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  Subjects -> MATHEMATICS (Total: 1040 journals)
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    - MATHEMATICS (770 journals)
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MATHEMATICS (770 journals)                  1 2 3 4 | 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: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 38)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 12)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 9)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 21)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 17)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 10)
Advances in Materials Science     Open Access   (Followers: 17)
Advances in Mathematical Physics     Open Access   (Followers: 7)
Advances in Mathematics     Full-text available via subscription   (Followers: 15)
Advances in Nonlinear Analysis     Open Access  
Advances in Numerical Analysis     Open Access   (Followers: 7)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 8)
Advances in Pure Mathematics     Open Access   (Followers: 9)
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: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 2)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 3)
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: 4)
Annals of Data Science     Hybrid Journal   (Followers: 13)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 7)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
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  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics     Open Access   (Followers: 8)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
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: 3)
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: 25)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 3)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
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: 1)
Basin Research     Hybrid Journal   (Followers: 5)
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: 2)
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: 13)
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: 2)
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  
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: 20)
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: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access  
ChemSusChem     Hybrid Journal   (Followers: 8)
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: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 15)
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: 4)
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: 9)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus Mathematique     Full-text available via subscription  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
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: 10)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
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)
Demographic Research     Open Access   (Followers: 15)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
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)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 2)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  

        1 2 3 4 | 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  [2574 journals]
  • Black Holes and Higher Depth Mock Modular Forms
    • Abstract: By enforcing invariance under S-duality in type IIB string theory compactified on a Calabi–Yau threefold, we derive modular properties of the generating function of BPS degeneracies of D4–D2–D0 black holes in type IIA string theory compactified on the same space. Mathematically, these BPS degeneracies are the generalized Donaldson-Thomas invariants counting coherent sheaves with support on a divisor \({\mathcal {D}}\), at the large volume attractor point. For \({\mathcal {D}}\) irreducible, this function is closely related to the elliptic genus of the superconformal field theory obtained by wrapping M5-brane on \({\mathcal {D}}\) and is therefore known to be modular. Instead, when \({\mathcal {D}}\) is the sum of n irreducible divisors \({\mathcal {D}}_i\), we show that the generating function acquires a modular anomaly. We characterize this anomaly for arbitrary n by providing an explicit expression for a non-holomorphic modular completion in terms of generalized error functions. As a result, the generating function turns out to be a (mixed) mock modular form of depth \(n-1\).
      PubDate: 2019-11-16
       
  • Classification of Quantum Groups via Galois Cohomology
    • Abstract: The first example of a quantum group was introduced by P. Kulish and N. Reshetikhin. In the paper Kulish et al. (J Soviet Math 23:2435–2441, 1983), they found a new algebra which was later called \(U_q (\mathfrak {sl}(2))\). Their example was developed independently by V. Drinfeld and M. Jimbo, which resulted in the general notion of quantum group. Later, a complimentary approach to quantum groups was developed by L. Faddeev, N. Reshetikhin, and L. Takhtajan in Faddeev et al. (Leningr Math J 1:193–225, 1990). Recently, the so-called Belavin–Drinfeld cohomology (twisted and non-twisted) have been introduced in the literature to study and classify certain families of quantum groups and Lie bialgebras. Later, the last two authors interpreted non-twisted Belavin–Drinfeld cohomology in terms of non-abelian Galois cohomology \(H^1({\mathbb {F}}, {\mathbf {H}})\) for a suitable algebraic \({\mathbb {F}}\)-group \({\mathbf {H}}\). Here \({\mathbb {F}}\) is an arbitrary field of zero characteristic. The non-twisted case is thus fully understood in terms of Galois cohomology. The twisted case has only been studied using Galois cohomology for the so-called (“standard”) Drinfeld–Jimbo structure. The aim of the present paper is to extend these results to all twisted Belavin–Drinfeld cohomology and thus, to present classification of quantum groups in terms of Galois cohomology and the so-called orders. Low dimensional cases \(\mathfrak {sl}(2)\) and \(\mathfrak {sl}(3)\) are considered in more details using a theory of cubic rings developed by B. N. Delone and D. K. Faddeev in Delone and Faddeev (The theory of irrationalities of the third degree. Translations of mathematical monographs, vol 10. AMS, Providence, 1964). Our results show that there exist yet unknown quantum groups for Lie algebras of the types \(A_n, D_{2n+1}, E_6\), not mentioned in Etingof et al. (J Am Math Soc 13:595–609, 2000).
      PubDate: 2019-11-14
       
  • Nonlinear Dirac Equations, Monotonicity Formulas and Liouville Theorems
    • Abstract: We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations. Finally, we extend our analysis to Dirac-harmonic maps with curvature term.
      PubDate: 2019-11-13
       
