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  • Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order
    Adv. Math. (IF 1.435) Pub Date : 2020-04-02
    Arvind Ayyer; Roger E. Behrend; Ilse Fischer

    For each α∈{0,1,−1}, we count diagonally and antidiagonally symmetric alternating sign matrices (DASASMs) of fixed odd order with a maximal number of α's along the diagonal and the antidiagonal, as well as DASASMs of fixed odd order with a minimal number of 0's along the diagonal and the antidiagonal. In these enumerations, we encounter product formulas that have previously appeared in plane partition

    更新日期:2020-04-03
  • Topology of tensor ranks
    Adv. Math. (IF 1.435) Pub Date : 2020-03-31
    Pierre Comon; Lek-Heng Lim; Yang Qi; Ke Ye

    We study path-connectedness and homotopy groups of sets of tensors defined by tensor rank, border rank, multilinear rank, as well as their symmetric counterparts for symmetric tensors. We show that over C, the set of rank-r tensors and the set of symmetric rank-r symmetric tensors are both path-connected if r is not more than the complex generic rank; these results also extend to border rank and symmetric

    更新日期:2020-03-31
  • Yoneda lemma for enriched ∞-categories
    Adv. Math. (IF 1.435) Pub Date : 2020-03-30
    Vladimir Hinich

    We continue the study of enriched ∞-categories, using a definition equivalent to that of Gepner and Haugseng. In our approach enriched ∞-categories are associative monoids in an especially designed monoidal category of enriched quivers. We prove that, in the case where the monoidal structure in the basic category M comes from the direct product, our definition is essentially equivalent to the approach

    更新日期:2020-03-30
  • Bratteli–Vershik models and graph covering models
    Adv. Math. (IF 1.435) Pub Date : 2020-03-30
    Takashi Shimomura

    Based on our previous graph covering method, we introduce weighted graph covering models and flexible graph covering models that are almost equivalent to the well-known Bratteli–Vershik models. These models play important roles in showing that every invertible dynamical system on compact metrizable zero-dimensional space admits a non-trivial Bratteli–Vershik model and a basic set. We can also obtain

    更新日期:2020-03-30
  • Frieze varieties: A characterization of the finite-tame-wild trichotomy for acyclic quivers
    Adv. Math. (IF 1.435) Pub Date : 2020-03-30
    Kyungyong Lee; Li Li; Matthew Mills; Ralf Schiffler; Alexandra Seceleanu

    We introduce a new class of algebraic varieties which we call frieze varieties. Each frieze variety is determined by an acyclic quiver. The frieze variety is defined in an elementary recursive way by constructing a set of points in affine space. From a more conceptual viewpoint, the coordinates of these points are specializations of cluster variables in the cluster algebra associated to the quiver

    更新日期:2020-03-30
  • Calabi-Yau algebras and the shifted noncommutative symplectic structure
    Adv. Math. (IF 1.435) Pub Date : 2020-03-27
    Xiaojun Chen; Farkhod Eshmatov

    In this paper we show that for a Koszul Calabi-Yau algebra, there is a shifted bi-symplectic structure in the sense of Crawley-Boevey-Etingof-Ginzburg [15], on the cobar construction of its co-unitalized Koszul dual coalgebra, and hence its DG representation schemes, in the sense of Berest-Khachatryan-Ramadoss [3], have a shifted symplectic structure in the sense of Pantev-Toën-Vaquié-Vezzosi [28]

    更新日期:2020-03-27
  • Reduced spectral synthesis and compact operator synthesis
    Adv. Math. (IF 1.435) Pub Date : 2020-03-26
    V.S. Shulman; I.G. Todorov; L. Turowska

    We introduce and study the notion of reduced spectral synthesis, which unifies the concepts of spectral synthesis and uniqueness in locally compact groups. We exhibit a number of examples and prove that every non-discrete locally compact group with an open abelian subgroup has a subset that fails reduced spectral synthesis. We introduce compact operator synthesis as an operator algebraic counterpart

    更新日期:2020-03-27
  • Compactness of self-shrinkers in R3 with fixed genus
    Adv. Math. (IF 1.435) Pub Date : 2020-03-19
    Ao Sun; Zhichao Wang

    We prove the compactness of self-shrinkers in R3 with bounded entropy and fixed genus. As a corollary, we show that numbers of ends of such surfaces are uniformly bounded by the entropy and genus.

