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  • A surface in odd characteristic with discrete and non-finitely generated automorphism group
    Adv. Math. (IF 1.494) Pub Date : 2020-09-16
    Keiji Oguiso

    It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose automorphism group is discrete and not finitely generated. In this paper, after observing finite generation of the automorphism group of any smooth projective surface birational to any K3 surface over any algebraic closure of the prime field of odd characteristic, we will show that there is a smooth projective

    更新日期:2020-09-16
  • Asymptotic behavior and stability of mean curvature flow with a conical end
    Adv. Math. (IF 1.494) Pub Date : 2020-09-14
    Siao-Hao Guo

    If the initial hypersurface of an immortal mean curvature flow is asymptotic to a regular cone whose entropy is small, the flow will become asymptotically self-expanding. Moreover, the expander that gives rise to the limiting flow is asymptotically stable as an equilibrium solution of the normalized mean curvature flow.

    更新日期:2020-09-14
  • 3D quadratic NLS equation with electromagnetic perturbations
    Adv. Math. (IF 1.494) Pub Date : 2020-09-11
    Tristan Léger

    In this paper we study the asymptotic behavior of a quadratic Schrödinger equation with electromagnetic potentials. We prove that small solutions scatter. The proof builds on earlier work of the author for quadratic NLS with a non magnetic potential. The main novelty is the use of various smoothing estimates for the linear Schrödinger flow in place of boundedness of wave operators to deal with the

    更新日期:2020-09-11
  • Analytic torsion for surfaces with cusps II. Regularity, asymptotics and curvature theorem
    Adv. Math. (IF 1.494) Pub Date : 2020-09-11
    Siarhei Finski

    We study the Quillen metric on the determinant line bundle associated with a family of complex singular curves with hyperbolic cusp singularities. More precisely, we fix a family of complex curves, which admit at most double-point singularities. We endow the fibers of this family with Kähler metrics, which are defined away from a finite set of points, a divisor on the total space of the family, in

    更新日期:2020-09-11
  • On a uniqueness property of supercuspidal unipotent representations
    Adv. Math. (IF 1.494) Pub Date : 2020-09-10
    Yongqi Feng; Eric Opdam

    The formal degree of a unipotent discrete series character of a simple linear algebraic group over a non-archimedean local field (in the sense of Lusztig [17]), is a rational function of q evaluated at q=q, the cardinality of the residue field. The irreducible factors of this rational function are q and cyclotomic polynomials. We prove that the formal degree of a supercuspidal unipotent representation

    更新日期:2020-09-11
  • Constructing colimits by gluing vector bundles
    Adv. Math. (IF 1.494) Pub Date : 2020-09-10
    Daniel Schäppi

    As already observed by Gabriel, coherent sheaves on schemes obtained by gluing affine open subsets can be described by a simple gluing construction. An example due to Ferrand shows that this fails in general for pushouts along closed immersions, though the gluing construction still works for flat coherent sheaves. We show that by further restricting this gluing construction to vector bundles, we can

    更新日期:2020-09-10
  • Everything is possible for the domain intersection dom T ∩ dom T⁎
    Adv. Math. (IF 1.494) Pub Date : 2020-09-09
    Yury Arlinskiĭ; Christiane Tretter

    In this paper we show that for the domain intersection domT∩domT⁎ of a closed linear operator and its Hilbert space adjoint everything is possible for very common classes of operators with non-empty resolvent set. Apart from the most striking case of a maximal sectorial operator with domT∩domT⁎={0}, we construct classes of operators for which dim(domT∩domT⁎)=n∈N0; dim(domT∩domT⁎)=∞ and at the same

    更新日期:2020-09-10
  • Harmonic mean curvature flow and geometric inequalities
    Adv. Math. (IF 1.494) Pub Date : 2020-09-09
    Ben Andrews; Yingxiang Hu; Haizhong Li

    We employ the harmonic mean curvature flow of strictly convex closed hypersurfaces in hyperbolic space to prove Alexandrov-Fenchel type inequalities relating quermassintegrals to the total curvature, which is the integral of Gaussian curvature on the hypersurface. The resulting inequality allows us to use the inverse mean curvature flow to prove Alexandrov-Fenchel inequalities between the total curvature

