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  Subjects -> MATHEMATICS (Total: 889 journals)
    - APPLIED MATHEMATICS (73 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (659 journals)
    - MATHEMATICS (GENERAL) (42 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (76 journals)

MATHEMATICS (659 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 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: 25)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 8)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 5)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 9)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 7)
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   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 1)
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: 9)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)

        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  [3048 journals]
  • Modular characteristic classes for representations over finite fields
    • Authors: Anssi Lahtinen; David Sprehn
      Pages: 1 - 37
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Anssi Lahtinen, David Sprehn
      The cohomology of the degree-n general linear group over a finite field of characteristic p, with coefficients also in characteristic p, remains poorly understood. For example, the lowest degree previously known to contain nontrivial elements is exponential in n. In this paper, we introduce a new system of characteristic classes for representations over finite fields, and use it to construct a wealth of explicit nontrivial elements in these cohomology groups. In particular we obtain nontrivial elements in degrees linear in n. We also construct nontrivial elements in the mod p homology and cohomology of the automorphism groups of free groups, and the general linear groups over the integers. These elements reside in the unstable range where the homology and cohomology remain mysterious.

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

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

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

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

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

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

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

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

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

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.038
      Issue No: Vol. 323 (2017)
       
  • Spectral analysis of random-to-random Markov chains
    • Authors: A.B. Dieker; F.V. Saliola
      Pages: 427 - 485
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): A.B. Dieker, F.V. Saliola
      We compute the eigenvalues and eigenspaces of random-to-random Markov chains. We use a family of maps which reveal a remarkable recursive structure of the eigenspaces, yielding an explicit and effective construction of all eigenbases starting from bases of the kernels.

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.034
      Issue No: Vol. 323 (2017)
       
  • Integral solutions to boundary quantum Knizhnik–Zamolodchikov
           equations
    • Authors: Nicolai Reshetikhin; Jasper Stokman; Bart Vlaar
      Pages: 486 - 528
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar
      We construct integral representations of solutions to the boundary quantum Knizhnik–Zamolodchikov equations. These are difference equations taking values in tensor products of Verma modules of quantum affine sl 2 , with the K-operators acting diagonally. The integrands in question are products of scalar-valued elliptic weight functions with vector-valued trigonometric weight functions (boundary Bethe vectors). These integrals give rise to a basis of solutions of the boundary qKZ equations over the field of quasi-constant meromorphic functions in weight subspaces of the tensor product.

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.041
      Issue No: Vol. 323 (2017)
       
  • Late-time asymptotics for the wave equation on spherically symmetric,
           stationary spacetimes
    • Authors: Y. Angelopoulos; S. Aretakis; D. Gajic
      Pages: 529 - 621
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Y. Angelopoulos, S. Aretakis, D. Gajic
      We derive precise late-time asymptotics for solutions to the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes including as special cases the Schwarzschild and Reissner–Nordström families of black holes. We also obtain late-time asymptotics for the time derivatives of all orders and for the radiation field along null infinity. We show that the leading-order term in the asymptotic expansion is related to the existence of the conserved Newman–Penrose quantities on null infinity. As a corollary we obtain a characterization of all solutions which satisfy Price's polynomial law τ − 3 as a lower bound. Our analysis relies on physical space techniques and uses the vector field approach for almost-sharp decay estimates introduced in our companion paper. In the black hole case, our estimates hold in the domain of outer communications up to and including the event horizon. Our work is motivated by the stability problem for black hole exteriors and strong cosmic censorship for black hole interiors.

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.027
      Issue No: Vol. 323 (2017)
       
  • Hurwitz correspondences on compactifications of M0,N
    • Authors: Rohini Ramadas
      Pages: 622 - 667
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Rohini Ramadas
      Hurwitz correspondences are certain multi-valued self-maps of the moduli space M 0 , N . They arise in the study of Thurston's topological characterization of rational functions. We compare the dynamics of Hurwitz correspondence H on two different compactifications of M 0 , N : the Deligne-Mumford compactification M ‾ 0 , N , as well as a Hassett space of weighted stable curves. We use this comparison to show that the k-th dynamical degree of H is the absolute value of the dominant eigenvalue of the pushforward induced by H on a natural quotient of H 2 k ( M ‾ 0 , N ) .

