• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 |$U: 更新日期：2020-06-11 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-11 Takuro Abe We prove the Anzis–Tohăneanu conjecture, that is, the Dirac–Motzkin conjecture for supersolvable line arrangements in the projective plane over an arbitrary field of characteristic zero. Moreover, we show that a divisionally free arrangements of lines contain at least one double point that can be regarded as the Sylvester–Gallai theorem for some free arrangements. This is a corollary of a general result 更新日期：2020-06-11 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-10 Robert J Archbold; Ilja Gogić We give a number of equivalent conditions (including weak centrality) for a general |$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$|⁠ 更新日期：2020-06-10 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-10 Jongkeun Choi; Hongjie Dong We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain |$\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 $| is such that the divergence equation is solvable there. We also establish global pointwise 更新日期：2020-06-10 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09 Dmitrii Pirozhkov Let |$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)$|⁠. We also prove a global 更新日期：2020-06-09 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09 Wolfgang Rump Quantum analogues of sets are defined by two simple assumptions, allowing enumeration, reminiscent of the Gram–Schmidt orthogonalization process. It is shown that any symmetric quantum set is a classical set of irreducible components, and that each irreducible component of size |$>3$| is representable by an orthomodular space over a skew field with involution. For finite or sufficiently large irreducible 更新日期：2020-06-09 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09 Simon Larson AbstractWe wish to point out errors in the paper “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”, International Mathematics Research Notices, Vol. 2017, No. 00, pp. 1–29. The main error concerns the symmetry of the “ramified case” of the height pairing, which relies on the vanishing of the Bockstein map in Proposition 3.5. The surjectivity claimed in the 1st line of the proof 更新日期：2020-06-09 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09 Tobias Diez; Bas Janssens; Karl-Hermann Neeb; Cornelia Vizman Let |$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}})$| 更新日期：2020-06-09 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-09 Anton Fonarev We show fullness of the exceptional collections of maximal length constructed by Kuznetsov and Polishchuk in the bounded derived categories of coherent sheaves on Lagrangian Grassmannians. 更新日期：2020-06-09 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-04 Hunter Dinkins; Andrey Smirnov We consider the moduli spaces of quasimaps to zero-dimensional |$A_{\infty }$| Nakajima quiver varieties. An explicit combinatorial formula for the equivariant Euler characteristic of these moduli spaces is obtained and applications to symplectic duality are discussed. 更新日期：2020-06-04 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03 Giorgis Petridis; Oliver Roche-Newton; Misha Rudnev; Audie Warren We prove a nontrivial energy bound for a finite set of affine transformations over a general field and discuss a number of implications. These include new bounds on growth in the affine group, a quantitative version of a theorem by Elekes about rich lines in grids. We also give a positive answer to a question of Yufei Zhao that for a plane point set |$P$| for which no line contains a positive proportion 更新日期：2020-06-03 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03 Frits Beukers; Masha Vlasenko We give a generalization of |$p$|-adic congruences for truncated period functions that were originally discovered for a class of hypergeometric functions by Bernard Dwork. 更新日期：2020-06-03 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03 Connor Mooney We construct examples of complex-valued singular solutions to linear, uniformly parabolic equations with complex coefficients in dimension |$n \geq 2$|⁠, which are exactly as irregular as parabolic energy estimates allow. 更新日期：2020-06-03 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03 Evelia R García Barroso; Janusz Gwoździewicz A quasi-ordinary polynomial is a monic polynomial with coefficients in the power series ring such that its discriminant equals a monomial up to unit. In this paper, we study higher derivatives of quasi-ordinary polynomials, also called higher order polars. We find factorizations of these polars. Our research in this paper goes in two directions. We generalize the results of Casas–Alvero and our previous 更新日期：2020-06-03 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03 Ching-Wei Ho We propose a boundary regularity condition for the |$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}})$|-valued 更新日期：2020-06-03 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03 J Helton; Igor Klep; Jurij Volčič This article gives