Subjects -> MATHEMATICS (Total: 1118 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (819 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (819 journals)                  1 2 3 4 5 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 5)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Accounting Perspectives     Full-text available via subscription   (Followers: 9)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 17)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 9)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 44)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
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: 13)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 8)
Advances in Complex Systems     Hybrid Journal   (Followers: 12)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 5)
Advances in Fixed Point Theory     Open Access   (Followers: 9)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 22)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 10)
Advances in Materials Science     Open Access   (Followers: 22)
Advances in Mathematical Physics     Open Access   (Followers: 10)
Advances in Mathematics     Full-text available via subscription   (Followers: 22)
Advances in Numerical Analysis     Open Access   (Followers: 8)
Advances in Operations Research     Open Access   (Followers: 14)
Advances in Operator Theory     Hybrid Journal   (Followers: 4)
Advances in Porous Media     Full-text available via subscription   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 11)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 12)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 7)
Afrika Matematika     Hybrid Journal   (Followers: 3)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 4)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 1)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 6)
Algebra and Logic     Hybrid Journal   (Followers: 8)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 14)
Algorithms Research     Open Access   (Followers: 2)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 10)
American Journal of Mathematical Analysis     Open Access   (Followers: 2)
American Journal of Mathematical and Management Sciences     Hybrid Journal   (Followers: 1)
American Journal of Mathematics     Full-text available via subscription   (Followers: 9)
American Journal of Operations Research     Open Access   (Followers: 8)
American Mathematical Monthly     Full-text available via subscription   (Followers: 7)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 13)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 10)
Analysis Mathematica     Full-text available via subscription  
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access   (Followers: 8)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 17)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 8)
Annals of Functional Analysis     Hybrid Journal   (Followers: 4)
Annals of Mathematics     Full-text available via subscription   (Followers: 4)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 6)
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   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 2)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 10)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 13)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 2)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 3)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 2)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 6)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 4)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 24)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 4)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 7)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
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: 3)
British Journal for the History of Mathematics     Hybrid Journal  
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: 15)
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: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 3)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access   (Followers: 2)
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 23)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 3)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access   (Followers: 1)
CODEE Journal     Open Access   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 5)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 11)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 3)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 9)
Computational Mechanics     Hybrid Journal   (Followers: 10)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 11)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access   (Followers: 1)
Contributions to Discrete Mathematics     Open Access   (Followers: 1)
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access   (Followers: 1)
Demographic Research     Open Access   (Followers: 16)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access   (Followers: 3)
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: 4)

        1 2 3 4 5 | Last

Similar Journals
Journal Cover
Communications in Mathematical Physics
Journal Prestige (SJR): 1.682
Citation Impact (citeScore): 2
Number of Followers: 4  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0916 - ISSN (Online) 0010-3616
Published by Springer-Verlag Homepage  [2658 journals]
  • Correction to: Non-local Markovian Symmetric Forms on Infinite Dimensional
           Spaces I. The Closability and Quasi-Regularity

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      PubDate: 2021-11-01
       
  • Solvable Intermittent Shell Model of Turbulence

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      Abstract: We introduce a shell model of turbulence featuring intermittent behaviour with anomalous power-law scaling of structure functions. This model is solved analytically with the explicit derivation of anomalous exponents. The solution associates the intermittency with the hidden symmetry for Kolmogorov multipliers, making our approach relevant for real turbulence.
      PubDate: 2021-11-01
       
  • Delocalization Transition for Critical Erdős–Rényi Graphs

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      Abstract: We analyse the eigenvectors of the adjacency matrix of a critical Erdős–Rényi graph \({\mathbb {G}}(N,d/N)\) , where d is of order \(\log N\) . We show that its spectrum splits into two phases: a delocalized phase in the middle of the spectrum, where the eigenvectors are completely delocalized, and a semilocalized phase near the edges of the spectrum, where the eigenvectors are essentially localized on a small number of vertices. In the semilocalized phase the mass of an eigenvector is concentrated in a small number of disjoint balls centred around resonant vertices, in each of which it is a radial exponentially decaying function. The transition between the phases is sharp and is manifested in a discontinuity in the localization exponent \(\gamma (\varvec{\mathrm {w}})\) of an eigenvector \(\varvec{\mathrm {w}}\) , defined through \(\Vert \varvec{\mathrm {w}} \Vert _\infty / \Vert \varvec{\mathrm {w}} \Vert _2 = N^{-\gamma (\varvec{\mathrm {w}})}\) . Our results remain valid throughout the optimal regime \(\sqrt{\log N} \ll d \leqslant O(\log N)\) .
      PubDate: 2021-11-01
       