    更新日期:2020-03-20
  • Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up. II
    Adv. Math. (IF 1.435) Pub Date : 2020-03-19
    James Isenberg; Haotian Wu; Zhou Zhang

    We continue the study, initiated by the first two authors in [15], of Type-II curvature blow-up in mean curvature flow of complete noncompact hypersurfaces embedded in Euclidean space. In particular, we construct mean curvature flow solutions, in the rotationally symmetric class, with the following precise asymptotics near the “vanishing” time T: (1) The highest curvature concentrates at the tip of

    更新日期:2020-03-20
  • Fundamental tones of clamped plates in nonpositively curved spaces
    Adv. Math. (IF 1.435) Pub Date : 2020-03-19
    Alexandru Kristály

    We study Lord Rayleigh's problem for clamped plates on an arbitrary n-dimensional (n≥2) Cartan-Hadamard manifold (M,g) with sectional curvature K≤−κ2 for some κ≥0. We first prove a McKean-type spectral gap estimate, i.e. the fundamental tone of any domain in (M,g) is universally bounded from below by (n−1)416κ4 whenever the κ-Cartan-Hadamard conjecture holds on (M,g), e.g. in 2- and 3-dimensions due

    更新日期:2020-03-20
  • An odd Khovanov homotopy type
    Adv. Math. (IF 1.435) Pub Date : 2020-03-19
    Sucharit Sarkar; Christopher Scaduto; Matthew Stoffregen

    For each link L⊂S3 and every quantum grading j, we construct a stable homotopy type Xoj(L) whose cohomology recovers Ozsváth-Rasmussen-Szabó's odd Khovanov homology, H˜i(Xoj(L))=Khoi,j(L), following a construction of Lawson-Lipshitz-Sarkar of the even Khovanov stable homotopy type. Furthermore, the odd Khovanov homotopy type carries a Z/2 action whose fixed point set is a desuspension of the even Khovanov

    更新日期:2020-03-20
  • Poincaré-Lovelock metrics on conformally compact manifolds
    Adv. Math. (IF 1.435) Pub Date : 2020-03-16
    Pierre Albin

    An important tool in the study of conformal geometry, and the AdS/CFT correspondence in physics, is the Fefferman-Graham expansion of conformally compact Einstein metrics. We show that conformally compact metrics satisfying a generalization of the Einstein equation, Poincaré-Lovelock metrics, also have Fefferman-Graham expansions. Moreover we show that conformal classes of metrics that are near that

    更新日期:2020-03-16
  • Ilyashenko algebras based on transserial asymptotic expansions
    Adv. Math. (IF 1.435) Pub Date : 2020-03-13
    Zeinab Galal; Tobias Kaiser; Patrick Speissegger

    We construct a Hardy field that contains Ilyashenko's class of germs at +∞ of almost regular functions found in [12] as well as all log-exp-analytic germs. This implies non-oscillatory behaviour of almost regular germs with respect to all log-exp-analytic germs. In addition, each germ in this Hardy field is uniquely characterized by an asymptotic expansion that is an LE-series as defined by van den

    更新日期:2020-03-16
  • Involutions, obstructions and mirror symmetry
    Adv. Math. (IF 1.435) Pub Date : 2020-03-13
    Jake P. Solomon

    Consider a Maslov zero Lagrangian submanifold diffeomorphic to a Lie group on which an anti-symplectic involution acts by the inverse map of the group. We show that the Fukaya A∞ endomorphism algebra of such a Lagrangian is quasi-isomorphic to its de Rham cohomology tensored with the Novikov field. In particular, it is unobstructed, formal, and its Floer and de Rham cohomologies coincide. Our result

    更新日期:2020-03-16
  • Logarithmic concavity for morphisms of matroids
    Adv. Math. (IF 1.435) Pub Date : 2020-03-10
    Christopher Eur; June Huh

    Morphisms of matroids are combinatorial abstractions of linear maps and graph homomorphisms. We introduce the notion of a basis for morphisms of matroids, and show that its generating function is strongly log-concave. As a consequence, we obtain a generalization of Mason's conjecture on the f-vectors of independent subsets of matroids to arbitrary morphisms of matroids. To establish this, we define

    更新日期:2020-03-10
  • On a Calabi-type estimate for pluriclosed flow
    Adv. Math. (IF 1.435) Pub Date : 2020-03-06
    Joshua Jordan; Jeffrey Streets

