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  • Complete Kähler–Einstein Metric on Stein Manifolds With Negative Curvature
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-30
    Man-Chun Lee

    We show the existence of complete negative Kähler–Einstein metric on Stein manifolds with holomorphic sectional curvature bounded from above by a negative constant. We prove that any Kähler metrics on such manifolds can be deformed to the complete negative Kähler–Einstein metric using the normalized Kähler–Ricci flow.

    更新日期:2020-06-30
  • Global Rigidity of 2D Linearly Constrained Frameworks
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-27
    Hakan Guler; Bill Jackson; Anthony Nixon

    A linearly constrained framework in |$\mathbb{R}^d$| is a point configuration together with a system of constraints that fixes the distances between some pairs of points and additionally restricts some of the points to lie in given affine subspaces. It is globally rigid if the configuration is uniquely defined by the constraint system. We show that a generic linearly constrained framework in |$\mathbb{R}^2$|

    更新日期:2020-06-30
  • Low Degree Points on Curves
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-27
    Geoffrey Smith; Isabel Vogt

    In this paper, we investigate an arithmetic analogue of the gonality of a smooth projective curve |$C$| over a number field |$k$|⁠: the minimal |$e$| such that there are infinitely many points |$P \in C(\bar{k})$| with |$[k(P):k] \leqslant e$|⁠. Developing techniques that make use of an auxiliary smooth surface containing the curve, we show that this invariant can take any value subject to constraints

    更新日期:2020-06-30
  • A Note on Real Operator Monotone Functions
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-27
    Marcell Gaál; Miklós Pálfia

    In this paper, we initiate the study of real operator monotonicity for functions of tuples of operators, which are multivariate structured maps with a functional calculus called free functions that preserve the order between real parts (or Hermitian parts) of bounded linear Hilbert space operators. We completely characterize such functions on open convex free domains in terms of ordinary operator monotone

    更新日期:2020-06-27
  • Complete Ricci Solitons via Estimates on the Soliton Potential
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-25
    Matthias Wink

    In this paper, a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady and expanding Ricci solitons in the setups of Lü–Page–Pope [ 24] and Dancer–Wang [ 17]. It also provides a different approach to the two summands system [ 30] that applies to all known geometric examples.

    更新日期:2020-06-27
  • Planarity in Higher-Dimensional Contact Manifolds
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-25
    Bahar Acu; Agustin Moreno

    We obtain several results for (iterated) planar contact manifolds in higher dimensions. (1) Iterated planar contact manifolds are not weakly symplectically co-fillable. This generalizes a 3D result of Etnyre [ 14] to a higher-dimensional setting, where the notion of weak fillability is that due to Massot-Niederkrüger-Wendl [ 38]. (2) They do not arise as nonseparating weak contact-type hypersurfaces

    更新日期:2020-06-25
  • Corrigendum to: A Characterization of Some Fano 4-folds Through Conic Fibrations
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-24
    Pedro Montero; Eleonora Anna Romano

    AbstractWe wish to point out errors in the paper “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”, International Mathematics Research Notices, Vol. 2017, No. 00, pp. 1–29. The main error concerns the symmetry of the “ramified case” of the height pairing, which relies on the vanishing of the Bockstein map in Proposition 3.5. The surjectivity claimed in the 1st line of the proof

    更新日期:2020-06-24
  • A Question of Norton–Sullivan in the Analytic Case
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-23
    Jian Wang; Hui Yang

    In 1996, A. Norton and D. Sullivan asked the following question: If |$f:\mathbb{T}^2\rightarrow \mathbb{T}^2$| is a diffeomorphism, |$h:\mathbb{T}^2\rightarrow \mathbb{T}^2$| is a continuous map homotopic to the identity, and |$h f=T_{\rho } h$|⁠, where |$\rho \in \mathbb{R}^2$| is a totally irrational vector and |$T_{\rho }:\mathbb{T}^2\rightarrow \mathbb{T}^2,\, z\mapsto z+\rho $| is a translation

    更新日期:2020-06-24
  • Deformation Cones of Nested Braid Fans
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-20
    Federico Castillo; Fu Liu

    Generalized permutohedra are deformations of regular permutohedra and arise in many different fields of mathematics. One important characterization of generalized permutohedra is the Submodularity Theorem, which is related to the deformation cone of the Braid fan. We lay out general techniques for determining deformation cones of a fixed polytope and apply it to the Braid fan to obtain a natural combinatorial

    更新日期:2020-06-23
  • On the Minkowski Formula for Hypersurfaces in Complex Space Forms
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-19
    Vittorio Martino; Giulio Tralli

    In this paper, we discuss various Minkowski-type formulas for real hypersurfaces in complex space forms. In particular, we investigate the formulas suggested by the natural splitting of the tangent space. In this direction, our main result concerns a new kind of 2nd Minkowski formula.