    更新日期:2020-09-10
  • Rearrangement and polarization
    Adv. Math. (IF 1.494) Pub Date : 2020-09-04
    Gabriele Bianchi; Richard J. Gardner; Paolo Gronchi; Markus Kiderlen

    The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on Rn. Rearrangements are maps that are monotonic (up to sets of measure zero) and equimeasurable, i.e., they preserve the measure of super-level sets of functions. All the principal known symmetrization processes for functions, such as Steiner and Schwarz symmetrization

    更新日期:2020-09-05
  • The Dirichlet problem for orthodiagonal maps
    Adv. Math. (IF 1.494) Pub Date : 2020-09-04
    Ori Gurel-Gurevich; Daniel C. Jerison; Asaf Nachmias

    We prove that the discrete harmonic function corresponding to smooth Dirichlet boundary conditions on orthodiagonal maps, that is, plane graphs having quadrilateral faces with orthogonal diagonals, converges to its continuous counterpart as the mesh size goes to 0. This provides a convergence statement for discrete holomorphic functions, similar to the one obtained by Chelkak and Smirnov [4] for isoradial

    更新日期:2020-09-05
  • Pure pairs. I. Trees and linear anticomplete pairs
    Adv. Math. (IF 1.494) Pub Date : 2020-09-03
    Maria Chudnovsky; Alex Scott; Paul Seymour; Sophie Spirkl

    The Erdős-Hajnal conjecture asserts that for every graph H there is a constant c>0 such that every graph G that does not contain H as an induced subgraph has a clique or stable set of cardinality at least |G|c. In this paper, we prove a conjecture of Liebenau and Pilipczuk [10], that for every forest H there exists c>0, such that every graph G with |G|>1 contains either an induced copy of H, or a vertex

    更新日期:2020-09-03
  • Classification of solutions of an equation related to a conformal log Sobolev inequality
    Adv. Math. (IF 1.494) Pub Date : 2020-09-03
    Rupert L. Frank; Tobias König; Hanli Tang

    We classify all finite energy solutions of an equation which arises as the Euler–Lagrange equation of a conformally invariant logarithmic Sobolev inequality on the sphere due to Beckner. Our proof uses an extension of the method of moving spheres from Rn to Sn and a classification result of Li and Zhu. Along the way we prove a small volume maximum principle and a strong maximum principle for the underlying

    更新日期:2020-09-03
  • Separable elements and splittings of Weyl groups
    Adv. Math. (IF 1.494) Pub Date : 2020-08-31
    Christian Gaetz; Yibo Gao

    We continue the study of separable elements in finite Weyl groups, introduced in [11]. These elements generalize the well-studied class of separable permutations. We show that the multiplication map W/U×U→W is a length-additive bijection or splitting of the Weyl group W when U is an order ideal in right weak order generated by a separable element, where W/U denotes the generalized quotient. This generalizes

    更新日期:2020-08-31
  • Categorical mirror symmetry on cohomology for a complex genus 2 curve
    Adv. Math. (IF 1.494) Pub Date : 2020-08-31
    Catherine Cannizzo

    Motivated by observations in physics, mirror symmetry is the concept that certain manifolds come in pairs X and Y such that the complex geometry on X mirrors the symplectic geometry on Y. It allows one to deduce symplectic information about Y from known complex properties of X. Strominger-Yau-Zaslow [61] described how such pairs arise geometrically as torus fibrations with the same base and related

    更新日期:2020-08-31
  • Mapping ideals of quantum group multipliers
    Adv. Math. (IF 1.494) Pub Date : 2020-08-31
    Mahmood Alaghmandan; Jason Crann; Matthias Neufang

    We study the dual relationship between quantum group convolution maps L1(G)→L∞(G) and completely bounded multipliers of Gˆ. For a large class of locally compact quantum groups G, we completely isomorphically identify the mapping ideal of row Hilbert space factorizable convolution maps with Mcb(L1(Gˆ)), yielding a quantum Gilbert representation for completely bounded multipliers. We also identify the