      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.10.044
      Issue No: Vol. 323 (2017)
       
  • Moduli space of cubic Newton maps
    • Authors: Pascale Roesch; Xiaoguang Wang; Yongcheng Yin
      Pages: 1 - 59
      Abstract: Publication date: 15 December 2017
      Source:Advances in Mathematics, Volume 322
      Author(s): Pascale Roesch, Xiaoguang Wang, Yongcheng Yin
      In this article, we study the topology and bifurcations of the moduli space M 3 of cubic Newton maps. It's a subspace of the moduli space of cubic rational maps, carrying the Riemann orbifold structure ( C ˆ , ( 2 , 3 , ∞ ) ) . We prove two results: • The boundary of the unique unbounded hyperbolic component is a Jordan arc and the boundaries of all other hyperbolic components are Jordan curves; • The Head's angle map is surjective and monotone. The fibers of this map are characterized completely. The first result is a moduli space analogue of the first author's dynamical regularity theorem [37]. The second result confirms a conjecture of Tan Lei.

      PubDate: 2017-10-14T15:00:36Z
      DOI: 10.1016/j.aim.2017.10.004
      Issue No: Vol. 322 (2017)
       
  • Landweber flat real pairs and ER(n)-cohomology
    • Authors: Nitu Kitchloo; Vitaly Lorman; W. Stephen Wilson
      Pages: 60 - 82
      Abstract: Publication date: 15 December 2017
      Source:Advances in Mathematics, Volume 322
      Author(s): Nitu Kitchloo, Vitaly Lorman, W. Stephen Wilson
      We take advantage of the internal algebraic structure of the Bockstein spectral sequence converging to E R ( n ) ⁎ ( p t ) to prove that for spaces Z that are part of Landweber flat real pairs with respect to E ( n ) (see Definition 2.9), the cohomology ring E R ( n ) ⁎ ( Z ) can be obtained from E ( n ) ⁎ ( Z ) by base change. In particular, our results allow us to compute the Real Johnson–Wilson cohomology of the Eilenberg–MacLane spaces Z = K ( Z , 2 m + 1 ) , K ( Z / 2 q , 2 m ) , K ( Z / 2 , m ) for any natural numbers m and q, as well as connective covers of BO: BO , BSO , BSpin and BO 〈 8 〉 .

      PubDate: 2017-10-14T15:00:36Z
      DOI: 10.1016/j.aim.2017.10.003
      Issue No: Vol. 322 (2017)
       
  • Adjoints to a Fourier–Mukai functor
    • Authors: Alice Rizzardo
      Pages: 83 - 96
      Abstract: Publication date: 15 December 2017
      Source:Advances in Mathematics, Volume 322
      Author(s): Alice Rizzardo
      Given a Fourier–Mukai functor Φ in the general setting of singular schemes, under various hypotheses we provide both left and a right adjoints to Φ, and also give explicit formulas for them. These formulas are simple and natural, and recover the usual formulas when the Fourier–Mukai kernel is a perfect complex. This extends previous work of [1,12,13] and has applications to the twist autoequivalences of [9].

      PubDate: 2017-10-21T21:20:18Z
      DOI: 10.1016/j.aim.2017.10.015
      Issue No: Vol. 322 (2017)
       
  • On the biregular geometry of the Fulton–MacPherson compactification
    • Authors: Alex Massarenti
      Pages: 97 - 131
      Abstract: Publication date: 15 December 2017
      Source:Advances in Mathematics, Volume 322
      Author(s): Alex Massarenti
      Let X [ n ] be the Fulton–MacPherson compactification of the configuration space of n ordered points on a smooth projective variety X. We prove that if either n ≠ 2 or dim ⁡ ( X ) ≥ 2 , then the connected component of the identity of Aut ( X [ n ] ) is isomorphic to the connected component of the identity of Aut ( X ) . When X = C is a curve of genus g ( C ) ≠ 1 we classify the dominant morphisms C [ n ] → C [ r ] , and thanks to this we manage to compute the whole automorphism group of C [ n ] , namely Aut ( C [ n ] ) ≅ S n × Aut ( C ) for any n ≠ 2 , while Aut ( C [ 2 ] ) ≅ S 2 ⋉ ( Aut ( C ) × Aut ( C ) ) . Furthermore, we extend these results on the automorphisms to the case where X = C 1 × . . . × C r is a product of curves of genus g ( C i ) ≥ 2 . Finally, using the techniques developed to deal with Fulton–MacPherson spaces, we study the automorphism groups of some Kontsevich moduli spaces M ‾ 0 , n ( P N , d ) .