    The regularity theory for pluriclosed flow hinges on obtaining Cα regularity for the metric assuming uniform equivalence to a background metric. This estimate was established in [14] by an adaptation of ideas from Evans-Krylov, the key input being a sharp differential inequality satisfied by the associated ‘generalized metric’ defined on T⊕T⁎. In this work we give a sharpened form of this estimate

    更新日期:2020-03-06
  • The B-model connection and mirror symmetry for Grassmannians
    Adv. Math. (IF 1.435) Pub Date : 2020-03-05
    R.J. Marsh; K. Rietsch

    We consider the Grassmannian X=Grn−k(Cn) and describe a ‘mirror dual’ Landau-Ginzburg model (Xˇ∘,Wq:Xˇ∘→C), where Xˇ∘ is the complement of a particular anti-canonical divisor in a Langlands dual Grassmannian Xˇ, and we express W succinctly in terms of Plücker coordinates. First of all, we show this Landau-Ginzburg model to be isomorphic to one proposed for homogeneous spaces in a previous work by the

    更新日期:2020-03-05
  • Determining a Riemannian metric from minimal areas
    Adv. Math. (IF 1.435) Pub Date : 2020-03-05
    Spyros Alexakis; Tracey Balehowsky; Adrian Nachman

    We prove that if (M,g) is a topological 3-ball with a C4-smooth Riemannian metric g, and mean-convex boundary ∂M, then knowledge of least areas circumscribed by simple closed curves γ⊂∂M uniquely determines the metric g, under some additional geometric assumptions. These are that g is either a) C3-close to Euclidean or b) satisfies much weaker geometric conditions which hold when the manifold is to

    更新日期:2020-03-05
  • On irregularities of Fourier transforms of regular holonomic D-modules
    Adv. Math. (IF 1.435) Pub Date : 2020-03-05
    Yohei Ito; Kiyoshi Takeuchi

    We study Fourier transforms of regular holonomic D-modules. By using the theory of Fourier-Sato transforms of enhanced ind-sheaves developed by Kashiwara-Schapira and D'Agnolo-Kashiwara, a formula for their enhanced solution complexes will be obtained. Moreover we show that some parts of their characteristic cycles and irregularities are expressed by the geometries of the original D-modules.

    更新日期:2020-03-05
  • Finite-dimensional differential graded algebras and their geometric realizations
    Adv. Math. (IF 1.435) Pub Date : 2020-03-05
    Dmitri Orlov

    We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with a full separable semi-exceptional collection. Moreover, we also show that it gives a characterization of such categories assuming that a subcategory is idempotent

    更新日期:2020-03-05
  • The Drinfeld centre of a symmetric fusion category is 2-fold monoidal
    Adv. Math. (IF 1.435) Pub Date : 2020-03-04
    Thomas A. Wasserman

    We show that the Drinfeld centre of a symmetric fusion category over an algebraically closed field of characteristic zero is a bilax 2-fold monoidal category. That is, it carries two monoidal structures, the convolution and symmetric tensor products, that are bilax monoidal functors with respect to each other. We additionally show that the braiding and symmetry for the convolution and symmetric tensor

    更新日期:2020-03-04
  • Standard conjecture D for matrix factorizations
    Adv. Math. (IF 1.435) Pub Date : 2020-03-04
    Michael K. Brown; Mark E. Walker

    We prove the non-commutative analogue of Grothendieck's Standard Conjecture D for the dg-category of matrix factorizations of an isolated hypersurface singularity in characteristic 0. Along the way, we show the Euler pairing for such dg-categories of matrix factorizations is positive semi-definite.

    更新日期:2020-03-04
  • Algebrability of the set of hypercyclic vectors for backward shift operators
    Adv. Math. (IF 1.435) Pub Date : 2020-03-02
    Javier Falcó; Karl-G. Grosse-Erdmann

    We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Fréchet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case, we obtain that the sets of hypercyclic vectors for Rolewicz's and MacLane's operators are algebrable.