  • Conformal Field Theories with Sporadic Group Symmetry

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      Abstract: The monster sporadic group is the automorphism group of a central charge \(c=24\) vertex operator algebra (VOA) or meromorphic conformal field theory (CFT). In addition to its \(c=24\) stress tensor T(z), this theory contains many other conformal vectors of smaller central charge; for example, it admits 48 commuting \(c=\frac{1}{2}\) conformal vectors whose sum is T(z). Such decompositions of the stress tensor allow one to construct new CFTs from the monster CFT in a manner analogous to the Goddard-Kent-Olive (GKO) coset method for affine Lie algebras. We use this procedure to produce evidence for the existence of a number of CFTs with sporadic symmetry groups and employ a variety of techniques, including Hecke operators, modular linear differential equations, and Rademacher sums, to compute the characters of these CFTs. Our examples include (extensions of) nine of the sporadic groups appearing as subquotients of the monster, as well as the simple groups \({}^2{\textit{E}}_6(2)\) and \({\textit{F}}_4(2)\) of Lie type. Many of these examples are naturally associated to McKay’s \(\widehat{E_8}\) correspondence, and we use the structure of Norton’s monstralizer pairs more generally to organize our presentation.
      PubDate: 2021-11-01
       
  • Kato Smoothing, Strichartz and Uniform Sobolev Estimates for Fractional
           Operators With Sharp Hardy Potentials

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      Abstract: Let \(0<\sigma <n/2\) and \(H=(-\Delta )^\sigma +V(x)\) be Schrödinger type operators on \({\mathbb {R}}^n\) with a class of scaling-critical potentials V(x), which include the Hardy potential \(a x ^{-2\sigma }\) with a sharp coupling constant \(a\ge -C_{\sigma ,n}\) ( \(C_{\sigma ,n}\) is the best constant of Hardy’s inequality of order \(\sigma \) ). In the present paper we consider several sharp global estimates for the resolvent and the solution to the time-dependent Schrödinger equation associated with H. In the case of the subcritical coupling constant \(a>-C_{\sigma ,n}\) , we first prove uniform resolvent estimates of Kato–Yajima type for all \(0<\sigma <n/2\) , which turn out to be equivalent to Kato smoothing estimates for the Cauchy problem. We then establish Strichartz estimates for \(\sigma >1/2\) and uniform Sobolev estimates of Kenig–Ruiz–Sogge type for \(\sigma \ge n/(n+1)\) . These extend the same properties for the Schrödinger operator with the inverse-square potential to the higher-order and fractional cases. Moreover, we also obtain improved Strichartz estimates with a gain of regularities for general initial data if \(1<\sigma <n/2\) and for radially symmetric data if \(n/(2n-1)<\sigma \le 1\) , which extends the corresponding results for the free evolution to the case with Hardy potentials. These arguments can be further applied to a large class of higher-order inhomogeneous elliptic operators and even to certain long-range metric perturbations of the Laplace operator. Finally, in the critical coupling constant case (i.e., \(a=-C_{\sigma ,n}\) ), we show that the same results as in the subcritical case still hold for functions orthogonal to radial functions.
      PubDate: 2021-11-01
       
  • Limiting Absorption Principle and Equivalence of Feynman Propagators on
           Asymptotically Minkowski Spacetimes

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      Abstract: In this paper, we show the limiting absorption principle for the wave operator on asymptotically Minkowski spacetimes. This problem was previously considered by Vasy (J Spectr Theory 10:439–461, 2020). Here, we employ Mourre theory which seems a more transparent tool. Moreover, we also prove that the anti-Feynman propagator defined by Gérard and Wrochna coincides with the outgoing resolvent.
      PubDate: 2021-11-01
       
  • Non Uniqueness of Power-Law Flows

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      Abstract: We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension \(d\ge 3\) . For the power index q below the compactness threshold, i.e. \(q \in (1, \frac{2d}{d+2})\) , we show ill-posedness of Leray–Hopf solutions. For a wider class of indices \(q \in (1, \frac{3d+2}{d+2})\) we show ill-posedness of distributional (non-Leray–Hopf) solutions, extending the seminal paper of Buckmaster & Vicol [10]. In this wider class we also construct non-unique solutions for every datum in \(L^2\) .
      PubDate: 2021-11-01
       