    更新日期:2020-06-19
  • Invariants of a General Branched Cover of P1
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-18
    Gabriel Bujokas; Anand Patel

    We investigate the resolution of a general branched cover |$\alpha \colon C \to \mathbf{P}^1$| in its relative canonical embedding |$C \subset \mathbf{P} E$|⁠. We conjecture that the syzygy bundles appearing in the resolution are balanced for a general cover, provided that the genus is sufficiently large compared to the degree. We prove this for the Casnati–Ekedahl bundle, or bundle of quadrics|$F$|—the

    更新日期:2020-06-19
  • Meromorphic Modular Forms with Rational Cycle Integrals
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-18
    Steffen Löbrich; Markus Schwagenscheidt

    We study rationality properties of geodesic cycle integrals of meromorphic modular forms associated to positive definite binary quadratic forms. In particular, we obtain finite rational formulas for the cycle integrals of suitable linear combinations of these meromorphic modular forms.

    更新日期:2020-06-19
  • Counting Bounded Elements of a Number Field
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-18
    Mikołaj Fraczyk; Gergely Harcos; Péter Maga

    We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers.

    更新日期:2020-06-18
  • Bykovskii-Type Theorem for the Picard Manifold
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-16
    Antal Balog; András Biró; Giacomo Cherubini; Niko Laaksonen

    We generalise a result of Bykovskii to the Gaussian integers and prove an asymptotic formula for the prime geodesic theorem in short intervals on the Picard manifold. Previous works show that individually the remainder is bounded by |$O(X^{13/8+\epsilon })$| and |$O(X^{3/2+\theta +\epsilon })$|⁠, where |$\theta$| is the subconvexity exponent for quadratic Dirichlet |$L$|-functions over |$\mathbb{Q}(i)$|⁠

    更新日期:2020-06-18
  • Axisymmetric Diffeomorphisms and Ideal Fluids on Riemannian 3-Manifolds
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-16
    Leandro Lichtenfelz; Gerard Misiołek; Stephen C Preston

    We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the |$L^2$| exponential map on the group of volume-preserving diffeomorphisms of a |$3$|-manifold is Fredholm along axisymmetric flows with sufficiently small swirl. Along the way, we define the notions of axisymmetric and swirl-free diffeomorphisms of any manifold with suitable symmetries and show that such diffeomorphisms

    更新日期:2020-06-16
  • Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-12
    Fabrizio Caselli; Michele D’Adderio; Mario Marietti

    We provide a weaker version of the generalized lifting property that holds in complete generality for all Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also describe some combinatorial properties of the associated polytopes.

    更新日期:2020-06-12
  • The GL4 Rapoport–Zink Space
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-11
    Maria Fox

    We give a description of the |$\textrm{GL}_4$| Rapoport–Zink space, including the connected components, irreducible components, intersection behavior of the irreducible components, and Ekedahl–Oort stratification. As an application of this, we also give a description of the supersingular locus of the Shimura variety for the group |$\textrm{GU}(2,2)$| over a prime split in the relevant imaginary quadratic

    更新日期:2020-06-11
  • On BMO and Carleson Measures on Riemannian Manifolds
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-11
    Denis Brazke; Armin Schikorra; Yannick Sire

    Let |$\mathcal{M}$| be a Riemannian |$n$|-manifold with a metric such that the manifold is Ahlfors regular. We also assume either non-negative Ricci curvature or the Ricci curvature is bounded from below together with a bound on the gradient of the heat kernel. We characterize BMO-functions |$u: \mathcal{M} \to \mathbb{R}$| by a Carleson measure condition of their |$\sigma $|-harmonic extension |$U:

    更新日期:2020-06-11
  • Double Points of Free Projective Line Arrangements
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-11
    Takuro Abe