  • Isospectral Flows Related to Frobenius–Stickelberger–Thiele
           Polynomials
    • Abstract: The isospectral deformations of the Frobenius–Stickelberger–Thiele (FST) polynomials introduced in Spiridonov et al. (Commun Math Phys 272:139–165, 2007) are studied. For a specific choice of the deformation of the spectral measure, one is led to an integrable lattice (FST lattice), which is indeed an isospectral flow connected with a generalized eigenvalue problem. In the second part of the paper the spectral problem used previously in the study of the modified Camassa–Holm (mCH) peakon lattice is interpreted in terms of the FST polynomials together with the associated FST polynomials, resulting in a map from the mCH peakon lattice to a negative flow of the finite FST lattice. Furthermore, it is pointed out that the degenerate case of the finite FST lattice unexpectedly maps to the interlacing peakon ODE system associated with the two-component mCH equation studied in Chang et al. (Adv Math 299:1–35, 2016).
      PubDate: 2019-11-13
       
  • Pairings in Mirror Symmetry Between a Symplectic Manifold and a
           Landau–Ginzburg B -Model
    • Abstract: We find a relation between Lagrangian Floer pairing of a symplectic manifold and Kapustin–Li pairing of the mirror Landau–Ginzburg model under localized mirror functor. They are conformally equivalent with an interesting conformal factor\((vol^{Floer}/vol)^2\), which can be described as a ratio of Lagrangian Floer volume class and classical volume class. For this purpose, we introduce B-invariant of Lagrangian Floer cohomology with values in Jacobian ring of the mirror potential function. And we prove what we call a multi-crescent Cardy identity under certain conditions, which is a generalized form of Cardy identity. As an application, we discuss the case of general toric manifold, and the relation to the work of Fukaya–Oh–Ohta–Ono and their Z-invariant. Also, we compute the conformal factor \((vol^{Floer}/vol)^2\) for the elliptic curve quotient \(\mathbb {P}^1_{3,3,3}\), which gives a modular form.
      PubDate: 2019-11-12
       
  • Equidistribution of Random Waves on Small Balls
    • Abstract: In this paper, we investigate the small scale equidistribution properties of randomised sums of Laplacian eigenfunctions (i.e. random waves) on a compact manifold. We prove small scale expectation and variance results for random waves on all compact manifolds. Here, “small scale” refers to balls of radius \(r(\lambda )\rightarrow 0\) such that \(r/r_{\text {Planck}}\rightarrow \infty \), where \(r_{\text {Planck}}\) is the Planck scale. For balls at a larger scale (although still \(r(\lambda )\rightarrow 0\)) we also obtain estimates showing that the probability that a random wave fails to equidistribute decays exponentially with the eigenvalue.
      PubDate: 2019-11-11
       
  • Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma
           Models on Manifolds with Boundary
    • Abstract: We describe a covariant framework to construct a globalized version for the perturbative quantization of nonlinear split AKSZ Sigma Models on manifolds with and without boundary, and show that it captures the change of the quantum state as one changes the constant map around which one perturbs. This is done by using concepts of formal geometry. Moreover, we show that the globalized quantum state can be interpreted as a closed section with respect to an operator that squares to zero. This condition is a generalization of the modified Quantum Master Equation as in the BV-BFV formalism, which we call the modified “differential” Quantum Master Equation.
      PubDate: 2019-11-08
       
  • Toda Conformal Blocks, Quantum Groups, and Flat Connections
    • Abstract: This paper investigates the relations between the Toda conformal field theories, quantum group theory and the quantisation of moduli spaces of flat connections. We use the free field representation of the \({{\mathcal {W}}}\)-algebras to define natural bases for spaces of conformal blocks of the Toda conformal field theory associated to the Lie algebra \({\mathfrak {s}}{\mathfrak {l}}_3\) on the three-punctured sphere with representations of generic type associated to the three punctures. The operator-valued monodromies of degenerate fields can be used to describe the quantisation of the moduli spaces of flat \(\mathrm {SL}(3)\)-connections. It is shown that the matrix elements of the monodromies can be expressed as Laurent polynomials of more elementary operators which have a simple definition in the free field representation. These operators are identified as quantised counterparts of natural higher rank analogs of the Fenchel–Nielsen coordinates from Teichmüller theory. Possible applications to the study of the non-Lagrangian SUSY field theories are briefly outlined.
      PubDate: 2019-11-07
       
  • Maximal Fluctuations on Periodic Lattices: An Approach via Quantitative
           Wulff Inequalities
    • Abstract: We consider the Wulff problem arising from the study of the Heitmann–Radin energy of N atoms sitting on a periodic lattice. Combining the sharp quantitative Wulff inequality in the continuum setting with a notion of quantitative closeness between discrete and continuum energies, we provide very short proofs of fluctuation estimates of Voronoi-type sets associated with almost minimizers of the discrete problem about the continuum limit Wulff shape. In the particular case of exact energy minimizers, we recover the well-known, sharp \(N^{3/4}\) scaling law for all considered planar lattices, as well as a sub-optimal scaling law for the cubic lattice in dimension \(d\ge 3\).
      PubDate: 2019-11-06
       