  • Flat F-Manifolds, F-CohFTs, and Integrable Hierarchies

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      Abstract: We define the double ramification hierarchy associated to an F-cohomological field theory and use this construction to prove that the principal hierarchy of any semisimple (homogeneous) flat F-manifold possesses a (homogeneous) integrable dispersive deformation at all orders in the dispersion parameter. The proof is based on the reconstruction of an F-CohFT starting from a semisimple flat F-manifold and additional data in genus 1, obtained in our previous work. Our construction of these dispersive deformations is quite explicit and we compute several examples. In particular, we provide a complete classification of rank 1 hierarchies of DR type at the order 9 approximation in the dispersion parameter and of homogeneous DR hierarchies associated with all 2-dimensional homogeneous flat F-manifolds at genus 1 approximation.
      PubDate: 2021-11-01
       
  • Product Rigidity in Von Neumann and C $$^*$$ ∗ -Algebras Via
           S-Malleable Deformations

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      Abstract: We provide a new large class of countable icc groups \({\mathcal {A}}\) for which the product rigidity result from Chifan et al. (Geom Funct Anal 26(1): 136–159, 2016) holds: if \(\Gamma _1,\ldots ,\Gamma _n\in {\mathcal {A}}\) and \(\Lambda \) is any group such that \(L(\Gamma _1\times \dots \times \Gamma _n)\cong L(\Lambda )\) , then there exists a product decomposition \(\Lambda =\Lambda _1\times \dots \times \Lambda _n\) such that \(L(\Lambda _i)\) is stably isomorphic to \(L(\Gamma _i)\) , for any \(1\le i\le n\) . Class \({\mathcal {A}}\) consists of groups \(\Gamma \) for which \(L(\Gamma )\) admits an s-malleable deformation in the sense of Sorin Popa and it includes all non-amenable groups \(\Gamma \) such that either (a) \(\Gamma \) admits an unbounded 1-cocycle into its left regular representation, or (b) \(\Gamma \) is an arbitrary wreath product group with amenable base. As a byproduct of these results, we obtain new examples of W \(^*\) -superrigid groups and new rigidity results in the C \(^*\) -algebra theory.
      PubDate: 2021-11-01
       
  • Remarks on Anomalous Symmetries of C*-Algebras

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      Abstract: For a group G and \(\omega \in Z^{3}(G, \text {U}(1))\) , an \(\omega \) -anomalous action on a C*-algebra B is a \(\text {U}(1)\) -linear monoidal functor between 2-groups , where the latter denotes the 2-group of \(*\) -automorphisms of B. The class \([\omega ]\in H^{3}(G, \text {U}(1))\) is called the anomaly of the action. We show that for every \(n\ge 2\) and every finite group G, every anomaly can be realized on the stabilization of a commutative C*-algebra \(C(M)\otimes {\mathcal {K}}\) for some closed connected n-manifold M. We also show that although there are no anomalous symmetries of Roe C*-algebras of coarse spaces, for every finite group G, every anomaly can be realized on the Roe corona \(C^{*}(X)/{\mathcal {K}}\) of some bounded geometry metric space X with property A.
      PubDate: 2021-11-01
       
  • Gauge Theory on Noncommutative Riemannian Principal Bundles

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      Abstract: We present a new, general approach to gauge theory on principal G-spectral triples, where G is a compact connected Lie group. We introduce a notion of vertical Riemannian geometry for G- \(C^*\) -algebras and prove that the resulting noncommutative orbitwise family of Kostant’s cubic Dirac operators defines a natural unbounded \(KK^G\) -cycle in the case of a principal G-action. Then, we introduce a notion of principal G-spectral triple and prove, in particular, that any such spectral triple admits a canonical factorisation in unbounded \(KK^G\) -theory with respect to such a cycle: up to a remainder, the total geometry is the twisting of the basic geometry by a noncommutative superconnection encoding the vertical geometry and underlying principal connection. Using these notions, we formulate an approach to gauge theory that explicitly generalises the classical case up to a groupoid cocycle and is compatible in general with this factorisation; in the unital case, it correctly yields a real affine space of noncommutative principal connections with affine gauge action. Our definitions cover all locally compact classical principal G-bundles and are compatible with \(\theta \) -deformation; in particular, they cover the \(\theta \) -deformed quaternionic Hopf fibration \(C^\infty (S^7_\theta ) \hookleftarrow C^\infty (S^4_\theta )\) as a noncommutative principal \({{\,\mathrm{SU}\,}}(2)\) -bundle.
      PubDate: 2021-11-01
       
  • Correction to: A C*-algebraic Approach to Interacting Quantum Field
           Theories