      PubDate: 2017-10-21T21:20:18Z
      DOI: 10.1016/j.aim.2017.10.012
      Issue No: Vol. 322 (2017)
       
  • On orbifold theory
    • Authors: Chongying Dong; Li Ren; Feng Xu
      Pages: 1 - 30
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Chongying Dong, Li Ren, Feng Xu
      Let V be a simple vertex operator algebra and G a finite automorphism group of V such that V G is regular. It is proved that every irreducible V G -module occurs in an irreducible g-twisted V-module for some g ∈ G . Moreover, the quantum dimensions of irreducible V G -modules are determined and a global dimension formula for V in terms of twisted modules is obtained. In particular, the orbifold theory conjecture is completely solved if G is solvable.

      PubDate: 2017-09-30T13:46:43Z
      DOI: 10.1016/j.aim.2017.09.032
      Issue No: Vol. 321 (2017)
       
  • Unstable entropies and variational principle for partially hyperbolic
           diffeomorphisms
    • Authors: Huyi Hu; Yongxia Hua; Weisheng Wu
      Pages: 31 - 68
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Huyi Hu, Yongxia Hua, Weisheng Wu
      We study entropies caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy and unstable topological entropy, and establish a variational principle for partially hyperbolic diffeomorphisms, which states that the unstable topological entropy is the supremum of the unstable metric entropy taken over all invariant measures. The unstable metric entropy for an invariant measure is defined as a conditional entropy along unstable manifolds, and it turns out to be the same as that given by Ledrappier–Young, though we do not use increasing partitions. The unstable topological entropy is defined equivalently via separated sets, spanning sets and open covers along a piece of unstable leaf, and it coincides with the unstable volume growth along unstable foliation. We also obtain some properties for the unstable metric entropy such as affineness, upper semi-continuity and a version of Shannon–McMillan–Breiman theorem.

      PubDate: 2017-09-30T13:46:43Z
      DOI: 10.1016/j.aim.2017.09.039
      Issue No: Vol. 321 (2017)
       
  • Counting isospectral manifolds
    • Authors: Mikhail Belolipetsky; Benjamin Linowitz
      Pages: 69 - 79
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Mikhail Belolipetsky, Benjamin Linowitz
      Given a simple Lie group H of real rank at least 2 we show that the maximum cardinality of a set of isospectral non-isometric H-locally symmetric spaces of volume at most x grows at least as fast as x c log ⁡ x / ( log ⁡ log ⁡ x ) 2 where c = c ( H ) is a positive constant. In contrast with the real rank 1 case, this bound comes surprisingly close to the total number of such spaces as estimated in a previous work of Belolipetsky and Lubotzky [2]. Our proof uses Sunada's method, results of [2], and some deep results from number theory. We also discuss an open number-theoretical problem which would imply an even faster growth estimate.

      PubDate: 2017-09-30T13:46:43Z
      DOI: 10.1016/j.aim.2017.09.040
      Issue No: Vol. 321 (2017)
       
  • Parallelotope tilings and q-decomposition numbers
    • Authors: Joseph Chuang; Hyohe Miyachi; Kai Meng Tan
      Pages: 80 - 159
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Joseph Chuang, Hyohe Miyachi, Kai Meng Tan
      We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of U q ( sl ˆ e ) . These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of the Ext 1 -quivers of v-Schur algebras at complex e-th roots of unity generated by simple modules corresponding to these canonical basis vectors are given by the 1-skeletons of the polytopal complexes.