    更新日期:2020-08-31
  • Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications
    Adv. Math. (IF 1.494) Pub Date : 2020-08-31
    Dmitri I. Panyushev

    Let g be a simple Lie algebra, h a Levi subalgebra, and Ch∈U(h) the Casimir element defined via the restriction of the Killing form on g to h. We study Ch-eigenvalues in g/h and related h-modules. Without loss of generality, one may assume that h is a maximal Levi. Then g is equipped with the natural Z-grading g=⨁i∈Zg(i) such that g(0)=h and g(i) is a simple h-module for i≠0. We give explicit formulae

    更新日期:2020-08-31
  • Measurable versions of Vizing's theorem
    Adv. Math. (IF 1.494) Pub Date : 2020-08-31
    Jan Grebík; Oleg Pikhurko

    We establish two versions of Vizing's theorem for Borel multi-graphs whose vertex degrees and edge multiplicities are uniformly bounded by respectively Δ and π. The “approximate” version states that, for any Borel probability measure on the edge set and any ϵ>0, we can properly colour all but ϵ-fraction of edges with Δ+π colours in a Borel way. The “measurable” version, which is our main result, states

    更新日期:2020-08-31
  • Locally connected Smale spaces, pinched spectrum, and infra-nilmanifolds
    Adv. Math. (IF 1.494) Pub Date : 2020-08-27
    Volodymyr Nekrashevych

    We show that if (X,f) is a locally connected Smale space (e.g., a basic set of an Axiom-A diffeomorphism) such that the local product structure on X can be lifted by a covering with virtually nilpotent group of deck transformations to a global direct product, then (X,f) is topologically conjugate to a hyperbolic infra-nilmanifold automorphism. We use this result to give a generalization to Smale spaces

    更新日期:2020-08-28
  • C2(R2) nonnegative extension by bounded-depth operators
    Adv. Math. (IF 1.494) Pub Date : 2020-08-27
    Fushuai Jiang; Garving K. Luli

    In this paper, we prove the existence of a nonnegative parameter-dependent (nonlinear) C2(R2) extension operator with bounded depth.

    更新日期:2020-08-27
  • The tilting theory of contraction algebras
    Adv. Math. (IF 1.494) Pub Date : 2020-08-27
    Jenny August

    To every minimal model of a complete local isolated cDV singularity Donovan–Wemyss associate a finite dimensional symmetric algebra known as the contraction algebra. We construct the first known standard derived equivalences between these algebras and then use the structure of an associated hyperplane arrangement to control the compositions, obtaining a faithful group action on the bounded derived

    更新日期:2020-08-27
  • Lucas atoms
    Adv. Math. (IF 1.494) Pub Date : 2020-08-27
    Bruce E. Sagan; Jordan Tirrell

    Given two variables s and t, the associated sequence of Lucas polynomials is defined inductively by {0}=0, {1}=1, and {n}=s{n−1}+t{n−2} for n≥2. An integer (e.g., a Catalan number) defined by an expression of the form ∏ini/∏jkj has a Lucas analogue obtained by replacing each factor with the corresponding Lucas polynomial. There has been interest in deciding when such expressions, which are a priori

    更新日期:2020-08-27
  • Boundary characterization of holomorphic isometric embeddings between indefinite hyperbolic spaces
    Adv. Math. (IF 1.494) Pub Date : 2020-08-27
    Xiaojun Huang; Jin Lu; Xiaomin Tang; Ming Xiao

    We provide in this paper a boundary characterization in terms of the boundary CR invariants (or pseudo-Hermitian invariants) for holomorphic isometric embeddings between indefinite hyperbolic spaces of general codimensions.