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      PubDate: 2021-11-01
       
  • Stable Knots and Links in Electromagnetic Fields

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      Abstract: Persistent topological structures in physical systems have become increasingly important over the last years. Electromagnetic fields with knotted field lines play a special role among these, since they can be used to transfer their knottedness to other systems like plasmas and quantum fluids. In null electromagnetic fields the electric and the magnetic field lines evolve like unbreakable elastic filaments in a fluid flow. In particular, their topology is preserved for all time, so that all knotted closed field lines maintain their knot type. We use an approach due to Bateman to prove that for every link L there is such an electromagnetic field that satisfies Maxwell’s equations in free space and that has closed electric and magnetic field lines in the shape of L for all time. The knotted and linked field lines turn out to be projections of real analytic Legendrian links with respect to the standard contact structure on the 3-sphere.
      PubDate: 2021-11-01
       
  • Emergence of Jumps in Quantum Trajectories via Homogenization

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      Abstract: In the strong noise regime, we study the homogenization of quantum trajectories i.e. stochastic processes appearing in the context of quantum measurement. When the generator of the average semigroup can be separated into three distinct time scales, we start by describing a homogenized limiting semigroup. This result is of independent interest and is formulated outside of the scope of quantum trajectories. Going back to the quantum context, we show that, in the Meyer–Zheng topology, the time-continuous quantum trajectories converge weakly to the discontinuous trajectories of a pure jump Markov process. Notably, this convergence cannot hold in the usual Skorokhod topology.
      PubDate: 2021-11-01
       
  • On the Parabolic and Hyperbolic Liouville Equations

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      Abstract: We study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic damped nonlinear wave equation (SdNLW) with an exponential nonlinearity \(\lambda \beta e^{\beta u }\) , forced by an additive space-time white noise. (i) We first study SNLH for general \(\lambda \in {\mathbb {R}}\) . By establishing higher moment bounds of the relevant Gaussian multiplicative chaos and exploiting the positivity of the Gaussian multiplicative chaos, we prove local well-posedness of SNLH for the range \(0< \beta ^2 < \frac{8 \pi }{3 + 2 \sqrt{2}} \simeq 1.37 \pi \) . Our argument yields stability under the noise perturbation, thus improving Garban’s local well-posedness result (2020). (ii) In the defocusing case \(\lambda >0\) , we exploit a certain sign-definite structure in the equation and the positivity of the Gaussian multiplicative chaos. This allows us to prove global well-posedness of SNLH for the range: \(0< \beta ^2 < 4\pi \) . (iii) As for SdNLW in the defocusing case \(\lambda > 0\) , we go beyond the Da Prato-Debussche argument and introduce a decomposition of the nonlinear component, allowing us to recover a sign-definite structure for a rough part of the unknown, while the other part enjoys a stronger smoothing property. As a result, we reduce SdNLW into a system of equations (as in the paracontrolled approach for the dynamical \(\Phi ^4_3\) -model) and prove local well-posedness of SdNLW for the range: \(0< \beta ^2 < \frac{32 - 16\sqrt{3}}{5}\pi \simeq 0.86\pi \) . This result (translated to the context of random data well-posedness for the deterministic nonlinear wave equation with an exponential nonlinearity) solves an open question posed by Sun and Tzvetkov (2020). (iv) When \(\lambda > 0\) , these models formally preserve the associated Gibbs measures with the exponential nonlinearity. Under the same assumption on \(\beta \) as in (ii) and (iii) above, we prove almost sure global well-posedness (in particular for SdNLW) and invariance of the Gibbs measures in both the parabolic and hyperbolic settings. (v) In Appendix, we present an argument for proving local well-posedness of SNLH for general \(\lambda \in {\mathbb {R}}\) without using the positivity of the Gaussian multiplicative chaos. This proves local well-posedness of SNLH for the range \(0< \beta ^2 < \frac{4}{3} \pi \simeq 1.33 \pi \) , slightly smaller than that in (i), but provides Lipschitz continuity of the solution map in initial data as well as the noise.
      PubDate: 2021-11-01
       
  • Curvature Formulas Related to a Family of Stable Higgs Bundles

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      Abstract: In this paper, we investigate the geometry of the base complex manifold of an effectively parametrized holomorphic family of stable Higgs bundles over a fixed compact Kähler manifold. The starting point of our study is Schumacher–Toma/Biswas–Schumacher’s curvature formulas for Weil–Petersson-type metrics, in Sect. 2, we give some applications of their formulas on the geometric properties of the base manifold. In Sect. 3, we calculate the curvature on the higher direct image bundle, which recovers Biswas–Schumacher’s curvature formula. In Sect. 4, we construct a smooth and strongly pseudo-convex complex Finsler metric for the base manifold, the corresponding holomorphic sectional curvature is calculated explicitly.
      PubDate: 2021-11-01
       