    更新日期:2020-03-03
  • Super-exponential stability for generic real-analytic elliptic equilibrium points
    Adv. Math. (IF 1.435) Pub Date : 2020-03-02
    Abed Bounemoura; Bassam Fayad; Laurent Niederman

    We consider the dynamics in a neighborhood of an elliptic equilibrium point with a Diophantine frequency of a symplectic real analytic vector field and we prove the following result of effective stability. Generically, both in a topological and measure-theoretical sense, any solution starting sufficiently close to the equilibrium point remains close to it for an interval of time which is doubly exponentially

    更新日期:2020-03-03
  • Equivariant factorization homology of global quotient orbifolds
    Adv. Math. (IF 1.435) Pub Date : 2020-03-02
    T.A.N. Weelinck

    We introduce equivariant factorization homology, extending the axiomatic framework of Ayala-Francis to encompass multiplicative invariants of manifolds equipped with finite group actions. Examples of such equivariant factorization homology theories include Bredon equivariant homology and (twisted versions of) Hochschild homology. Our main result is that equivariant factorization homology satisfies

    更新日期:2020-03-03
  • Geometric differentiability of Riemann's non-differentiable function
    Adv. Math. (IF 1.435) Pub Date : 2020-03-03
    Daniel Eceizabarrena

    Riemann's non-differentiable function is a classic example of a continuous function which is almost nowhere differentiable, and many results concerning its analytic regularity have been shown so far. However, it can also be given a geometric interpretation, so questions on its geometric regularity arise. This point of view is developed in the context of the evolution of vortex filaments, modelled by

    更新日期:2020-03-03
  • Matroidal representations of groups
    Adv. Math. (IF 1.435) Pub Date : 2020-02-27
    Noah Giansiracusa; Jacob Manaker

    We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic one modular representation theory, or a matroidal representation theory—and we draw from all three perspectives. After some general properties and constructions,

    更新日期:2020-02-28
  • Noncyclic division algebras over fields of Brauer dimension one
    Adv. Math. (IF 1.435) Pub Date : 2020-02-28
    Eric Brussel

    Let K be a complete discretely valued field of rank one, with residue field Qp. It is well known that period equals index in Br(K). We prove that when p=2 there exist noncyclic K-division algebras of every 2-power degree divisible by four. Otherwise, every K-division algebra is cyclic. This gives the first published example of a field whose Brauer dimension and cyclic length are not equal.

    更新日期:2020-02-28
  • Reconstructing the Bost–Connes semigroup actions from K-theory
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    Yosuke Kubota; Takuya Takeishi

    We complete the classification of Bost–Connes systems. We show that two Bost–Connes C*-algebras for number fields are isomorphic if and only if the original semigroups actions are conjugate. Together with recent reconstruction results in number theory by Cornelissen–de Smit–Li–Marcolli–Smit, we conclude that two Bost–Connes C*-algebras are isomorphic if and only if the original number fields are isomorphic

    更新日期:2020-02-27
  • A stable ∞-category of Lagrangian cobordisms
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    David Nadler; Hiro Lee Tanaka

    Given an exact symplectic manifold M and a support Lagrangian Λ⊂M, we construct an ∞-category LagΛ(M) which we conjecture to be equivalent (after specialization of the coefficients) to the partially wrapped Fukaya category of M relative to Λ. Roughly speaking, the objects of LagΛ(M) are Lagrangian branes inside of M×T⁎Rn, for large n, and the morphisms are Lagrangian cobordisms that are non-characteristic

    更新日期:2020-02-27
  • A class of invariant valuations on Lip(Sn−1)
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    Andrea Colesanti; Daniele Pagnini; Pedro Tradacete; Ignacio Villanueva

    We provide an integral representation for continuous valuations defined on the space Lip(Sn−1) of Lipschitz continuous functions on the unit (n−1)-sphere, which are invariant under rotations and under the addition of linear functions restricted to the unit sphere (Λ-invariant).

    更新日期:2020-02-27
  • The automorphism group and limit set of a bounded domain I: The finite type case
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    Andrew Zimmer

    For bounded pseudoconvex domains with finite type we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different points of the boundary, then the automorphism group has finitely many components and is the almost direct product of a compact group and connected Lie group locally isomorphic to Aut(Bk). Further, the limit set is a smooth

    更新日期:2020-02-27
  • Distinguished representations, Shintani base change and a finite field analogue of a conjecture of Prasad
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    Chang Yang

    Let E/F be a quadratic extension of fields, and G a connected quasi-split reductive group over F. Let Gop be the opposition group obtained by twisting G by the duality involution considered by Prasad. Assume that the field F is finite. Let π be an irreducible generic representation of G(E). When π is a Shintani base change lift of some representation of Gop(F), we give an explicit nonzero G(F)-invariant

    更新日期:2020-02-27
  • Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties
    Adv. Math. (IF 1.435) Pub Date : 2020-02-27
    Yohsuke Matsuzawa

    We prove Kawaguchi-Silverman conjecture (KSC) and Shibata's conjecture on ample canonical heights for endomorphisms on several classes of algebraic varieties including varieties of Fano type and projective toric varieties. We also prove KSC for group endomorphisms of linear algebraic groups. We also propose a possible approach to the conjecture using equivariant MMP.