    更新日期:2020-08-27
  • Inward/outward energy theory of non-radial solutions to 3D semi-linear wave equation
    Adv. Math. (IF 1.494) Pub Date : 2020-08-26
    Ruipeng Shen

    The topic of this paper is a semi-linear, energy sub-critical, defocusing wave equation ∂t2u−Δu=−|u|p−1u in the 3-dimensional space with 3≤p<5. We generalize inward/outward energy theory and weighted Morawetz estimates for radial solutions to the non-radial case. As an application we show that if 35−p2, then the solution scatters as long as the initial data (u0,u1) satisfy∫R3(|x|κ+1)(12|∇u0|2+12|u

    更新日期:2020-08-27
  • Character ratios, representation varieties and random generation of finite groups of Lie type
    Adv. Math. (IF 1.494) Pub Date : 2020-08-26
    Martin W. Liebeck; Aner Shalev; Pham Huu Tiep

    We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.

    更新日期:2020-08-27
  • When are multidegrees positive?
    Adv. Math. (IF 1.494) Pub Date : 2020-08-26
    Federico Castillo; Yairon Cid-Ruiz; Binglin Li; Jonathan Montaño; Naizhen Zhang

    Let k be an arbitrary field, P=Pkm1×k⋯×kPkmp be a multiprojective space over k, and X⊆P be a closed subscheme of P. We provide necessary and sufficient conditions for the positivity of the multidegrees of X. As a consequence of our methods, we show that when X is irreducible, the support of multidegrees forms a discrete algebraic polymatroid. In algebraic terms, we characterize the positivity of the

    更新日期:2020-08-27
  • Continuity of capacity of a holomorphic motion
    Adv. Math. (IF 1.494) Pub Date : 2020-08-24
    Thomas Ransford; Malik Younsi; Wen-hui Ai

    We study the behavior of various set-functions under holomorphic motions. We show that, under such deformations, logarithmic capacity varies continuously, while analytic capacity may not.

    更新日期:2020-08-24
  • Integral transforms and quantum correspondences
    Adv. Math. (IF 1.494) Pub Date : 2020-08-21
    Mark Shoemaker

    We reframe a collection of well-known comparison results in genus zero Gromov–Witten theory in order to relate these to integral transforms between derived categories. This implies that various comparisons among Gromov–Witten theories and FJRW theory are compatible with the integral structure introduced by Iritani. We conclude with a proof that a version of the LG/CY correspondence relating quantum

    更新日期:2020-08-23
  • Prime geodesic theorem for the Picard manifold
    Adv. Math. (IF 1.494) Pub Date : 2020-08-21
    Olga Balkanova; Dmitry Frolenkov

    Let Γ=PSL(2,Z[i]) be the Picard group and H3 be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient Γ∖H3, called the Picard manifold, obtaining an error term of size O(X3/2+θ/2+ϵ), where θ denotes a subconvexity exponent for quadratic Dirichlet L-functions defined over Gaussian integers.

    更新日期:2020-08-21
  • Moduli of Weierstrass fibrations with marked section
    Adv. Math. (IF 1.494) Pub Date : 2020-08-19
    Giovanni Inchiostro

    We study the moduli space of stable pairs (X,sS+∑aiFi) consisting of a Weierstrass fibration X, its section S, and some fibers Fi. We find a compactification which is a DM stack, and we describe the objects on the boundary. We show that the fibration in the definition of Weierstrass fibration extends to the boundary, and it is equidimensional when s≪1. We prove that there are wall-crossing morphisms

    更新日期:2020-08-20
  • Mellin-Barnes presentations for Whittaker wave functions
    Adv. Math. (IF 1.494) Pub Date : 2020-08-19
    S. Kharchev; S. Khoroshkin

    We obtain certain Mellin-Barnes integrals which present Whittaker wave functions related to classical real split forms of simple complex Lie groups.

    更新日期:2020-08-20
  • Four deviations suffice for rank 1 matrices
    Adv. Math. (IF 1.494) Pub Date : 2020-08-19
    Rasmus Kyng; Kyle Luh; Zhao Song

    We prove a matrix discrepancy bound that strengthens the famous Kadison-Singer result of Marcus, Spielman, and Srivastava. Consider any independent scalar random variables ξ1,…,ξn with finite support, e.g. {±1} or {0,1}-valued random variables, or some combination thereof. Let u1,…,un∈m andσ2=‖∑i=1nVar[ξi](uiui⁎)2‖. Then there exists a choice of outcomes ε1,…,εn in the support of ξ1,…,ξn s.t.‖∑i=1