      PubDate: 2017-09-30T13:46:43Z
      DOI: 10.1016/j.aim.2017.09.024
      Issue No: Vol. 321 (2017)
       
  • Combinatorics of the two-species ASEP and Koornwinder moments
    • Authors: Sylvie Corteel; Olya Mandelshtam; Lauren Williams
      Pages: 160 - 204
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Sylvie Corteel, Olya Mandelshtam, Lauren Williams
      In previous work [12–14], the first and third authors introduced staircase tableaux, which they used to give combinatorial formulas for the stationary distribution of the asymmetric simple exclusion process (ASEP) and for the moments of the Askey–Wilson weight function. The fact that the ASEP and Askey–Wilson moments are related at all is unexpected, and is due to [45]. The ASEP is a model of particles hopping on a one-dimensional lattice of N sites with open boundaries; particles can enter and exit at both left and right borders. It was introduced around 1970 [34,43] and is cited as a model for both traffic flow and translation in protein synthesis. Meanwhile, the Askey–Wilson polynomials are a family of orthogonal polynomials in one variable which sit at the top of the hierarchy of classical orthogonal polynomials. So from this previous work, we have the relationship ASEP −− staircase tableaux −− Askey–Wilson moments. The Askey–Wilson polynomials can be viewed as the one-variable case of the multivariate Koornwinder polynomials, which are also known as the Macdonald polynomials attached to the non-reduced affine root system ( C n ∨ , C n ). It is natural then to ask whether one can generalize the relationships among the ASEP, Askey–Wilson moments, and staircase tableaux, in such a way that Koornwinder moments replace Askey–Wilson moments. In [15], we made a precise link between Koornwinder moments and the two-species ASEP, a generalization of the ASEP which has two species of particles with different “weights.” In this article we introduce rhombic staircase tableaux, and show that we have the relationship 2-species ASEP −− rhombic staircase tableaux −− Koornwinder moments. In particular, we give formulas for the stationary distribution of the two-species ASEP and for Koornwinder moments, in terms of rhombic staircase tableaux.

      PubDate: 2017-09-30T13:46:43Z
      DOI: 10.1016/j.aim.2017.09.034
      Issue No: Vol. 321 (2017)
       
  • Necessary conditions and nonexistence results for connected submanifolds
           in a Riemannian manifold
    • Authors: Keomkyo Seo
      Pages: 205 - 220
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Keomkyo Seo
      In this paper, we derive density estimates for submanifolds with variable mean curvature in a Riemannian manifold with sectional curvature bounded above by a constant. This leads to distance estimates for the boundaries of compact connected submanifolds. As applications, we give several necessary conditions and nonexistence results for compact connected minimal submanifolds, Bryant surfaces, and surfaces with small L 2 norm of the mean curvature vector in a Riemannian manifold.

      PubDate: 2017-09-30T13:46:43Z
      DOI: 10.1016/j.aim.2017.09.038
      Issue No: Vol. 321 (2017)
       
  • Extensions of the universal theta divisor
    • Authors: Jesse Leo Kass; Nicola Pagani
      Pages: 221 - 268
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Jesse Leo Kass, Nicola Pagani
      The Jacobian varieties of smooth curves fit together to form a family, the universal Jacobian, over the moduli space of smooth pointed curves, and the theta divisors of these curves form a divisor in the universal Jacobian. In this paper we describe how to extend these families over the moduli space of stable pointed curves using a stability parameter. We then prove a wall-crossing formula describing how the theta divisor varies with this parameter. We use this result to analyze divisors on the moduli space of smooth pointed curves that have recently been studied by Grushevsky–Zakharov, Hain and Müller. Finally, we compute the pullback of the theta divisor studied in Alexeev's work on stable semiabelic varieties and in Caporaso's work on theta divisors of compactified Jacobians.