    更新日期:2020-02-27
  • On the K-theory of truncated polynomial algebras, revisited
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    Martin Speirs

    We revisit the computation, due to Hesselholt and Madsen, of the K-theory of truncated polynomial algebras for perfect fields of positive characteristic. The resulting K-groups are expressed in terms of big Witt vectors of the field. The original proof relied on an understanding of cyclic polytopes in order to determine the genuine equivariant homotopy type of the cyclic bar construction for a suitable

    更新日期:2020-02-27
  • Operations and poly-operations in algebraic cobordism
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    Alexander Vishik

    In the case of a field of characteristic zero, we describe all operations (including non-additive ones) from a theory A⁎ obtained from Algebraic Cobordism Ω⁎ of M. Levine-F. Morel by change of coefficients to any oriented cohomology theory B⁎ (in the sense of Definition 2.1). We prove that such an operation can be reconstructed out of it's action on the products of projective spaces. This reduces the

    更新日期:2020-02-27
  • L1-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    Annalisa Baldi; Bruno Franchi; Pierre Pansu

    In this paper, we prove interior Poincaré and Sobolev inequalities in Euclidean spaces and in Heisenberg groups, in the limiting case where the exterior (resp. Rumin) differential of a differential form is measured in L1 norm. Unlike for Lp, p>1, the estimates are doomed to fail in top degree. The singular integral estimates are replaced with inequalities which go back to Bourgain-Brezis in Euclidean

    更新日期:2020-02-26
  • Stochastic order on metric spaces and the ordered Kantorovich monad
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    Tobias Fritz; Paolo Perrone

    In earlier work, we had introduced the Kantorovich probability monad on complete metric spaces, extending a construction due to van Breugel. Here we extend the Kantorovich monad further to a certain class of ordered metric spaces, by endowing the spaces of probability measures with the usual stochastic order. It can be considered a metric analogue of the probabilistic powerdomain. Our proof of antisymmetry

    更新日期:2020-02-26
  • Purity of reciprocity sheaves
    Adv. Math. (IF 1.435) Pub Date : 2020-02-26
    Shuji Saito

    The purpose of this paper is to prove a conjecture of Kahn-Saito-Yamazaki [8, Conj.1(1)]. This is accomplished by extending Voevodsky's fundamental results on homotopy invariant (pre)sheaves with transfers [18] to its generalizations, reciprocity sheaves and cube-invariant sheaves in the context of theory of modulus (pre)sheave with transfers [6]. The main results of this paper is expected to play

    更新日期:2020-02-26
  • Dispersive estimate for quasi-periodic Schrödinger operators on 1-d lattices
    Adv. Math. (IF 1.435) Pub Date : 2020-02-24
    Dario Bambusi; Zhiyan Zhao

    Consider the one-dimensional discrete Schrödinger operator Hθ:(Hθq)n=−(qn+1+qn−1)+V(θ+nω)qn,n∈Z, with ω∈Rd Diophantine, and V a real-analytic function on Td=(R/2πZ)d. For V sufficiently small, we prove the dispersive estimate: for every ϕ∈ℓ1(Z),(1)‖e−itHθϕ‖ℓ∞≤K0|ln⁡ε0|a(ln⁡ln⁡(2+〈t〉))2d〈t〉13‖ϕ‖ℓ1,〈t〉:=1+t2, with a and K0 two absolute constants and ε0 an analytic norm of V. The estimate holds for every

    更新日期:2020-02-24
  • Greedy approximations by signed harmonic sums and the Thue–Morse sequence
    Adv. Math. (IF 1.435) Pub Date : 2020-02-21
    Sandro Bettin; Giuseppe Molteni; Carlo Sanna

    Given a real number τ, we study the approximation of τ by signed harmonic sums σN(τ):=∑n≤Nsn(τ)/n, where the sequence of signs (sN(τ))N∈N is defined “greedily” by setting sN+1(τ):=+1 if σN(τ)≤τ, and sN+1(τ):=−1 otherwise. More precisely, we compute the limit points and the decay rate of the sequence (σN(τ)−τ)N∈N. Moreover, we give an accurate description of the behavior of the sequence of signs (sN(τ))N∈N