    更新日期:2020-08-20
  • Analogues of entropy in bi-free probability theory: Non-microstate
    Adv. Math. (IF 1.494) Pub Date : 2020-08-18
    Ian Charlesworth; Paul Skoufranis

    In this paper, we extend the notion of non-microstate free entropy to the bi-free setting. Using a diagrammatic approach involving bi-non-crossing diagrams, bi-free difference quotients are constructed as analogues of the free partial derivations. Adjoints of bi-free difference quotients are discussed and used to define bi-free conjugate variables. Notions of bi-free Fisher information, non-microstate

    更新日期:2020-08-19
  • C1 Hartman Theorem for random dynamical systems
    Adv. Math. (IF 1.494) Pub Date : 2020-08-18
    Kening Lu; Weinian Zhang; Wenmeng Zhang

    The C1 Hartman Theorem states that every C1,1 contraction in Rd admits C1 linearization. In this paper we prove C1,β linearizability for C1,α contractive (or expansive) random diffeomorphisms with appropriate constants 0<α<1 and 0<β<1, which implies a random version of the C1 Hartman Theorem. Moreover, the conjugacy is proved to be tempered. This result strengthens related results even in the deterministic

    更新日期:2020-08-19
  • Solutions to arithmetic differential equations in algebraically closed fields
    Adv. Math. (IF 1.494) Pub Date : 2020-08-18
    Alexandru Buium; Lance Edward Miller

    Arithmetic differential equations or δ-geometry exploits analogies between derivations and p-derivations δ arising from lifts of Frobenius to study problems in arithmetic geometry. Along the way, two main classes such functions, describable as series, arose prominently namely δ-characters of abelian schemes and (isogeny covariant) δ-modular forms. However, the theory of these δ-functions is not as

    更新日期:2020-08-19
  • Plethysm and cohomology representations of external and symmetric products
    Adv. Math. (IF 1.494) Pub Date : 2020-08-19
    Laurenţiu Maxim; Jörg Schürmann

    We prove refined generating series formulae for characters of (virtual) cohomology representations of external products of suitable coefficients, e.g., (complexes of) constructible or coherent sheaves, or (complexes of) mixed Hodge modules on spaces such as (possibly singular) complex quasi-projective varieties. These formulae generalize our previous results for symmetric and alternating powers of

    更新日期:2020-08-19
  • Bilinear forms in Weyl sums for modular square roots and applications
    Adv. Math. (IF 1.494) Pub Date : 2020-08-19
    Alexander Dunn; Bryce Kerr; Igor E. Shparlinski; Alexandru Zaharescu

    Let q be a prime, P⩾1 and let Nq(P) denote the number of rational primes p⩽P that split in the imaginary quadratic field Q(−q). The first part of this paper establishes various unconditional and conditional (under existence of a Siegel zero) lower bounds for Nq(P) in the range q1/4+ε⩽P⩽q, for any fixed ε>0. This improves upon what is implied by work of Pollack and Benli–Pollack. The second part of

    更新日期:2020-08-19
  • Plethystic formulas for permutation enumeration
    Adv. Math. (IF 1.494) Pub Date : 2020-08-18
    Ira M. Gessel; Yan Zhuang

    We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas involve certain kinds of plethystic substitutions on quasisymmetric generating functions, and the permutation statistics we consider include the descent number, peak number, left peak number, and the number

    更新日期:2020-08-19
  • Approximation by piecewise-regular maps
    Adv. Math. (IF 1.494) Pub Date : 2020-08-17
    Marcin Bilski; Wojciech Kucharz

    A real algebraic variety W of dimension m is said to be uniformly rational if each of its points has a Zariski open neighborhood which is biregularly isomorphic to a Zariski open subset of Rm. Let l be any nonnegative integer. We prove that every map of class Cl from a compact subset of a real algebraic variety into a uniformly rational real algebraic variety can be approximated in the Cl topology

    更新日期:2020-08-18
  • Invariant subspaces for Bishop operators and beyond
    Adv. Math. (IF 1.494) Pub Date : 2020-08-17
    Fernando Chamizo; Eva A. Gallardo-Gutiérrez; Miguel Monsalve-López; Adrián Ubis

