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  • Optimal lower bounds for Donaldson's J-functional
    Adv. Math. (IF 1.494) Pub Date : 2020-07-07
    Zakarias Sjöström Dyrefelt

    In this paper we provide an explicit formula for the optimal lower bound of Donaldson's J-functional, in the sense of finding explicitly the optimal constant in the definition of coercivity, which always exists and takes negative values in general. This constant is positive precisely if the J-equation admits a solution, and the explicit formula has a number of applications. First, this leads to new

  • Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms
    Adv. Math. (IF 1.494) Pub Date : 2020-07-07
    Zhen-Qing Chen; Takashi Kumagai; Jian Wang

    In this paper, we consider the following symmetric Dirichlet forms on a metric measure space (M,d,μ):E(f,g)=E(c)(f,g)+∫M×M(f(x)−f(y))(g(x)−g(y))J(dx,dy), where E(c) is a strongly local symmetric bilinear form and J(dx,dy) is a symmetric Radon measure on M×M. Under general volume doubling condition on (M,d,μ) and some mild assumptions on scaling functions, we establish stability results for upper bounds

  • Hodge theory of SKT manifolds
    Adv. Math. (IF 1.494) Pub Date : 2020-07-04
    Gil R. Cavalcanti

    We use tools from generalized complex geometry to develop the theory of SKT (a.k.a. pluriclosed Hermitian) manifolds and more generally manifolds with special holonomy with respect to a metric connection with closed skew-symmetric torsion. We develop Hodge theory on such manifolds showing how the reduction of the holonomy group causes a decomposition of the twisted cohomology. For SKT manifolds this

  • The Abel map for surface singularities II. Generic analytic structure
    Adv. Math. (IF 1.494) Pub Date : 2020-06-30
    János Nagy; András Némethi

    We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with respect to a fixed topological type), under the condition that the link is a rational homology sphere. The list of analytic invariants includes: the geometric genus

  • Lecture hall tableaux
    Adv. Math. (IF 1.494) Pub Date : 2020-06-29
    Sylvie Corteel; Jang Soo Kim

    We introduce lecture hall tableaux, which are fillings of a skew Young diagram satisfying certain conditions. Lecture hall tableaux generalize both lecture hall partitions and anti-lecture hall compositions, and also contain reverse semistandard Young tableaux as a limit case. We show that the coefficients in the Schur expansion of multivariate little q-Jacobi polynomials are generating functions for

  • k-Schur expansions of Catalan functions
    Adv. Math. (IF 1.494) Pub Date : 2020-06-25
    Jonah Blasiak; Jennifer Morse; Anna Pun; Daniel Summers

    We make a broad conjecture about the k-Schur positivity of Catalan functions, symmetric functions which generalize the (parabolic) Hall-Littlewood polynomials. We resolve the conjecture with positive combinatorial formulas in cases which address the k-Schur expansion of (1) Hall-Littlewood polynomials, proving the q=0 case of the strengthened Macdonald positivity conjecture from [24]; (2) the product

  • Stationary discs and finite jet determination for CR mappings in higher codimension
    Adv. Math. (IF 1.494) Pub Date : 2020-06-16
    Alexander Tumanov

    We discuss stationary discs for generic CR manifolds and apply them to the problem of finite jet determination for CR mappings. We prove that a C2-smooth CR diffeomorphism of two C4-smooth strictly pseudoconvex Levi generating CR manifolds is uniquely determined by its 2-jet at a given point. A new key element of the proof is the existence of non-defective stationary discs.

  • One-boson scattering processes in the massless Spin-Boson model – A non-perturbative formula
    Adv. Math. (IF 1.494) Pub Date : 2020-06-16
    Miguel Ballesteros; Dirk-André Deckert; Felix Hänle

    In scattering experiments, physicists observe so-called resonances as peaks at certain energy values in the measured scattering cross sections per solid angle. These peaks are usually associate with certain scattering processes, e.g., emission, absorption, or excitation of certain particles and systems. On the other hand, mathematicians define resonances as poles of an analytic continuation of the

  • Radiality of definable sets
    Adv. Math. (IF 1.494) Pub Date : 2020-06-12
    John Welliaveetil

    In this article we use techniques developed by Hrushovski-Loeser to study certain metric properties of the Berkovich analytification of a finite morphism of smooth connected projective curves. In recent work, M. Temkin proved a radiality statement for the topological ramification locus associated to such finite morphisms. We generalize this result in two directions. We prove a radiality statement for