    更新日期:2020-02-21
  • Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices
    Adv. Math. (IF 1.435) Pub Date : 2020-02-21
    K. De Commer; M. Matassa

    Let U be a connected, simply connected compact Lie group with complexification G. Let u and g be the associated Lie algebras. Let Γ be the Dynkin diagram of g with underlying set I, and let Uq(u) be the associated quantized universal enveloping ⁎-algebra of u for some 0

    更新日期:2020-02-21
  • From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Haonan Zhang

    In this paper we study the joint convexity/concavity of the trace functionsΨp,q,s(A,B)=Tr(Bq2K⁎ApKBq2)s,p,q,s∈R, where A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of (p,q,s)∈R3 for Ψp,q,s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of

    更新日期:2020-02-20
  • Operator means of probability measures
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Fumio Hiai; Yongdo Lim

    Let P be the complete metric space consisting of positive invertible operators on an infinite-dimensional Hilbert space with the Thompson metric. We introduce the notion of operator means of probability measures on P, in parallel with Kubo and Ando's definition of two-variable operator means, and show that every operator mean is contractive for the ∞-Wasserstein distance. By means of a fixed point

    更新日期:2020-02-20
  • Three-dimensional normal pseudomanifolds with relatively few edges
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Biplab Basak; Ed Swartz

    Let Δ be a d-dimensional normal pseudomanifold, d≥3. A relative lower bound for the number of edges in Δ is that g2 of Δ is at least g2 of the link of any vertex. When this inequality is sharp Δ has relatively minimal g2. For example, whenever the one-skeleton of Δ equals the one-skeleton of the star of a vertex, then Δ has relatively minimal g2. Subdividing a facet in such an example also gives a

    更新日期:2020-02-20
  • Exponential improvements for superball packing upper bounds
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Ashwin Sah; Mehtaab Sawhney; David Stoner; Yufei Zhao

    We prove that for all fixed p>2, the translative packing density of unit ℓp-balls in Rn is at most 2(γp+o(1))n with γp<−1/p. This is the first exponential improvement in high dimensions since van der Corput and Schaake (1936).

    更新日期:2020-02-20
  • Truncated Hecke-Rogers type series
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Chun Wang; Ae Ja Yee

    The recent work of George Andrews and Mircea Merca on the truncated version of Euler's pentagonal number theorem has opened up a new study on truncated theta series. Since then several papers on the topic have followed. The main purpose of this paper is to generalize the study to Hecke-Rogers type double series, which are associated with some interesting partition functions. Our proofs heavily rely

    更新日期:2020-02-20
  • Stability conditions and the A2 quiver
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Tom Bridgeland; Yu Qiu; Tom Sutherland

    For each integer n⩾2 we describe the space of stability conditions on the derived category of the n-dimensional Ginzburg algebra associated to the A2 quiver. The form of our results points to a close relationship between these spaces and the Frobenius-Saito structure on the unfolding space of the A2 singularity.

    更新日期:2020-02-20
  • Extreme points of the set of elements majorised by an integrable function: Resolution of a problem by Luxemburg and of its noncommutative counterpart
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    D. Dauitbek; J. Huang; F. Sukochev

    Let f be an arbitrary integrable function on a finite measure space (X,Σ,ν). We characterise the extreme points of the set Ω(f) of all measurable functions on (X,Σ,ν) majorised by f, providing a complete answer to a problem raised by W.A.J. Luxemburg in 1967. Moreover, we obtain a noncommutative version of this result.

    更新日期:2020-02-20
  • Geometrical logarithmic capacitance
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Jie Xiao

    This paper is devoted to a novel and nontrivial exploration of eight aspects of the geometrical logarithmic capacitance (a very key notion in mathematical physics, quasiconformal geometry and variational calculus) through: (1) identifying with the reduced conformal module; (2) evaluating the minimal log-potential energy; (3) relating to both the volume-radius and the surface-radius; (4) linking with

    更新日期:2020-02-20
  • Towards a categorical boson-fermion correspondence
    Adv. Math. (IF 1.435) Pub Date : 2020-02-14
    Yin Tian

    We construct a Heisenberg counterpart of a Clifford categorification. It is a modification of Khovanov's Heisenberg categorification. We relate generators of the Heisenberg category with a complex of generators of the Clifford category. Certain vertex operators associated to the Clifford algebra are lifted to endofunctors of the Fock space categorification.