    Bishop operators Tα acting on L2[0,1) were proposed by E. Bishop in the fifties as possible operators which might entail counterexamples for the Invariant Subspace Problem. We prove that all the Bishop operators are biquasitriangular and, derive as a consequence that they are norm limits of nilpotent operators. Moreover, by means of arithmetical techniques along with a theorem of Atzmon, the set of

    更新日期:2020-08-18
  • Nonnegative C2(R2) interpolation
    Adv. Math. (IF 1.494) Pub Date : 2020-08-17
    Fushuai Jiang; Garving K. Luli

    In this paper, we prove two improved versions of the Finiteness Principle for nonnegative C2(R2) interpolation, previously proven by Fefferman, Israel, and Luli. The first version sharpens the finiteness constant to 64, and the second version carries better computational practicality. Along the way, we also provide a detailed construction of nonnegative C2 interpolants in one-dimension, and prove the

    更新日期:2020-08-18
  • A generalization of Voiculescu's theorem for normal operators to semifinite von Neumann algebras
    Adv. Math. (IF 1.494) Pub Date : 2020-08-13
    Qihui Li; Junhao Shen; Rui Shi

    In this paper, we provide a generalized version of Voiculescu's theorem for normal operators by showing that, in a von Neumann algebra with separable pre-dual and a faithful, normal, semifinite, tracial weight τ, each normal operator is an arbitrarily small (max⁡{‖⋅‖,‖⋅‖2})-norm perturbation of a diagonal operator. Furthermore, in a countably decomposable, properly infinite von Neumann algebra with

    更新日期:2020-08-14
  • Adelic models of tensor-triangulated categories
    Adv. Math. (IF 1.494) Pub Date : 2020-08-14
    Scott Balchin; J.P.C. Greenlees

    We show that a well behaved Noetherian, finite dimensional, stable, monoidal model category has a model built from categories of modules over completed rings in an adelic fashion. Special cases include abelian groups (the Hasse square), chromatic homotopy theory (a module theoretic chromatic fracture square), and rational torus-equivariant homotopy theory (first step to the model of [30]).

    更新日期:2020-08-14
  • Semisimplification of the category of tilting modules for GLn
    Adv. Math. (IF 1.494) Pub Date : 2020-08-14
    Jonathan Brundan; Inna Entova-Aizenbud; Pavel Etingof; Victor Ostrik

    We describe the semisimplification of the monoidal category of tilting modules for the algebraic group GLn in characteristic p>0. In particular, we compute the dimensions of the indecomposable tilting modules modulo p.

    更新日期:2020-08-14
  • Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
    Adv. Math. (IF 1.494) Pub Date : 2020-08-14
    Yalong Cao; Martijn Kool

    Recently, Cao-Maulik-Toda defined stable pair invariants of a compact Calabi-Yau 4-fold X. Their invariants are conjecturally related to the Gopakumar-Vafa type invariants of X defined using Gromov-Witten theory by Klemm-Pandharipande. In this paper, we consider curve counting invariants of X using Hilbert schemes of curves and conjecture a DT/PT correspondence which relates these to stable pair invariants

    更新日期:2020-08-14
  • Late-time asymptotics for the wave equation on extremal Reissner–Nordström backgrounds
    Adv. Math. (IF 1.494) Pub Date : 2020-08-14
    Y. Angelopoulos; S. Aretakis; D. Gajic

    We derive the precise late-time asymptotics for solutions to the wave equation on extremal Reissner–Nordström black holes and explicitly express the leading-order coefficients in terms of the initial data. Our method is based on purely physical space techniques. We derive novel weighted energy hierarchies and develop a singular time inversion theory which allow us to uncover the subtle contribution

    更新日期:2020-08-14
  • Fourier transform of self-affine measures
    Adv. Math. (IF 1.494) Pub Date : 2020-08-10
    Jialun Li; Tuomas Sahlsten