      PubDate: 2017-09-30T13:46:43Z
      DOI: 10.1016/j.aim.2017.09.021
      Issue No: Vol. 321 (2017)
       
  • Revisiting the nilpotent polynomial Hales–Jewett theorem
    • Authors: John H. Johnson; Florian Karl Richter
      Pages: 269 - 286
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): John H. Johnson, Florian Karl Richter
      Answering a question posed by Bergelson and Leibman in [6], we establish a nilpotent version of the Polynomial Hales–Jewett Theorem that contains the main theorem in [6] as a special case. Important to the formulation and the proof of our main theorem is the notion of a relative syndetic set (relative with respect to a closed non-empty subsets of β G ) [25]. As a corollary of our main theorem we prove an extension of the restricted van der Waerden Theorem to nilpotent groups, which involves nilprogressions.

      PubDate: 2017-10-08T14:37:17Z
      DOI: 10.1016/j.aim.2017.09.033
      Issue No: Vol. 321 (2017)
       
  • A tight bound for Green's arithmetic triangle removal lemma in vector
           spaces
    • Authors: Jacob Fox; László Miklós Lovász
      Pages: 287 - 297
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Jacob Fox, László Miklós Lovász
      Let p be a fixed prime. A triangle in F p n is an ordered triple ( x , y , z ) of points satisfying x + y + z = 0 . Let N = p n = F p n . Green proved an arithmetic triangle removal lemma which says that for every ϵ > 0 and prime p, there is a δ > 0 such that if X , Y , Z ⊂ F p n and the number of triangles in X × Y × Z is at most δ N 2 , then we can delete ϵN elements from X, Y, and Z and remove all triangles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in particular, asked whether a polynomial bound holds. Despite considerable attention, prior to this paper, the best known bound, due to the first author, showed that 1 / δ can be taken to be an exponential tower of twos of height logarithmic in 1 / ϵ . We solve Green's problem, proving an essentially tight bound for Green's arithmetic triangle removal lemma in F p n . We show that a polynomial bound holds, and further determine the best possible exponent. Namely, there is an explicit number C p such that we may take δ = ( ϵ / 3 ) C p , and we must have δ ≤ ϵ C p − o ( 1 ) . In particular, C 2 = 1 + 1 / ( 5 / 3 − log 2 ⁡ 3 ) ≈ 13.239 , and C 3 = 1 + 1 / c 3 with c 3 = 1 − log ⁡ b log ⁡ 3 , b = a − 2 / 3 + a 1 / 3 + a 4 / 3 , and a = 33 − 1 8 , which gives C 3 ≈ 13.901 . The proof uses the essentially sharp bound on mu...
      PubDate: 2017-10-08T14:37:17Z
      DOI: 10.1016/j.aim.2017.09.037
      Issue No: Vol. 321 (2017)
       
  • D-modules, Bernstein–Sato polynomials and F-invariants of direct
           summands
    • Authors: Josep Àlvarez Montaner; Craig Huneke; Luis Núñez-Betancourt
      Pages: 298 - 325
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Josep Àlvarez Montaner, Craig Huneke, Luis Núñez-Betancourt
      We study the structure of D-modules over a ring R which is a direct summand of a polynomial or a power series ring S with coefficients over a field. We relate properties of D-modules over R to D-modules over S. We show that the localization R f and the local cohomology module H I i ( R ) have finite length as D-modules over R. Furthermore, we show the existence of the Bernstein–Sato polynomial for elements in R. In positive characteristic, we use this relation between D-modules over R and S to show that the set of F-jumping numbers of an ideal I ⊆ R is contained in the set of F-jumping numbers of its extension in S. As a consequence, the F-jumping numbers of I in R form a discrete set of rational numbers. We also relate the Bernstein–Sato polynomial in R with the F-thresholds and the F-jumping numbers in R.

      PubDate: 2017-10-08T14:37:17Z
      DOI: 10.1016/j.aim.2017.09.019
      Issue No: Vol. 321 (2017)
       
  • Infinite loop spaces from operads with homological stability
    • Authors: Maria Basterra; Irina Bobkova; Kate Ponto; Ulrike Tillmann; Sarah Yeakel
      Pages: 391 - 430
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Maria Basterra, Irina Bobkova, Kate Ponto, Ulrike Tillmann, Sarah Yeakel
      Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions. We prove that such operads are infinite loop space operads in the sense that the group completions of their algebras are infinite loop spaces. The recent, strong homological stability results of Galatius and Randal-Williams for moduli spaces of even dimensional manifolds can be used to construct examples of operads with homological stability. As a consequence diffeomorphism groups and mapping class groups are shown to give rise to infinite loop spaces. Furthermore, the map to K-theory defined by the action of the diffeomorphisms on the middle dimensional homology is shown to be a map of infinite loop spaces.

