for Journals by Title or ISSN
for Articles by Keywords
help
  Subjects -> MATHEMATICS (Total: 886 journals)
    - APPLIED MATHEMATICS (72 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (656 journals)
    - MATHEMATICS (GENERAL) (42 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (77 journals)

MATHEMATICS (656 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: 22)
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: 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: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 8)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 9)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (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: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 8)
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)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Advances in Mathematics
  [SJR: 3.261]   [H-I: 65]   [10 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 0001-8708 - ISSN (Online) 1090-2082
   Published by Elsevier Homepage  [3043 journals]
  • 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)
       
  • 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)
       
  • 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)
       
  • The slice method for G-torsors
    • Authors: Roland Lötscher; Mark MacDonald
      Pages: 329 - 360
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Roland Lötscher, Mark MacDonald
      The notion of a ( G , N ) -slice of a G-variety was introduced by P.I. Katsylo in the early 80's for an algebraically closed base field of characteristic 0. Slices (also known under the name of relative sections) have ever since provided a fundamental tool in invariant theory, allowing reduction of rational or regular invariants of an algebraic group G to invariants of a “simpler” group. We refine this notion for a G-scheme over an arbitrary field, and use it to get reduction of structure group results for G-torsors. Namely we show that any ( G , N ) -slice of a versal G-scheme gives surjective maps H 1 ( L , N ) → H 1 ( L , G ) in fppf-cohomology for infinite fields L containing F. We show that every stabilizer in general position H for a geometrically irreducible G-variety V gives rise to a ( G , N G ( H ) ) -slice in our sense. The combination of these two results is applied in particular to obtain a striking new upper bound on the essential dimension of the simply connected split algebraic group of type E 7 .

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

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

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

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

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

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

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.09.001
      Issue No: Vol. 320 (2017)
       
  • Finite topology self-translating surfaces for the mean curvature flow in
           R3
    • Authors: Juan Dávila; Manuel del Pino; Xuan Hien Nguyen
      Pages: 674 - 729
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Juan Dávila, Manuel del Pino, Xuan Hien Nguyen
      Finite topology self-translating surfaces for the mean curvature flow constitute a key element in the analysis of Type II singularities from a compact surface because they arise as limits after suitable blow-up scalings around the singularity. We prove the existence of such a surface M ⊂ R 3 that is orientable, embedded, complete, and with three ends asymptotically paraboloidal. The fact that M is self-translating means that the moving surface S ( t ) = M + t e z evolves by mean curvature flow, or equivalently, that M satisfies the equation H M = ν ⋅ e z where H M denotes mean curvature, ν is a choice of unit normal to M, and e z is a unit vector along the z-axis. This surface M is in correspondence with the classical three-end Costa–Hoffman–Meeks minimal surface with large genus, which has two asymptotically catenoidal ends and one planar end, and a long array of small tunnels in the intersection region resembling a periodic Scherk surface. This example is the first non-trivial one of its kind, and it suggests a strong connection between this problem and the theory of embedded complete minimal surfaces with finite total curvature.

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

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

      PubDate: 2017-09-17T11:43:03Z
      DOI: 10.1016/j.aim.2017.09.018
      Issue No: Vol. 320 (2017)
       
  • On polynomially integrable convex bodies
    • Authors: Alexander Koldobsky; Alexander S. Merkurjev; Vladyslav Yaskin
      Pages: 876 - 886
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Alexander Koldobsky, Alexander S. Merkurjev, Vladyslav Yaskin
      An infinitely smooth convex body in R n is called polynomially integrable of degree N if its parallel section functions are polynomials of degree N. We prove that the only smooth convex bodies with this property in odd dimensions are ellipsoids, if N ≥ n − 1 . This is in contrast with the case of even dimensions and the case of odd dimensions with N < n − 1 , where such bodies do not exist, as it was recently shown by Agranovsky.