    更新日期:2020-02-20
  • A graphical category for higher modular operads
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Philip Hackney; Marcy Robertson; Donald Yau

    We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Quillen model structure on the collection of simplicial presheaves for a certain category of undirected graphs. This new category of undirected graphs, denoted U, plays a similar role for modular operads that the dendroidal

    更新日期:2020-02-20
  • Nested Hilbert schemes on surfaces: Virtual fundamental class
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Amin Gholampour; Artan Sheshmani; Shing-Tung Yau

    We construct virtual fundamental classes on nested Hilbert schemes of points and curves in complex nonsingular projective surfaces. These classes recover the virtual classes of Seiberg-Witten theory as well as the (reduced) stable theory, and play a crucial role in the reduced Donaldson-Thomas theory of local-surface-threefolds that we study in [15]. We show that certain integrals against the virtual

    更新日期:2020-02-20
  • Coxeter submodular functions and deformations of Coxeter permutahedra
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Federico Ardila; Federico Castillo; Christopher Eur; Alexander Postnikov

    We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This class of polytopes contains important families such as weight polytopes, signed graphic zonotopes, Coxeter matroids, root cones, and Coxeter associahedra. Our description extends the known correspondence between generalized permutahedra, polymatroids

    更新日期:2020-02-20
  • Representations of mock theta functions
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Dandan Chen; Liuquan Wang

    Motivated by the works of Liu, we provide a unified approach to find Appell-Lerch series and Hecke-type series representations for mock theta functions. We establish a number of parameterized identities with two parameters a and b. Specializing the choices of (a,b), we not only give various known and new representations for the mock theta functions of orders 2, 3, 5, 6 and 8, but also present many

    更新日期:2020-02-20
  • The moduli space of smooth ample hypersurfaces in Abelian varieties
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Fabrizio Catanese; Yongnam Lee

    We give a characterization of smooth ample Hypersurfaces in Abelian Varieties and also describe the connected component of the moduli space containing such hypersurfaces of a given polarization type: we show that this component is irreducible and that it consists of these Hypersurfaces, plus the smooth iterated univariate coverings of normal type (of the same polarization type). The above manifolds

    更新日期:2020-02-20
  • A rigorous derivation of the Hamiltonian structure for the nonlinear Schrödinger equation
    Adv. Math. (IF 1.435) Pub Date : 2020-02-14
    Dana Mendelson; Andrea R. Nahmod; Nataša Pavlović; Matthew Rosenzweig; Gigliola Staffilani

    We consider the cubic nonlinear Schrödinger equation (NLS) in any spatial dimension, which is a well-known example of an infinite-dimensional Hamiltonian system. Inspired by the knowledge that the NLS is an effective equation for a system of interacting bosons as the particle number tends to infinity, we provide a derivation of the Hamiltonian structure, which is comprised of both a Hamiltonian functional

    更新日期:2020-02-20
  • Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Atsufumi Honda; Kentaro Saji; Keisuke Teramoto

    A mixed type surface is a connected regular surface in a Lorentzian 3-manifold with non-empty spacelike and timelike point sets. The induced metric of a mixed type surface is a signature-changing metric, and their lightlike points may be regarded as singular points of such metrics. In this paper, we investigate the behavior of Gaussian curvature at a non-degenerate lightlike point of a mixed type surface

    更新日期:2020-02-20
  • Spectrum of composition operators on S(R) with polynomial symbols
    Adv. Math. (IF 1.435) Pub Date : 2020-02-13
    Carmen Fernández; Antonio Galbis; Enrique Jordá

    We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to {0}, while the spectrum of any non mean ergodic composition operator with a polynomial always contains the closed unit disc except perhaps the origin. We obtain

    更新日期:2020-02-20
  • Uniqueness of very weak solutions for a fractional filtration equation
    Adv. Math. (IF 1.435) Pub Date : 2020-02-14
    Gabriele Grillo; Matteo Muratori; Fabio Punzo

    We prove existence and uniqueness of distributional, bounded solutions to a fractional filtration equation in Rd. With regards to uniqueness, it was shown even for more general equations in [22] that if two bounded solutions u,w of (1.1) satisfy u−w∈L1(Rd×(0,T)), then u=w. We obtain here that this extra assumption can in fact be removed and establish uniqueness in the class of merely bounded solutions

    更新日期:2020-02-20
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