  • Stability of Large-Amplitude Viscous Shock Under Periodic Perturbation for
           1-d Isentropic Navier–Stokes Equations

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      Abstract: The stability of solutions under periodic perturbations for both inviscid and viscous conservation laws is an interesting and important problem. In this paper, a large-amplitude viscous shock under space-periodic perturbation for the isentropic Navier–Stokes equations is considered. It is shown that if the initial perturbation around the shock is suitably small and satisfies a zero-mass type condition (2.17), then the solution of the N–S equations tends to the viscous shock with a shift, which is partially determined by the periodic oscillations. In other words, the viscous shock is nonlinearly stable even though the perturbation oscillates at the far fields. The key point is to construct a suitable ansatz \( (\tilde{v},\tilde{u}) \) , which carries the same oscillations of the solution (v, u) at the far fields, so that the difference \( (v-\tilde{v},u-\tilde{u}) \) belongs to the \( H^2(\mathbb {R}) \) space for all \( t\ge 0. \)
      PubDate: 2021-11-01
       
  • Hyperbolic SRB Measures and the Leaf Condition

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      Abstract: Let M be a Riemannian, boundaryless, and compact manifold, with \(\dim M\ge 2\) and let f be a \(C^{1+}\) diffeomorphism. We show that there is a hyperbolic SRB measure if and only if there exists an unstable leaf with a subset of positive leaf volume of hyperbolic points which return to some Pesin set with positive frequency. This answers a question of Pesin.
      PubDate: 2021-11-01
       
  • Tau-Functions and Monodromy Symplectomorphisms

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      Abstract: We derive a new Hamiltonian formulation of Schlesinger equations in terms of the dynamical r-matrix structure. The corresponding symplectic form is shown to be the pullback, under the monodromy map, of a natural symplectic form on the extended monodromy manifold. We show that Fock–Goncharov coordinates are log-canonical for the symplectic form. Using these coordinates we define the symplectic potential on the monodromy manifold and interpret the Jimbo–Miwa–Ueno tau-function as the generating function of the monodromy map. This, in particular, solves a recent conjecture by A. Its, O. Lisovyy and A. Prokhorov.
      PubDate: 2021-10-12
       
  • Gaussian Random Permutation and the Boson Point Process

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      Abstract: We construct an infinite volume spatial random permutation \(({{\textsf {X}}},\sigma )\) , where \({{\textsf {X}}}\subset {\mathbb {R}}^d\) is locally finite and \(\sigma :{{\textsf {X}}}\rightarrow {{\textsf {X}}}\) is a permutation, associated to the formal Hamiltonian $$\begin{aligned} H({{\textsf {X}}},\sigma ) = \sum _{x\in {{\textsf {X}}}} \Vert x-\sigma (x)\Vert ^2. \end{aligned}$$ The measures are parametrized by the point density \(\rho \) and the temperature \(\alpha \) . Spatial random permutations are naturally related to boson systems through a representation originally due to Feynman (Phys Rev 91:1291–1301, 1953). Let \(\rho _c=\rho _c(\alpha )\) be the critical density for Bose–Einstein condensation in Feynman’s representation. Each finite cycle of \(\sigma \) induces a loop of points of  \({{\textsf {X}}}\) . For \(\rho \le \rho _c\) we define \(({{\textsf {X}}}, \sigma )\) as a Poisson process of finite unrooted loops of a random walk with Gaussian increments that we call Gaussian loop soup, analogous to the Brownian loop soup of Lawler and Werner (Probab Theory Related Fields 128(4):565–588, 2004). We also construct Gaussian random interlacements, a Poisson process of doubly infinite trajectories of random walks with Gaussian increments analogous to the Brownian random interlacements of Sznitman (Ann Math 2 171(3):2039–2087, 2010). For \(d\ge 3\) and \(\rho >\rho _c\) we define \(({{\textsf {X}}},\sigma )\) as the superposition of independent realizations of the Gaussian loop soup at density \(\rho _c\) and the Gaussian random interlacements at density \(\rho -\rho _c\) . In either case we call \(({{\textsf {X}}}, \sigma )\) a Gaussian random permutation at density \(\rho \) and temperature \(\alpha \) . The resulting measure satisfies a Markov property and it is Gibbs for the Hamiltonian H. Its point marginal \({{\textsf {X}}}\) has the same distribution as the boson point process introduced by Shirai-Takahashi (J Funct Anal 205(2):414–463, 2003) in the subcritical case, and by Tamura-Ito (J Funct Anal 243(1): 207–231, 2007) in the supercritical case.
      PubDate: 2021-10-04
       
 
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