    Suppose F is a self-affine set on Rd, d≥2, which is not a singleton, associated to affine contractions fj=Aj+bj, Aj∈GL(d,R), bj∈Rd, j∈A, for some finite A. We prove that if the group Γ generated by the matrices Aj, j∈A, forms a proximal and totally irreducible subgroup of GL(d,R), then any self-affine measure μ=∑pjfjμ, ∑pj=1, 0

    更新日期:2020-08-10
  • Cellular Legendrian contact homology for surfaces, part I
    Adv. Math. (IF 1.494) Pub Date : 2020-08-10
    Dan Rutherford; Michael Sullivan

    We give a computation of the Legendrian contact homology (LCH) DGA for an arbitrary generic Legendrian surface L in the 1-jet space of a surface. As input we require a suitable cellular decomposition of the base projection of L. A collection of generators is associated to each cell, and the differential is given by explicit matrix formulas. In the present article, we prove that the equivalence class

    更新日期:2020-08-10
  • Introducing totally nonparallel immersions
    Adv. Math. (IF 1.494) Pub Date : 2020-08-10
    Michael Harrison

    An immersion of a smooth n-dimensional manifold M→Rq is called totally nonparallel if, for every distinct x,y∈M, the tangent spaces at f(x) and f(y) contain no parallel lines; equivalently, they span a 2n-dimensional space. Given a manifold M, we seek the minimum dimension TN(M) such that there exists a totally nonparallel immersion M→RTN(M). In analogy with the totally skew embeddings studied by Ghomi

    更新日期:2020-08-10
  • Cyclic sieving phenomenon on dominant maximal weights over affine Kac-Moody algebras
    Adv. Math. (IF 1.494) Pub Date : 2020-08-10
    Young-Hun Kim; Se-jin Oh; Young-Tak Oh

    We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal weights for level ℓ highest weight modules over an affine Kac-Moody algebra with exactly one highest weight being taken for each equivalence class, in a way not depending on types, ranks and levels. In order to do that, we introduce S-evaluation on the set of dominant maximal weights for each highest modules, and generalize

    更新日期:2020-08-10
  • Cohen-Macaulay differential graded modules and negative Calabi-Yau configurations
    Adv. Math. (IF 1.494) Pub Date : 2020-08-10
    Haibo Jin

    In this paper, we introduce the class of Cohen-Macaulay (=CM) dg (=differential graded) modules over Gorenstein dg algebras and study their basic properties. We show that the category of CM dg modules forms a Frobenius extriangulated category, in the sense of Nakaoka and Palu, and it admits almost split extensions. We also study representation-finite d-self-injective dg algebras A in detail for some

    更新日期:2020-08-10
  • Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules
    Adv. Math. (IF 1.494) Pub Date : 2020-08-10
    Ivan Cherednik; Syu Kato

    We consider expansions of products of theta-functions associated with arbitrary root systems in terms of nonsymmetric Macdonald polynomials at t=∞ divided by their norms. The latter are identified with the graded characters of Demazure slices, some canonical quotients of thick (upper) level-one Demazure modules, directly related to recent theory of generalized (nonsymmetric) global Weyl modules. The

    更新日期:2020-08-10
  • Cocharacters for the weak polynomial identities of the Lie algebra of 3 × 3 skew-symmetric matrices
    Adv. Math. (IF 1.494) Pub Date : 2020-08-07
    Mátyás Domokos; Vesselin Drensky

    Let so3(K) be the Lie algebra of 3×3 skew-symmetric matrices over a field K of characteristic 0. The ideal I(M3(K),so3(K)) of the weak polynomial identities of the pair (M3(K),so3(K)) consists of the elements f(x1,…,xn) of the free associative algebra K〈X〉 with the property that f(a1,…,an)=0 in the algebra M3(K) of all 3×3 matrices for all a1,…,an∈so3(K). The generators of I(M3(K),so3(K)) were found

    更新日期:2020-08-08
  • Singular improper affine spheres from a given Lagrangian submanifold
    Adv. Math. (IF 1.494) Pub Date : 2020-08-07
    Marcos Craizer; Wojciech Domitrz; Pedro de M. Rios