  • Operator-Algebraic Construction of Gauge Theories and Jones’ Actions of
           Thompson’s Groups
    • Abstract: Using ideas from Jones, lattice gauge theory and loop quantum gravity, we construct \(1+1\) -dimensional gauge theories on a spacetime cylinder. Given a separable compact group G, we construct localized time-zero fields on the spatial torus as a net of C*-algebras together with an action of the gauge group that is an infinite product of G over the dyadic rationals and, using a recent machinery of Jones, an action of Thompson’s group T as a replacement of the spatial diffeomorphism group. Adding a family of probability measures on the unitary dual of G we construct a state and obtain a net of von Neumann algebras carrying a state-preserving gauge group action. For abelian G, we provide a very explicit description of our algebras. For a single measure on the dual of G, we have a state-preserving action of Thompson’s group and semi-finite von Neumann algebras. For \(G={\mathbf {S}}\) the circle group together with a certain family of heat-kernel states providing the measures, we obtain hyperfinite type III factors with a normal faithful state providing a nontrivial time evolution via Tomita–Takesaki theory (KMS condition). In the latter case, we additionally have a non-singular action of the group of rotations with dyadic angles, as a subgroup of Thompson’s group T, for geometrically motivated choices of families of heat-kernel states.
      PubDate: 2019-11-04
       
  • The Tutte Embedding of the Poisson–Voronoi Tessellation of the Brownian
           Disk Converges to $$\sqrt{8/3}$$ 8 / 3 -Liouville Quantum Gravity
    • Abstract: Recent works have shown that an instance of a Brownian surface (such as the Brownian map or Brownian disk) a.s. has a canonical conformal structure under which it is equivalent to a \(\sqrt{8/3}\) -Liouville quantum gravity (LQG) surface. In particular, Brownian motion on a Brownian surface is well-defined. The construction in these works is indirect, however, and leaves open a basic question: is Brownian motion on a Brownian surface the limit of simple random walk on increasingly fine discretizations of that surface, the way Brownian motion on \(\mathbb {R}^2\) is the \(\epsilon \rightarrow 0\) limit of simple random walk on \(\epsilon \mathbb {Z}^2\) ' We answer this question affirmatively by showing that Brownian motion on a Brownian surface is (up to time change) the \(\lambda \rightarrow \infty \) limit of simple random walk on the Voronoi tessellation induced by a Poisson point process whose intensity is \(\lambda \) times the associated area measure. Among other things, this implies that as \(\lambda \rightarrow \infty \) the Tutte embedding (a.k.a. harmonic embedding) of the discretized Brownian disk converges to the canonical conformal embedding of the continuum Brownian disk, which in turn corresponds to \(\sqrt{8/3}\) -LQG. Along the way, we obtain other independently interesting facts about conformal embeddings of Brownian surfaces, including information about the Euclidean shapes of embedded metric balls and Voronoi cells. For example, we derive moment estimates that imply, in a certain precise sense, that these shapes are unlikely to be very long and thin.
      PubDate: 2019-11-04
       
  • Asymptotic Properties of Linear Field Equations in Anti-de Sitter Space
    • Abstract: We study the global dynamics of the wave equation, Maxwell’s equation and the linearized Bianchi equations on a fixed anti-de Sitter (AdS) background. Provided dissipative boundary conditions are imposed on the dynamical fields we prove uniform boundedness of the natural energy as well as both degenerate (near the AdS boundary) and non-degenerate integrated decay estimates. Remarkably, the non-degenerate estimates “lose a derivative”. We relate this loss to a trapping phenomenon near the AdS boundary, which itself originates from the properties of (approximately) gliding rays near the boundary. Using the Gaussian beam approximation we prove that non-degenerate energy decay without loss of derivatives does not hold. As a consequence of the non-degenerate integrated decay estimates, we also obtain pointwise-in-time decay estimates for the energy. Our paper provides the key estimates for a proof of the non-linear stability of the anti-de Sitter spacetime under dissipative boundary conditions. Finally, we contrast our results with the case of reflecting boundary conditions.
      PubDate: 2019-11-04
       
  • A Topological Approach to Indices of Geometric Operators on Manifolds with
           Fibered Boundaries
    • Abstract: In this paper, we investigate topological aspects of indices of twisted geometric operators on manifolds equipped with fibered boundaries. We define K-groups relative to the pushforward for boundary fibration, and show that indices of twisted geometric operators, defined by complete \(\Phi \) or edge metrics, can be regarded as the index pairing over these K-groups. We also prove various properties of these indices using groupoid deformation techniques. Using these properties, we give an application to the localization problem of signature operators for singular fiber bundles.
      PubDate: 2019-11-03
       