    We prove the Anzis–Tohăneanu conjecture, that is, the Dirac–Motzkin conjecture for supersolvable line arrangements in the projective plane over an arbitrary field of characteristic zero. Moreover, we show that a divisionally free arrangements of lines contain at least one double point that can be regarded as the Sylvester–Gallai theorem for some free arrangements. This is a corollary of a general result

    更新日期:2020-06-11
  • The Centre-Quotient Property and Weak Centrality for C*-Algebras
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-10
    Robert J Archbold; Ilja Gogić

    We give a number of equivalent conditions (including weak centrality) for a general |$C^*$|-algebra to have the centre-quotient property. We show that every |$C^*$|-algebra |$A$| has a largest weakly central ideal |$J_{wc}(A)$|⁠. For an ideal |$I$| of a unital |$C^*$|-algebra |$A$|⁠, we find a necessary and sufficient condition for a central element of |$A/I$| to lift to a central element of |$A$|⁠

    更新日期:2020-06-10
  • Green Functions for the Pressure of Stokes Systems
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-10
    Jongkeun Choi; Hongjie Dong

    We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain |$\Omega \subset \mathbb{R}^d$|⁠, where |$d\ge 2$|⁠. We construct the Green function when coefficients are merely measurable in one direction and have Dini mean oscillation in the other directions and |$\Omega $| is such that the divergence equation is solvable there. We also establish global pointwise

    更新日期:2020-06-10
  • Semiorthogonal Decompositions on Total Spaces of Tautological Bundles
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09
    Dmitrii Pirozhkov

    Let |$U$| be the tautological subbundle on the Grassmannian |$\operatorname{Gr}(k, n)$|⁠. There is a natural morphism |$\textrm{Tot}(U) \to{\mathbb{A}}^n$|⁠. Using it, we give a semiorthogonal decomposition for the bounded derived category |$D^b_{\!\textrm{coh}}(\textrm{Tot}(U))$| into several exceptional objects and several copies of |$D^b_{\!\textrm{coh}}({\mathbb{A}}^n)$|⁠. We also prove a global

    更新日期:2020-06-09
  • Symmetric Quantum Sets and L-Algebras
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09
    Wolfgang Rump

    Quantum analogues of sets are defined by two simple assumptions, allowing enumeration, reminiscent of the Gram–Schmidt orthogonalization process. It is shown that any symmetric quantum set is a classical set of irreducible components, and that each irreducible component of size |$>3$| is representable by an orthomodular space over a skew field with involution. For finite or sufficiently large irreducible

    更新日期:2020-06-09
  • A Sharp Multidimensional Hermite–Hadamard Inequality
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09
    Simon Larson

    AbstractWe wish to point out errors in the paper “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”, International Mathematics Research Notices, Vol. 2017, No. 00, pp. 1–29. The main error concerns the symmetry of the “ramified case” of the height pairing, which relies on the vanishing of the Bockstein map in Proposition 3.5. The surjectivity claimed in the 1st line of the proof

    更新日期:2020-06-09
  • Central Extensions of Lie Groups Preserving a Differential Form
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09
    Tobias Diez; Bas Janssens; Karl-Hermann Neeb; Cornelia Vizman

    Let |$M$| be a manifold with a closed, integral |$(k+1)$|-form |$\omega $|⁠, and let |$G$| be a Fréchet–Lie group acting on |$(M,\omega )$|⁠. As a generalization of the Kostant–Souriau extension for symplectic manifolds, we consider a canonical class of central extensions of |${\mathfrak{g}}$| by |${\mathbb{R}}$|⁠, indexed by |$H^{k-1}(M,{\mathbb{R}})^*$|⁠. We show that the image of |$H_{k-1}(M,{\mathbb{Z}})$|

    更新日期:2020-06-09
  • Full Exceptional Collections on Lagrangian Grassmannians
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09
    Anton Fonarev

    We show fullness of the exceptional collections of maximal length constructed by Kuznetsov and Polishchuk in the bounded derived categories of coherent sheaves on Lagrangian Grassmannians.