      PubDate: 2017-10-28T22:03:09Z
      DOI: 10.1016/j.aim.2017.09.036
      Issue No: Vol. 321 (2017)
       
  • Quantum groups, quantum tori, and the Grothendieck–Springer
           resolution
    • Authors: Gus Schrader; Alexander Shapiro
      Pages: 431 - 474
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Gus Schrader, Alexander Shapiro
      We construct an algebra embedding of the quantum group U q ( g ) into a central extension of the quantum coordinate ring O q [ G w 0 , w 0 / H ] of the reduced big double Bruhat cell in G. This embedding factors through the Heisenberg double H q of the quantum Borel subalgebra U ≥ 0 , which we relate to O q [ G ] via twisting by the longest element of the quantum Weyl group. Our construction is inspired by the Poisson geometry of the Grothendieck–Springer resolution studied in [10], and the quantum Beilinson–Bernstein theorem investigated in [2] and [36].

      PubDate: 2017-10-14T15:00:36Z
      DOI: 10.1016/j.aim.2017.09.010
      Issue No: Vol. 321 (2017)
       
  • A transversal of full outer measure
    • Authors: Ashutosh Kumar; Saharon Shelah
      Pages: 475 - 485
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Ashutosh Kumar, Saharon Shelah
      We show that for every partition of a set of reals into countable sets there is a transversal of the same outer measure.

      PubDate: 2017-10-14T15:00:36Z
      DOI: 10.1016/j.aim.2017.10.008
      Issue No: Vol. 321 (2017)
       
  • Simultaneous models for commuting holomorphic self-maps of the ball
    • Authors: Leandro Arosio; Filippo Bracci
      Pages: 486 - 512
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Leandro Arosio, Filippo Bracci
      We prove that a finite family of commuting holomorphic self-maps of the unit ball B q ⊂ C q admits a simultaneous holomorphic conjugacy to a family of commuting automorphisms of a possibly lower dimensional ball, and that such conjugacy satisfies a universal property. As an application we describe when a hyperbolic and a parabolic holomorphic self-map of B q can commute.

      PubDate: 2017-10-14T15:00:36Z
      DOI: 10.1016/j.aim.2017.10.002
      Issue No: Vol. 321 (2017)
       
  • On the μ-ordinary locus of a Shimura variety
    • Authors: Xuhua He; Sian Nie
      Pages: 513 - 528
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Xuhua He, Sian Nie
      In this paper, we study the μ-ordinary locus of a Shimura variety with parahoric level structure. Under the axioms in [12], we show that μ-ordinary locus is a union of certain maximal Ekedahl–Kottwitz–Oort–Rapoport strata introduced in [12] and we give criteria on the density of the μ-ordinary locus.

      PubDate: 2017-10-14T15:00:36Z
      DOI: 10.1016/j.aim.2017.10.005
      Issue No: Vol. 321 (2017)
       
  • A self-similar measure with dense rotations, singular projections and
           discrete slices
    • Authors: Ariel Rapaport
      Pages: 529 - 546
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Ariel Rapaport
      We construct a planar homogeneous self-similar measure, with strong separation, dense rotations and dimension greater than 1, such that there exist lines for which dimension conservation does not hold and the projection of the measure is singular. In fact, the set of such directions is residual and the typical slices of the measure, perpendicular to these directions, are discrete.