    Given a Lagrangian submanifold L of the affine symplectic 2n-space, one can canonically and uniquely define a center-chord and a special improper affine sphere of dimension 2n, both of whose sets of singularities contain L. Although these improper affine spheres (IAS) always present other singularities away from L (the off-shell singularities studied in [8]), they may also present singularities other

    更新日期:2020-08-08
  • Commutators and images of noncommutative polynomials
    Adv. Math. (IF 1.494) Pub Date : 2020-08-06
    Matej Brešar

    Let A be an algebra and let f be a nonconstant noncommutative polynomial. In the first part of the paper, we consider the relationship between [A,A], the linear span of commutators in A, and spanf(A), the linear span of the image of f in A. In particular, we show that [A,A]=A implies spanf(A)=A. In the second part, we establish some Waring type results for images of polynomials. For example, we show

    更新日期:2020-08-06
  • Remarks on a nonlocal transport
    Adv. Math. (IF 1.494) Pub Date : 2020-08-05
    Dong Li; Jose Rodrigo

    We consider a one dimensional nonlocal transport equation and its natural multi-dimensional analogues. By using a new pointwise inequality for the Hilbert transform, we give a short proof of a nonlinear inequality first proved by Córdoba, Córdoba and Fontelos in 2005. We also prove several new weighted inequalities for the Hilbert transform and various nonlinear versions. Some of these results generalize

    更新日期:2020-08-06
  • Connecting the q-multiplicative convolution and the finite difference convolution
    Adv. Math. (IF 1.494) Pub Date : 2020-08-06
    Jonathan Leake; Nick Ryder

    In [1], Brändén, Krasikov, and Shapiro study root location preservation properties of finite difference operators. They then conjecture a characterization of linear finite difference operators on polynomials of fixed degree which preserve root mesh properties, via a natural polynomial convolution. We prove this conjecture using two methods. The first develops a novel connection between the additive

    更新日期:2020-08-06
  • Uniqueness and non–uniqueness of prescribed mass NLS ground states on metric graphs
    Adv. Math. (IF 1.494) Pub Date : 2020-08-06
    Simone Dovetta; Enrico Serra; Paolo Tilli

    We consider the problem of uniqueness of ground states of prescribed mass for the Nonlinear Schrödinger Energy with power nonlinearity on noncompact metric graphs. We first establish that the Lagrange multiplier appearing in the NLS equation is constant on the set of ground states of mass μ, up to an at most countable set of masses. Then we apply this result to obtain uniqueness of ground states on

    更新日期:2020-08-06
  • Beta polytopes and Poisson polyhedra: f-vectors and angles
    Adv. Math. (IF 1.494) Pub Date : 2020-08-05
    Zakhar Kabluchko; Christoph Thäle; Dmitry Zaporozhets

    We study random polytopes of the form [X1,…,Xn] defined as convex hulls of independent and identically distributed random points X1,…,Xn in Rd with one of the following densities:fd,β(x)=cd,β(1−‖x‖2)β,‖x‖<1,(beta distribution, β>−1) orf˜d,β(x)=c˜d,β(1+‖x‖2)−β,x∈Rd,(beta' distribution, β>d/2). Here, cd,β and c˜d,β are normalizing constants. This setting also includes the uniform distribution on the

    更新日期:2020-08-06
  • Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras
    Adv. Math. (IF 1.494) Pub Date : 2020-08-06
    Robert McRae

    We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra gˆ, from g-module homomorphisms. When g=sl2, these results extend previous joint work with J. Yang, but the method used here is different. Here, we construct intertwining operators by solving Knizhnik-Zamolodchikov equations for three-point correlation

    更新日期:2020-08-06
  • Anisotropic decay and global well-posedness of viscous surface waves without surface tension
    Adv. Math. (IF 1.494) Pub Date : 2020-08-05
    Yanjin Wang

    We consider a viscous incompressible fluid below the air and above a fixed bottom. The fluid dynamics is governed by the gravity-driven incompressible Navier-Stokes equations, and the effect of surface tension is neglected on the free surface. The global well-posedness and long-time behavior of solutions near equilibrium have been intriguing questions since Beale (1981) [2]. It was proved by Guo and

    更新日期:2020-08-06
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