    更新日期:2020-06-09
  • Quasimaps to Zero-Dimensional A∞-Quiver Varieties
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-04
    Hunter Dinkins; Andrey Smirnov

    We consider the moduli spaces of quasimaps to zero-dimensional |$A_{\infty }$| Nakajima quiver varieties. An explicit combinatorial formula for the equivariant Euler characteristic of these moduli spaces is obtained and applications to symplectic duality are discussed.

    更新日期:2020-06-04
  • An Energy Bound in the Affine Group
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03
    Giorgis Petridis; Oliver Roche-Newton; Misha Rudnev; Audie Warren

    We prove a nontrivial energy bound for a finite set of affine transformations over a general field and discuss a number of implications. These include new bounds on growth in the affine group, a quantitative version of a theorem by Elekes about rich lines in grids. We also give a positive answer to a question of Yufei Zhao that for a plane point set |$P$| for which no line contains a positive proportion

    更新日期:2020-06-03
  • Dwork Crystals II
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03
    Frits Beukers; Masha Vlasenko

    We give a generalization of |$p$|-adic congruences for truncated period functions that were originally discovered for a class of hypergeometric functions by Bernard Dwork.

    更新日期:2020-06-03
  • Singularities of Complex-Valued Solutions to Linear Parabolic Equations
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03
    Connor Mooney

    We construct examples of complex-valued singular solutions to linear, uniformly parabolic equations with complex coefficients in dimension |$n \geq 2$|⁠, which are exactly as irregular as parabolic energy estimates allow.

    更新日期:2020-06-03
  • Higher Order Polars of Quasi-Ordinary Singularities
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03
    Evelia R García Barroso; Janusz Gwoździewicz

    A quasi-ordinary polynomial is a monic polynomial with coefficients in the power series ring such that its discriminant equals a monomial up to unit. In this paper, we study higher derivatives of quasi-ordinary polynomials, also called higher order polars. We find factorizations of these polars. Our research in this paper goes in two directions. We generalize the results of Casas–Alvero and our previous

    更新日期:2020-06-03
  • A Local Limit Theorem and Delocalization of Eigenvectors for Polynomials in Two Matrices
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03
    Ching-Wei Ho

    We propose a boundary regularity condition for the |$M_n({\mathbb{C}})$|-valued subordination functions in free probability to prove a local limit theorem and delocalization of eigenvectors for self-adjoint polynomials in two random matrices. We prove this through estimating the pair of |$M_n({\mathbb{C}})$|-valued approximate subordination functions for the sum of two |$M_n({\mathbb{C}})$|-valued

    更新日期:2020-06-03
  • Factorization of Noncommutative Polynomials and Nullstellensätze for the Free Algebra
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03
    J Helton; Igor Klep; Jurij Volčič

    This article gives a class of Nullstellensätze for noncommutative polynomials. The singularity set of a noncommutative polynomial |$f=f(x_1,\dots ,x_g)$| is |$\mathscr{Z}(\,f)=(\mathscr{Z}_n(\,f))_n$|⁠, where |$\mathscr{Z}_n(\,f)=\{X \in{\operatorname{M}}_{n}({\mathbb{C}})^g \colon \det f(X) = 0\}.$| The 1st main theorem of this article shows that the irreducible factors of |$f$| are in a natural bijective

    更新日期:2020-06-03
  • Prescribing Centro-Affine Curvature From One Convex Body to Another
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03
    Alina Stancu

    We study a curvature flow on smooth, closed, strictly convex hypersurfaces in |$\mathbb{R}^n$|⁠, which commutes with the action of |$SL(n)$|⁠. The flow shrinks the initial hypersurface to a point that, if rescaled to enclose a domain of constant volume, is a smooth, closed, strictly convex hypersurface in |$\mathbb{R}^n$| with centro-affine curvature proportional, but not always equal, to the centro-affine

    更新日期:2020-06-03
  • Leading Terms of SL3 Web Invariants
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-02
    Véronique Bazier-Matte; Guillaume Douville; Alexander Garver; Rebecca Patrias; Hugh Thomas; Emine Yıldırım

    We use Khovanov and Kuperberg’s web growth rules to identify the leading term in the invariant associated to an |$\textrm{SL}_3$| web diagram, with respect to a particular term order.