  • 5 / 6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators
           in a Magnetic Field
    • Abstract: We consider a one-dimensional infinite chain of coupled charged harmonic oscillators in a magnetic field with a small stochastic perturbation of order \(\epsilon \). We prove that for a space–time scale of order \(\epsilon ^{-1}\) the density of energy distribution (Wigner distribution) evolves according to a linear phonon Boltzmann equation. We also prove that an appropriately scaled limit of solutions of the linear phonon Boltzmann equation is a solution of the fractional diffusion equation with exponent 5 / 6.
      PubDate: 2019-11-01
       
  • Anomalies in Time-Ordered Products and Applications to the BV–BRST
           Formulation of Quantum Gauge Theories
    • Abstract: We show that every (graded) derivation on the algebra of free quantum fields and their Wick powers in curved spacetimes gives rise to a set of anomalous Ward identities for time-ordered products, with an explicit formula for their classical limit. We study these identities for the Koszul–Tate and the full BRST differential in the BV–BRST formulation of perturbatively interacting quantum gauge theories, and clarify the relation to previous results. In particular, we show that the quantum BRST differential, the quantum antibracket and the higher-order anomalies form an \(L_\infty \) algebra. The defining relations of this algebra ensure that the gauge structure is well-defined on cohomology classes of the quantum BRST operator, i.e., observables. Furthermore, we show that one can determine contact terms such that also the interacting time-ordered products of multiple interacting fields are well defined on cohomology classes. An important technical improvement over previous treatments is the fact that all our relations hold off-shell and are independent of the concrete form of the Lagrangian, including the case of open gauge algebras.
      PubDate: 2019-11-01
       
  • A Unique Connection for Born Geometry
    • Abstract: It has been known for a while that the effective geometrical description of compactified strings on d-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an O(d,d) pairing \({\eta}\) and an O(2d) generalized metric \({\mathcal{H}}\). More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing \({\omega}\). The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure \({(\eta,\omega,\mathcal{H})}\) and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics.
      PubDate: 2019-11-01
       
  • Freezing of the Optical-Branch Energy in a Diatomic FPU Chain
    • Abstract: We study the exchange of energy between the modes of the optical branch and those of the acoustic one in a diatomic chain of particles, with masses m1 and m2. We prove that, at small temperature and provided \({m_1\gg m_2}\), for the majority of the initial data the energy of each branch is approximately constant for times of order \({\beta^{S/2}}\), where \({S=\lfloor \sqrt{m_1/m_2}/2\rfloor}\) and \({\beta}\) is the inverse temperature. The result is uniform in the thermodynamic limit.
      PubDate: 2019-11-01
       
  • Bethe Subalgebras in Yangians and the Wonderful Compactification
    • Abstract: Let \({\mathfrak {g}}\) be a complex simple Lie algebra. We study the family of Bethe subalgebras in the Yangian \(Y({\mathfrak {g}})\) parameterized by the corresponding adjoint Lie group G. We describe their classical limits as subalgebras in the algebra of polynomial functions on the formal Lie group \(G_1[[t^{-1}]]\). In particular we show that, for regular values of the parameter, these subalgebras are free polynomial algebras with the same Poincaré series as the Cartan subalgebra of the Yangian. Next, we extend the family of Bethe subalgebras to the De Concini–Procesi wonderful compactification \(\overline{G}\supset G\) and describe the subalgebras corresponding to generic points of any stratum in \(\overline{G}\) as Bethe subalgebras in the Yangian of the corresponding Levi subalgebra in \({\mathfrak {g}}\). In particular, we describe explicitly all Bethe subalgebras corresponding to the closure of the maximal torus in the wonderful compactification.
      PubDate: 2019-11-01
       
  • Boundary Harmonic Coordinates on Manifolds with Boundary in Low Regularity
    • Abstract: In this paper, we prove the existence of \(H^2\)-regular coordinates on Riemannian 3-manifolds with boundary, assuming only \(L^2\)-bounds on the Ricci curvature, \(L^4\)-bounds on the second fundamental form of the boundary, and a positive lower bound on the volume radius. The proof follows by extending the theory of Cheeger–Gromov convergence to include manifolds with boundary in the above low regularity setting. The main tools are boundary harmonic coordinates together with elliptic estimates and a geometric trace estimate, and a rigidity argument using manifold doubling. Assuming higher regularity of the Ricci curvature, we also prove corresponding higher regularity estimates for the coordinates.
      PubDate: 2019-11-01
       
  • Quantum Differentiability on Quantum Tori
    • Abstract: We provide a full characterisation of quantum differentiability (in the sense of Connes) on quantum tori. We also prove a quantum integration formula which differs substantially from the commutative case.
      PubDate: 2019-11-01
       
 
 
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