consists of interpreting snake graphs as indecomposable modules. In order to show that our basis is a spanning set, we need to work in the associated cluster category where we explicitly calculate the middle terms of extensions and give bases of their extension spaces. We note that not all extensions in the cluster category give rise to extensions for the Jacobian algebra.

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.03.016
      Issue No: Vol. 313 (2017)
  • An infinite self-dual Ramsey theorem
    • Authors: Dimitris Vlitas
      Pages: 50 - 61
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Dimitris Vlitas
      In a recent paper [5] S. Solecki proved a finite self-dual Ramsey theorem that extends simultaneously the classical finite Ramsey theorem [4] and the Graham–Rothschild theorem [2]. In this paper we prove the corresponding infinite dimensional version of the self-dual theorem. As a consequence, we extend the classical infinite Ramsey theorem [4] and the Carlson–Simpson theorem [1].

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.04.004
      Issue No: Vol. 313 (2017)
  • Existence of Mori fibre spaces for 3-folds in char p
    • Authors: Caucher Birkar; Joe Waldron
      Pages: 62 - 101
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Caucher Birkar, Joe Waldron
      We prove the following results for projective klt pairs of dimension 3 over an algebraically closed field of characteristic p > 5 : the cone theorem, the base point free theorem, the contraction theorem, finiteness of minimal models, termination with scaling, existence of Mori fibre spaces, etc.

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.03.032
      Issue No: Vol. 313 (2017)
  • Angular billiard and algebraic Birkhoff conjecture
    • Authors: Misha Bialy; Andrey E. Mironov
      Pages: 102 - 126
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Misha Bialy, Andrey E. Mironov
      In this paper we introduce a new dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighborhood of the boundary curve this system turns out to be dual to the Birkhoff billiard. Using this system we get new results on algebraic Birkhoff conjecture on integrable billiards.

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.04.001
      Issue No: Vol. 313 (2017)
  • F-injectivity and Frobenius closure of ideals in Noetherian rings of
           characteristic p>0
    • Authors: Pham Hung Quy; Kazuma Shimomoto
      Pages: 127 - 166
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Pham Hung Quy, Kazuma Shimomoto
      The main aim of this article is to study the relation between F-injective singularity and the Frobenius closure of parameter ideals in Noetherian rings of positive characteristic. The paper consists of the following themes, including many other topics. (1) We prove that if every parameter ideal of a Noetherian local ring of prime characteristic p > 0 is Frobenius closed, then it is F-injective. (2) We prove a necessary and sufficient condition for the injectivity of the Frobenius action on H m i ( R ) for all i ≤ f m ( R ) , where f m ( R ) is the finiteness dimension of R. As applications, we prove the following results. (a) If the ring is F-injective, then every ideal generated by a filter regular sequence, whose length is equal to the finiteness dimension of the ring, is Frobenius closed. It is a generalization of a recent result of Ma and which is stated for generalized Cohen–Macaulay local rings. (b) Let ( R , m , k ) be a generalized Cohen–Macaulay ring of characteristic p > 0 . If the Frobenius action is injective on the local cohomology H m i ( R ) for all i < dim ⁡ R , then R is Buchsbaum. This gives an answer to a question of Takagi. (3) We consider the problem when the union of two F-injective closed subschemes of a Noetherian F p -scheme is F-injective. Using this idea, we construct an F-injective local ring R such that R has a parameter ideal that is not Frobenius closed. This result adds a new member to the family of F-singularities. (4) We give the first ideal-theoretic characterization of F-injectivity in terms the Frobenius closure and the limit closure. We also give an answer to the question about when the Frobenius action on the top local cohomology is injective.

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.04.002
      Issue No: Vol. 313 (2017)
  • Wave front sets of reductive Lie group representations III
    • Authors: Benjamin Harris; Tobias Weich
      Pages: 176 - 236
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Benjamin Harris, Tobias Weich
      Let G be a real, reductive algebraic group, and let X be a homogeneous space for G with a non-zero invariant density. We give an explicit description of a Zariski open, dense subset of the asymptotics of the tempered support of L 2 ( X ) . Under additional hypotheses, this result remains true for vector bundle valued harmonic analysis on X. These results follow from an upper bound on the wave front set of an induced Lie group representation under a uniformity condition.

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.03.025
      Issue No: Vol. 313 (2017)
  • Every linear order isomorphic to its cube is isomorphic to its square
    • Authors: Garrett Ervin
      Pages: 237 - 281
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Garrett Ervin
      In 1958, Sierpiński asked whether there exists a linear order X that is isomorphic to its lexicographically ordered cube but is not isomorphic to its square. The main result of this paper is that the answer is negative. More generally, if X is isomorphic to any one of its finite powers X n , n > 1 , it is isomorphic to all of them.

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.04.010
      Issue No: Vol. 313 (2017)
  • Quantum integrability and generalised quantum Schubert calculus
    • Authors: Vassily Gorbounov; Christian Korff
      Pages: 282 - 356
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Vassily Gorbounov, Christian Korff
      We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six-vertex model. Our approach offers a new perspective on already established and well-studied special cases, for example equivariant K-theory, and in addition allows us to formulate a conjecture on the so-far unknown case of quantum equivariant K-theory.