    更新日期:2020-06-02
  • Schemes Supported on the Singular Locus of a Hyperplane Arrangement in |$\mathbb P^n$|
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-29
    Juan Migliore; Uwe Nagel; Henry Schenck

    A hyperplane arrangement in |$\mathbb P^n$| is free if |$R/J$| is Cohen–Macaulay (CM), where |$R = k[x_0,\dots ,x_n]$| and |$J$| is the Jacobian ideal. We study the CM-ness of two related unmixed ideals: |$ J^{un}$|⁠, the intersection of height two primary components, and |$\sqrt{J}$|⁠, the radical. Under a mild hypothesis, we show these ideals are CM. Suppose the hypothesis fails. For equidimensional

    更新日期:2020-05-29
  • Real Tropicalization and Analytification of Semialgebraic Sets
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-29
    Philipp Jell; Claus Scheiderer; Josephine Yu

    Let |$K$| be a real closed field with a nontrivial non-archimedean absolute value. We study a refined version of the tropicalization map, which we call real tropicalization map, that takes into account the signs on |$K$|⁠. We study images of semialgebraic subsets of |$K^n$| under this map from a general point of view. For a semialgebraic set |$S \subseteq K^n$| we define a space |$S_r^{{\operatorname{an}}}$|

    更新日期:2020-05-29
  • Bar Category of Modules and Homotopy Adjunction for Tensor Functors
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-28
    Rina Anno; Timothy Logvinenko

    Given a differentially graded (DG)-category |${{\mathcal{A}}}$|⁠, we introduce the bar category of modules |${\overline{\textbf{{Mod}}}\text{-}{\mathcal{A}}}$|⁠. It is a DG enhancement of the derived category |$D({{\mathcal{A}}})$| of |${{\mathcal{A}}}$|⁠, which is isomorphic to the category of DG |${{\mathcal{A}}}$|-modules with |${A_{\infty }}$|-morphisms between them. However, it is defined intrinsically

    更新日期:2020-05-28
  • Erratum: “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2019-05-31
    Chung H, Kim D, Kim M, et al.

    AbstractWe wish to point out errors in the paper “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”, International Mathematics Research Notices, Vol. 2017, No. 00, pp. 1–29. The main error concerns the symmetry of the “ramified case” of the height pairing, which relies on the vanishing of the Bockstein map in Proposition 3.5. The surjectivity claimed in the 1st line of the proof

    更新日期:2020-05-26
  • The Automorphic Discrete Spectrum of |$\textrm{Mp}_4$|
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-25
    Wee Teck Gan; Atsushi Ichino

    We prove the multiplicity formula for the automorphic discrete spectrum of the metaplectic group |$\textrm{Mp}_4$| of rank |$2$|⁠.

    更新日期:2020-05-25
  • Characteristic Polynomials of Complex Random Matrices and Painlevé Transcendents
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-25
    Alfredo Deaño; Nick Simm

    We study expectations of powers and correlation functions for characteristic polynomials of |$N \times N$| non-Hermitian random matrices. For the |$1$|-point and |$2$|-point correlation function, we obtain several characterizations in terms of Painlevé transcendents, both at finite |$N$| and asymptotically as |$N \to \infty $|⁠. In the asymptotic analysis, two regimes of interest are distinguished:

    更新日期:2020-05-25
  • Dwork Crystals I
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-25
    Frits Beukers; Masha Vlasenko

    We present an elementary elaboration of Dwork’s idea of explicit |$p$|-adic limit formulas for zeta functions of toric hypersurfaces.

    更新日期:2020-05-25
  • p-Toral Approximations Compute Bredon Homology
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-22
    Gregory Arone; W G Dwyer; Kathryn Lesh

    We study Bredon homology approximations for spaces with an action of a compact Lie group G. We show that if M is a coMackey functor satisfying mild p-locality conditions, then Bredon homology of a G-space X with coefficients in M is determined by fixed points of p-toral subgroups of G acting on X. As an application we prove a vanishing result for the Bredon homology of the complex |${{\mathcal{L}}}_{n}$|

    更新日期:2020-05-22
  • Large Deviation Estimates and Hölder Regularity of the Lyapunov Exponents for Quasi-periodic Schrödinger Cocycles
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-21
    Rui Han; Shiwen Zhang

    We consider one-dimensional quasi-periodic Schrödinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates, which lead to refined Hölder continuity of the Lyapunov exponents and the integrated density of states, in both small Lyapunov exponent and large coupling regimes. Our results cover all the Diophantine frequencies and some Liouville

    更新日期:2020-05-21
  • Differential Graded Lie Algebras and Leibniz Algebra Cohomology
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-21
    Jacob Mostovoy

    In this note, we interpret Leibniz algebras as differential graded (DG) Lie algebras. Namely, we consider two fully faithful functors from the category of Leibniz algebras to that of DG Lie algebras and show that they naturally give rise to the Leibniz cohomology and the Chevalley–Eilenberg cohomology. As an application, we prove a conjecture stated by Pirashvili in [ 9].