a class of Nullstellensätze for noncommutative polynomials. The singularity set of a noncommutative polynomial |$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$| are in a natural bijective 更新日期：2020-06-03 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-03 Alina Stancu We study a curvature flow on smooth, closed, strictly convex hypersurfaces in |$\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$| with centro-affine curvature proportional, but not always equal, to the centro-affine 更新日期：2020-06-03 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-06-02 Véronique Bazier-Matte; Guillaume Douville; Alexander Garver; Rebecca Patrias; Hugh Thomas; Emine Yıldırım We use Khovanov and Kuperberg’s web growth rules to identify the leading term in the invariant associated to an |$\textrm{SL}_3$| web diagram, with respect to a particular term order. 更新日期：2020-06-02 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-29 Juan Migliore; Uwe Nagel; Henry Schenck A hyperplane arrangement in |$\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}$|⁠, the radical. Under a mild hypothesis, we show these ideals are CM. Suppose the hypothesis fails. For equidimensional 更新日期：2020-05-29 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-29 Philipp Jell; Claus Scheiderer; Josephine Yu Let |$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}}}$| 更新日期：2020-05-29 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-28 Rina Anno; Timothy Logvinenko Given a differentially graded (DG)-category |${{\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 }}$|-morphisms between them. However, it is defined intrinsically 更新日期：2020-05-28 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2019-05-31 Chung H, Kim D, Kim M, et al. AbstractWe wish to point out errors in the paper “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”, International Mathematics Research Notices, Vol. 2017, No. 00, pp. 1–29. The main error concerns the symmetry of the “ramified case” of the height pairing, which relies on the vanishing of the Bockstein map in Proposition 3.5. The surjectivity claimed in the 1st line of the proof 更新日期：2020-05-26 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-25 Wee Teck Gan; Atsushi Ichino We prove the multiplicity formula for the automorphic discrete spectrum of the metaplectic group |$\textrm{Mp}_4$| of rank |$2$|⁠. 更新日期：2020-05-25 • 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 $|⁠. In the asymptotic analysis, two regimes of interest are distinguished: 更新日期：2020-05-25 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-25 Frits Beukers; Masha Vlasenko We present an elementary elaboration of Dwork’s idea of explicit |$p$|-adic limit formulas for zeta functions of toric hypersurfaces. 更新日期：2020-05-25 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-22 Gregory Arone; W G Dwyer; Kathryn Lesh We study Bredon homology approximations for spaces with an action of a compact Lie group G. We show that if M is a coMackey functor satisfying mild p-locality conditions, then Bredon homology of a G-space X with coefficients in M is determined by fixed points of p-toral subgroups of G acting on X. As an application we prove a vanishing result for the Bredon homology of the complex |${{\mathcal{L}}}_{n}$| 更新日期：2020-05-22 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-21 Rui Han; Shiwen Zhang We consider one-dimensional quasi-periodic Schrödinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates, which lead to refined Hölder continuity of the Lyapunov exponents and the integrated density of states, in both small Lyapunov exponent and large coupling regimes. Our results cover all the Diophantine frequencies and some Liouville 更新日期：2020-05-21 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-21 Jacob Mostovoy In this note, we interpret Leibniz algebras as differential graded (DG) Lie algebras. Namely, we consider two fully faithful functors from the category of Leibniz algebras to that of DG Lie algebras and show that they naturally give rise to the Leibniz cohomology and the Chevalley–Eilenberg cohomology. As an application, we prove a conjecture stated by Pirashvili in [ 9]. 更新日期：2020-05-21 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-21 Gabriel C Drummond-Cole; Mehdi Tavakol For a family of Jacobians of smooth pointed curves, there is a notion of tautological algebra. There is an action of |${\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$|⁠, on an algebra consisting of punctured Riemann surfaces. As an application, we compare a class of tautological relations on moduli 更新日期：2020-05-21 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-20 Eric Hoffbeck; Johan Leray; Bruno Vallette In this paper, we initiate the generalization of the operadic calculus that governs the properties of homotopy algebras to a properadic calculus that governs the properties of homotopy gebras over a properad. In this first article of a series, we generalize the seminal notion of |${\infty }$|-morphisms and the ubiquitous homotopy transfer theorem. As an