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.03.030
      Issue No: Vol. 313 (2017)
  • On hyperbolic graphs induced by iterated function systems
    • Authors: Ka-Sing Lau; Xiang-Yang Wang
      Pages: 357 - 378
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Ka-Sing Lau, Xiang-Yang Wang
      For any contractive iterated function system (IFS, including the Moran systems), we show that there is a natural hyperbolic graph on the symbolic space, which yields the Hölder equivalence of the hyperbolic boundary and the invariant set of the IFS. This completes the previous studies ([16,20,30]) by eliminating superfluous conditions, and admits more classes of sets (e.g., the Moran sets). We also show that the bounded degree property of the graph can be used to characterize certain separation properties of the IFS (open set condition, weak separation condition); the bounded degree property is particularly important when we consider random walks on such graphs. This application and the other application to Lipschitz equivalence of self-similar sets will be discussed.

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.04.012
      Issue No: Vol. 313 (2017)
  • Whitney-type extension theorems for jets generated by Sobolev functions
    • Authors: Pavel Shvartsman
      Pages: 379 - 469
      Abstract: Publication date: 20 June 2017
      Source:Advances in Mathematics, Volume 313
      Author(s): Pavel Shvartsman
      Let L p m ( R n ) , 1 ≤ p ≤ ∞ , be the homogeneous Sobolev space, and let E ⊂ R n be a closed set. For each p > n and each non-negative integer m we give an intrinsic characterization of the restrictions { D α F E : α ≤ m } to E of m-jets generated by functions F ∈ L p m + 1 ( R n ) . Our trace criterion is expressed in terms of variations of corresponding Taylor remainders of m-jets evaluated on a certain family of “well separated” two point subsets of E. For p = ∞ this result coincides with the classical Whitney–Glaeser extension theorem for m-jets. Our approach is based on a representation of the Sobolev space L p m + 1 ( R n ) , p > n , as a union of C m , ( d ) ( R n ) -spaces where d belongs to a family of metrics on R n with certain “nice” properties. Here C m , ( d ) ( R n ) is the space of C m -functions on R n whose partial derivatives of order m are Lipschitz functions with respect to d. This enables us to show that, for every non-negative integer m and every p ∈ ( n , ∞ ) , the very same classical linear Whitney extension operator as in [31] provides an almost optimal extension of m-jets generated by L p m + 1 -functions.

      PubDate: 2017-05-21T04:16:58Z
      DOI: 10.1016/j.aim.2017.04.009
      Issue No: Vol. 313 (2017)
  • 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
  • Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry
    • Authors: Ugo Boscain; Robert Neel Luca Rizzi
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Ugo Boscain, Robert Neel, Luca Rizzi
      On a sub-Riemannian manifold we define two types of Laplacians. The macroscopic Laplacian Δ ω , as the divergence of the horizontal gradient, once a volume ω is fixed, and the microscopic Laplacian, as the operator associated with a sequence of geodesic random walks. We consider a general class of random walks, where all sub-Riemannian geodesics are taken in account. This operator depends only on the choice of a complement c to the sub-Riemannian distribution, and is denoted by L c . We address the problem of equivalence of the two operators. This problem is interesting since, on equiregular sub-Riemannian manifolds, there is always an intrinsic volume (e.g. Popp's one P ) but not a canonical choice of complement. The result depends heavily on the type of structure under investigation: • On contact structures, for every volume ω, there exists a unique complement c such that Δ ω = L c . • On Carnot groups, if H is the Haar volume, then there always exists a complement c such that Δ H = L c . However this complement is not unique in general. • For quasi-contact structures, in general, Δ P ≠ L c for any choice of c. In particular, L c is not symmetric with respect to Popp's measure. This is surprising especially in dimension 4 where, in a suitable sense, Δ P is the unique intrinsic macroscopic Laplacian. A crucial notion that we introduce here is the N-intrinsic volume, i.e. a volume that depends only on the set of parameters of the nilpotent approximation. When the nilpotent approximation does not depend on the point, a N-intrinsic volume is unique up to a scaling by a constant and the corresponding N-intrinsic sub-Laplacian is unique. This is what happens for dimension less than or equal to 4, and in particular in the 4-dimensional quasi-contact structure mentioned above. Finally, we prove a general theorem on the convergence of families of random walks to a diffusion, that gives, in particular, the convergence of the random walks mentioned above to the diffusion generated by L c .

      PubDate: 2017-06-09T14:58:03Z
  • Quantitative stability for the Brunn–Minkowski inequality
    • Authors: Alessio Figalli; David Jerison
      Abstract: Publication date: 9 July 2017
      Source:Advances in Mathematics, Volume 314
      Author(s): Alessio Figalli, David Jerison
      We prove a quantitative stability result for the Brunn–Minkowski inequality: if A = B = 1 , t ∈ [ τ , 1 − τ ] with τ > 0 , and t A + ( 1 − t ) B 1 / n ≤ 1 + δ for some small δ, then, up to a translation, both A and B are quantitatively close (in terms of δ) to a convex set K .

      PubDate: 2017-05-06T02:41:54Z
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