    更新日期:2020-05-21
  • An Action of the Polishchuk Differential Operator via Punctured Surfaces
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-21
    Gabriel C Drummond-Cole; Mehdi Tavakol

    For a family of Jacobians of smooth pointed curves, there is a notion of tautological algebra. There is an action of |${\mathfrak{s}}l_2$| on this algebra. We define and study a lifting of the Polishchuk operator, corresponding to |${\mathfrak{f}} \in{\mathfrak{s}}l_2$|⁠, on an algebra consisting of punctured Riemann surfaces. As an application, we compare a class of tautological relations on moduli

    更新日期:2020-05-21
  • Properadic Homotopical Calculus
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-20
    Eric Hoffbeck; Johan Leray; Bruno Vallette

    In this paper, we initiate the generalization of the operadic calculus that governs the properties of homotopy algebras to a properadic calculus that governs the properties of homotopy gebras over a properad. In this first article of a series, we generalize the seminal notion of |${\infty }$|-morphisms and the ubiquitous homotopy transfer theorem. As an application, we recover the homotopy properties

    更新日期:2020-05-20
  • Uniqueness and Symmetry for the Mean Field Equation on Arbitrary Flat Tori
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-20
    Guangze Gu; Changfeng Gui; Yeyao Hu; Qinfeng Li

    AbstractWe wish to point out errors in the paper “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”, International Mathematics Research Notices, Vol. 2017, No. 00, pp. 1–29. The main error concerns the symmetry of the “ramified case” of the height pairing, which relies on the vanishing of the Bockstein map in Proposition 3.5. The surjectivity claimed in the 1st line of the proof

    更新日期:2020-05-20
  • Simple Current Extensions of Tensor Products of Vertex Operator Algebras
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-20
    Hiromichi Yamada; Hiroshi Yamauchi

    We study simple current extensions of tensor products of two vertex operator algebras satisfying certain conditions. We establish the relationship between the fusion rule for the simple current extension and the fusion rule for a tensor factor. In a special case, we construct a chain of simple current extensions. We discuss certain irreducible twisted modules for the simple current extension as well

    更新日期:2020-05-20
  • Property RD and Hypercontractivity for Orthogonal Free Quantum Groups
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-19
    Michael Brannan; Roland Vergnioux; Sang-Gyun Youn

    We prove that the twisted property RD introduced in [ 2] fails to hold for all non-Kac type, non-amenable orthogonal free quantum groups. In the Kac case we revisit property RD, proving an analogue of the |$L_p-L_2$| non-commutative Khintchine inequality for free groups from [ 29]. As an application, we give new and improved hypercontractivity and ultracontractivity estimates for the generalized heat

    更新日期:2020-05-19
  • K-Theoretic Generalized Donaldson–Thomas Invariants
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-19
    Young-Hoon Kiem; Michail Savvas

    We introduce the notion of almost perfect obstruction theory on a Deligne–Mumford stack and show that stacks with almost perfect obstruction theories have virtual structure sheaves, which are deformation invariant. The main components in the construction are an induced embedding of the coarse moduli sheaf of the intrinsic normal cone into the associated obstruction sheaf stack and the construction

    更新日期:2020-05-19
  • On a Counting Theorem for Weakly Admissible Lattices
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-19
    Reynold Fregoli

    We give a precise estimate for the number of lattice points in certain bounded subsets of |$\mathbb{R}^{n}$| that involve “hyperbolic spikes” and occur naturally in multiplicative Diophantine approximation. We use Wilkie’s o-minimal structure |$\mathbb{R}_{\exp }$| and expansions thereof to formulate our counting result in a general setting. We give two different applications of our counting result