application, we recover the homotopy properties 更新日期：2020-05-20 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-20 Guangze Gu; Changfeng Gui; Yeyao Hu; Qinfeng Li AbstractWe wish to point out errors in the paper “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”, International Mathematics Research Notices, Vol. 2017, No. 00, pp. 1–29. The main error concerns the symmetry of the “ramified case” of the height pairing, which relies on the vanishing of the Bockstein map in Proposition 3.5. The surjectivity claimed in the 1st line of the proof 更新日期：2020-05-20 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-20 Hiromichi Yamada; Hiroshi Yamauchi We study simple current extensions of tensor products of two vertex operator algebras satisfying certain conditions. We establish the relationship between the fusion rule for the simple current extension and the fusion rule for a tensor factor. In a special case, we construct a chain of simple current extensions. We discuss certain irreducible twisted modules for the simple current extension as well 更新日期：2020-05-20 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-19 Michael Brannan; Roland Vergnioux; Sang-Gyun Youn We prove that the twisted property RD introduced in [ 2] fails to hold for all non-Kac type, non-amenable orthogonal free quantum groups. In the Kac case we revisit property RD, proving an analogue of the |$L_p-L_2$| non-commutative Khintchine inequality for free groups from [ 29]. As an application, we give new and improved hypercontractivity and ultracontractivity estimates for the generalized heat 更新日期：2020-05-19 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-19 Young-Hoon Kiem; Michail Savvas We introduce the notion of almost perfect obstruction theory on a Deligne–Mumford stack and show that stacks with almost perfect obstruction theories have virtual structure sheaves, which are deformation invariant. The main components in the construction are an induced embedding of the coarse moduli sheaf of the intrinsic normal cone into the associated obstruction sheaf stack and the construction 更新日期：2020-05-19 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-19 Reynold Fregoli We give a precise estimate for the number of lattice points in certain bounded subsets of |$\mathbb{R}^{n}$| that involve “hyperbolic spikes” and occur naturally in multiplicative Diophantine approximation. We use Wilkie’s o-minimal structure |$\mathbb{R}_{\exp }$| and expansions thereof to formulate our counting result in a general setting. We give two different applications of our counting result 更新日期：2020-05-19 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-15 Alex Iosevich; Chun-Kit Lai; Bochen Liu; Emmett Wyman In this paper, we show that the surface measure on the boundary of a convex body of everywhere positive Gaussian curvature does not admit a Fourier frame. This answers a question proposed by Lev and provides the 1st example of a uniformly distributed measure supported on a set of Lebesgue measure zero that does not admit a Fourier frame. In contrast, we show that the surface measure on the boundary 更新日期：2020-05-15 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-14 Yi Xie We prove a rank inequality on the instanton knot homology and the Khovanov homology of a link in |$S^3$|⁠. The key step of the proof is to construct a spectral sequence relating Baldwin–Levine–Sarkar’s pointed Khovanov homology to a singular instanton invariant for pointed links. 更新日期：2020-05-14 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-14 Daniel A Ramras; Mentor Stafa In this paper, we study homological stability for spaces |$\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$| ranges through any of the classical sequences of compact, connected Lie groups, or their complexifications. We prove similar results for rational 更新日期：2020-05-14 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-13 Corentin Darreye We study the probabilistic behavior of sums of Fourier coefficients in arithmetic progressions. We prove a result analogous to previous work of Fouvry–Ganguly–Kowalski–Michel and Kowalski–Ricotta in the context of half-integral weight holomorphic cusp forms and for prime power modulus. We actually show that these sums follow in a suitable range a mixed Gaussian distribution that comes from the asymptotic 更新日期：2020-05-13 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-11 Brandon Alberts; Jack Klys We compute all the moments of a normalization of the function that counts unramified |$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 • 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
• 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 |$HH^{\bullet 更新日期：2020-05-11 • Int. Math. Res. Notices (IF 1.291) Pub Date : 2020-05-11 Sergey Fomin; Linus Setiabrata Motivated by computational geometry of point configurations on the Euclidean plane, and by the theory of cluster algebras of type |$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
Contents have been reproduced by permission of the publishers.

down
wechat
bug