      PubDate: 2017-10-14T15:00:36Z
      DOI: 10.1016/j.aim.2017.10.007
      Issue No: Vol. 321 (2017)
       
  • Nonuniform spectrum on Banach spaces
    • Authors: Luis Barreira; Davor Dragičević; Claudia Valls
      Pages: 547 - 591
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Luis Barreira, Davor Dragičević, Claudia Valls
      For a sequence of bounded linear operators acting on a Banach space, we consider the notion of nonuniform spectrum. This is defined in terms of the existence of nonuniform exponential dichotomies with an arbitrarily small nonuniform part and can be seen as a nonuniform version of the spectrum introduced by Sacker and Sell in the case of a single trajectory, although now in the infinite-dimensional setting. We give a complete characterization of all possible forms of the nonuniform spectrum for sequences of compact linear operators and, more generally, for sequences of bounded linear operators satisfying a certain asymptotic compactness. Moreover, we provide explicit examples of sequences of compact linear operators acting on the l 2 space of sequences of real numbers for all the possible forms of the nonuniform spectrum. As nontrivial applications, we show that the nonuniform spectrum of a Lyapunov regular sequence is the set of Lyapunov exponents and that the asymptotic behavior persists under sufficiently small nonlinear perturbations, in the sense that the lower and upper Lyapunov exponents of the perturbed dynamics belong to a connected component of the nonuniform spectrum. Finally, we obtain appropriate versions of the results for nonuniformly hyperbolic cocycles.

      PubDate: 2017-10-14T15:00:36Z
      DOI: 10.1016/j.aim.2017.10.006
      Issue No: Vol. 321 (2017)
       
  • Euler class groups and the homology of elementary and special linear
           groups
    • Authors: Marco Schlichting
      Pages: 1 - 81
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Marco Schlichting
      We improve homology stability ranges for elementary and special linear groups over rings with many units. Our result implies stability for unstable Quillen K-groups and proves a conjecture of Bass. For commutative local rings with infinite residue fields, we show that the obstruction to further stability is given by Milnor–Witt K-theory. As an application we construct Euler classes of projective modules with values in the cohomology of the Milnor–Witt K-theory sheaf. For d-dimensional commutative noetherian rings with infinite residue fields we show that the vanishing of the Euler class is necessary and sufficient for an oriented projective module P of rank d to split off a rank 1 free direct summand. Along the way we obtain a new presentation of Milnor–Witt K-theory and of symplectic K 2 simplifying the classical Matsumoto–Moore presentation.

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

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

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

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

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

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

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

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.08.041
      Issue No: Vol. 320 (2017)
       
  • Equivariant split generation and mirror symmetry of special isogenous tori
    • Authors: Weiwei
      Abstract: Publication date: 7 January 2018
      Source:Advances in Mathematics, Volume 323
      Author(s): Weiwei Wu
      We prove a version of equivariant split generation of Fukaya category when a symplectic manifold admits a free action of a finite group G. Combining this with some generalizations of Seidel's algebraic frameworks from [35], we obtain new cases of homological mirror symmetry for some symplectic tori with non-split symplectic forms, which we call special isogenous tori. This extends the work of Abouzaid–Smith [2]. We also show that derived Fukaya categories are complete invariants of special isogenous tori.

      PubDate: 2017-11-12T02:49:38Z
       
  • A tribute to David Kazhdan
    • Authors: Roman Bezrukavnikov; Alexander Braverman; Michael Finkelberg; Dennis Gaitsgory; Alexander Goncharov; Yakov Varshavsky
      Abstract: Publication date: Available online 8 November 2017
      Source:Advances in Mathematics
      Author(s): Roman Bezrukavnikov, Alexander Braverman, Michael Finkelberg, Dennis Gaitsgory, Alexander Goncharov, Yakov Varshavsky


      PubDate: 2017-11-12T02:49:38Z
      DOI: 10.1016/j.aim.2017.08.017
       
  • Profinite completion of operads and the
           Grothendieck–Teichmüller group
    • Authors: Geoffroy Horel
      Abstract: Publication date: 1 December 2017
      Source:Advances in Mathematics, Volume 321
      Author(s): Geoffroy Horel
      In this paper, we prove that the group of homotopy automorphisms of the profinite completion of the operad of little 2-disks is isomorphic to the profinite Grothendieck–Teichmüller group. In particular, the absolute Galois group of Q acts faithfully on the profinite completion of E 2 in the homotopy category of profinite weak operads.

      PubDate: 2017-10-08T14:37:17Z
       
 
 
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