    更新日期:2020-05-19
  • Fourier Frames for Surface-Carried Measures
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-15
    Alex Iosevich; Chun-Kit Lai; Bochen Liu; Emmett Wyman

    In this paper, we show that the surface measure on the boundary of a convex body of everywhere positive Gaussian curvature does not admit a Fourier frame. This answers a question proposed by Lev and provides the 1st example of a uniformly distributed measure supported on a set of Lebesgue measure zero that does not admit a Fourier frame. In contrast, we show that the surface measure on the boundary

    更新日期:2020-05-15
  • Earrings, Sutures, and Pointed Links
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-14
    Yi Xie

    We prove a rank inequality on the instanton knot homology and the Khovanov homology of a link in |$S^3$|⁠. The key step of the proof is to construct a spectral sequence relating Baldwin–Levine–Sarkar’s pointed Khovanov homology to a singular instanton invariant for pointed links.

    更新日期:2020-05-14
  • Homological Stability for Spaces of Commuting Elements in Lie Groups
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-14
    Daniel A Ramras; Mentor Stafa

    In this paper, we study homological stability for spaces |$\textrm{Hom}({{\mathbb{Z}}}^n,G)$| of pairwise commuting |$n$|-tuples in a Lie group |$G$|⁠. We prove that for each |$n\geqslant 1$|⁠, these spaces satisfy rational homological stability as |$G$| ranges through any of the classical sequences of compact, connected Lie groups, or their complexifications. We prove similar results for rational

    更新日期:2020-05-14
  • Fourier Coefficients of Modular Forms of Half-Integral Weight in Arithmetic Progressions
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-13
    Corentin Darreye

    We study the probabilistic behavior of sums of Fourier coefficients in arithmetic progressions. We prove a result analogous to previous work of Fouvry–Ganguly–Kowalski–Michel and Kowalski–Ricotta in the context of half-integral weight holomorphic cusp forms and for prime power modulus. We actually show that these sums follow in a suitable range a mixed Gaussian distribution that comes from the asymptotic

    更新日期:2020-05-13
  • The Distribution of H8-Extensions of Quadratic Fields
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-11
    Brandon Alberts; Jack Klys

    We compute all the moments of a normalization of the function that counts unramified |$H_{8}$|-extensions of quadratic fields, where |$H_{8}$| is the quaternion group of order |$8$|⁠, and show that the values of this function determine a point mass distribution. As a consequence toward non-abelian Cohen–Lenstra heuristics of 2-groups, we show this implies that the probability is 0 for any fixed group

    更新日期:2020-05-11
  • N = 4 Superconformal Algebras and Diagonal Cosets
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-11
    Thomas Creutzig; Boris Feigin; Andrew R Linshaw

    Coset constructions of |${{\mathcal{W}}}$|-algebras have many applications and were recently given for principal |${{\mathcal{W}}}$|-algebras of |$A$|⁠, |$D$|⁠, and |$E$| types by Arakawa together with the 1st and 3rd authors. In this paper, we give coset constructions of the large and small |$N=4$| superconformal algebras, which are the minimal |${{\mathcal{W}}}$|-algebras of |${{\mathfrak{d}}}(2

    更新日期:2020-05-11
  • Computation of Quantum Cohomology From Fukaya Categories
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-11
    Fumihiko Sanda

    Assume the existence of a Fukaya category |$\textrm{Fuk}(X)$| of a compact symplectic manifold |$X$| with some expected properties. In this paper, we show |$\mathscr{A} \subset \textrm{Fuk}(X)$| split generates a summand |$\textrm{Fuk}(X)_e \subset \textrm{Fuk}(X)$| corresponding to an idempotent |$e \in QH^{\bullet }(X)$| if the Mukai pairing of |$\mathscr{A}$| is perfect. Moreover, we show |$HH^{\bullet

    更新日期:2020-05-11
  • Heronian Friezes
    Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-11
    Sergey Fomin; Linus Setiabrata

    Motivated by computational geometry of point configurations on the Euclidean plane, and by the theory of cluster algebras of type |$A$|⁠, we introduce and study Heronian friezes, the Euclidean analogues of Coxeter’s frieze patterns. We prove that a generic Heronian frieze possesses the glide symmetry (hence is periodic) and establish the appropriate version of the Laurent phenomenon. For a closely

    更新日期:2020-05-11
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