      PubDate: 2017-09-23T12:05:01Z
      DOI: 10.1016/j.aim.2017.09.028
      Issue No: Vol. 320 (2017)
       
  • Cuspidal characters and automorphisms
    • Authors: Gunter Malle
      Pages: 887 - 903
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Gunter Malle
      We investigate the action of outer automorphisms of finite groups of Lie type on their irreducible characters. We obtain a definite result for cuspidal characters. As an application we verify the inductive McKay condition for some further infinite families of simple groups at certain primes.

      PubDate: 2017-09-23T12:05:01Z
      DOI: 10.1016/j.aim.2017.09.026
      Issue No: Vol. 320 (2017)
       
  • Compressible Navier–Stokes system: Large solutions and
           incompressible limit
    • Authors: Raphaël Danchin; Piotr Bogusław Mucha
      Pages: 904 - 925
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Raphaël Danchin, Piotr Bogusław Mucha
      Here we prove the existence of global in time regular solutions to the two-dimensional compressible Navier–Stokes equations supplemented with arbitrary large initial velocity v 0 and almost constant density ϱ 0 , for large volume (bulk) viscosity. The result is generalized to the higher dimensional case under the additional assumption that the strong solution of the classical incompressible Navier–Stokes equations supplemented with the divergence-free projection of v 0 , is global. The systems are examined in R d with d ≥ 2 , in the critical B ˙ 2 , 1 s Besov spaces framework.

      PubDate: 2017-09-23T12:05:01Z
      DOI: 10.1016/j.aim.2017.09.025
      Issue No: Vol. 320 (2017)
       
  • Two-end solutions to the Allen–Cahn equation in R3
    • Authors: Changfeng Gui; Yong Liu; Juncheng Wei
      Pages: 926 - 992
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Changfeng Gui, Yong Liu, Juncheng Wei
      In this paper, we study axially symmetric solutions of Allen–Cahn equation in the three dimensional Euclidean space. Using a sophisticated continuation method, we show the existence of a complete family of axially symmetric solutions with a range of logarithmic growth rates, which may be regarded as the analogue of the family of catenoids and hence called two-end solutions. Nonexistence of two-end solution with a small growth rate is also shown, which differs from the theory of minimal surfaces.

      PubDate: 2017-09-23T12:05:01Z
      DOI: 10.1016/j.aim.2017.09.013
      Issue No: Vol. 320 (2017)
       
  • Adjoints to a Fourier–Mukai functor
    • 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
       
  • On the biregular geometry of the Fulton–MacPherson compactification
    • 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
       
  • Sharp bounds for the cubic Parsell–Vinogradov system in two
           dimensions
    • Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Jean Bourgain, Ciprian Demeter, Shaoming Guo
      We prove a sharp decoupling for a certain two dimensional surface in R 9 . As an application, we obtain the full range of expected estimates for the cubic Parsell–Vinogradov system in two dimensions.

      PubDate: 2017-10-21T21:20:18Z
       
  • 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
       
  • The distribution of zeros of ζ′(s) and gaps between zeros of
           ζ(s)
    • Authors: Fan
      Abstract: Publication date: 7 November 2017
      Source:Advances in Mathematics, Volume 320
      Author(s): Fan Ge
      Assume the Riemann Hypothesis. We establish a local structure theorem for zeros of the Riemann zeta-function ζ ( s ) and its derivative ζ ′ ( s ) . As an application, we prove a stronger form of half of a conjecture of Radziwiłł [18] concerning the global statistics of these zeros. Roughly speaking, we show that on the Riemann Hypothesis, if there occurs a small gap between consecutive zeta zeros, then there is exactly one zero of ζ ′ ( s ) lying not only very close to the critical line but also between that pair of zeta zeros. This refines a result of Zhang [22]. Some related results are also shown. For example, we prove a weak form of a conjecture of Soundararajan, and suggest a repulsion phenomena for zeros of ζ ′ ( s ) .

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

      PubDate: 2017-09-17T11:43:03Z
       
 
 
JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327
 
Home (Search)
Subjects A-Z
Publishers A-Z
Customise
APIs
Your IP address: 54.81.178.153
 
About JournalTOCs
API
Help
News (blog, publications)
JournalTOCs on Twitter   JournalTOCs on Facebook

JournalTOCs © 2009-2016