  • Morse-Novikov cohomology of almost nonnegatively curved manifolds
    Adv. Math. (IF 1.494) Pub Date : 2020-06-09
    Xiaoyang Chen

    Let Mn be a closed manifold of almost nonnegative sectional curvature and nonzero first de Rham cohomology group. Using a topological argument, we show that the Morse-Novikov cohomology group Hp(Mn,θ) vanishes for any p and [θ]∈HdR1(Mn),[θ]≠0. Based on a new integral formula, we also show that a similar result holds for a closed manifold of almost nonnegative Ricci curvature under the additional assumption

  • Tableau posets and the fake degrees of coinvariant algebras
    Adv. Math. (IF 1.494) Pub Date : 2020-06-09
    Sara C. Billey; Matjaž Konvalinka; Joshua P. Swanson

    We introduce two new partial orders on the standard Young tableaux of a given partition shape, in analogy with the strong and weak Bruhat orders on permutations. Both posets are ranked by the major index statistic offset by a fixed shift. The existence of such ranked poset structures allows us to classify the realizable major index statistics on standard tableaux of arbitrary straight shape and certain

  • Characterization of the traces on the boundary of functions in magnetic Sobolev spaces
    Adv. Math. (IF 1.494) Pub Date : 2020-06-08
    Hoai-Minh Nguyen; Jean Van Schaftingen

    We characterize the trace of magnetic Sobolev spaces defined in a half-space or in a smooth bounded domain in which the magnetic field A is differentiable and its exterior derivative corresponding to the magnetic field dA is bounded. In particular, we prove that, for d≥1 and p>1, the trace of the magnetic Sobolev space WA1,p(R+d+1) is exactly WA∥1−1/p,p(Rd) where A∥(x)=(A1,…,Ad)(x,0) for x∈Rd with

  • Scalar V-soliton equation and Kähler-Ricci flow on symplectic quotients
    Adv. Math. (IF 1.494) Pub Date : 2020-06-08
    Chang Li

    In this paper, we consider the V-soliton equation which is a degenerate fully nonlinear equation introduced by La Nave and Tian in their work on Kähler-Ricci flow on symplectic quotients. One can apply the interpretation to study finite time singularities of the Kähler-Ricci flow. As in the case of Kähler-Einstein metrics, we can also reduce the V-soliton equation to a scalar equation on Kähler potentials

  • Convergence of scalar curvature of Kähler-Ricci flow on manifolds of positive Kodaira dimension
    Adv. Math. (IF 1.494) Pub Date : 2020-06-05
    Wangjian Jian

    In this paper, we consider Kähler-Ricci flow on n-dimensional Kähler manifold with semi-ample canonical line bundle and 0

  • Matrix Poincaré inequalities and concentration
    Adv. Math. (IF 1.494) Pub Date : 2020-06-05
    Richard Aoun; Marwa Banna; Pierre Youssef

    We show that any probability measure satisfying a Matrix Poincaré inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carré du champ operator. This extends to the matrix setting a classical phenomenon in the scalar case. Moreover, the proof gives rise to new matrix trace inequalities which could be of

  • Long-time asymptotics for evolutionary crystal dislocation models
    Adv. Math. (IF 1.494) Pub Date : 2020-06-05
    Matteo Cozzi; Juan Dávila; Manuel del Pino

    We consider a family of evolution equations that generalize the Peierls-Nabarro model for crystal dislocations. They can be seen as semilinear parabolic reaction-diffusion equations in which the diffusion is regulated by a fractional Laplace operator of order 2s∈(0,2) acting in one space dimension and the reaction is determined by a 1-periodic multi-well potential. We construct solutions of these equations

  • On the κ-solutions of the Ricci flow on noncompact 3-manifolds
    Adv. Math. (IF 1.494) Pub Date : 2020-06-05
    Liang Cheng; Anqiang Zhu

    In this paper we prove that there is no κ-solution of Ricci flow on 3-dimensional noncompact manifold with strictly positive sectional curvature and blow up at some finite time T satisfying ∫0TT−tR(p0,t)dt<∞ for some point p0. This partially confirms a conjecture of Perelman.

  • Product theorem for K-stability
    Adv. Math. (IF 1.494) Pub Date : 2020-06-04
    Ziquan Zhuang

    We prove a product formula for delta invariant and as an application, we show that product of K-(semi, poly)stable Fano varieties is also K-(semi, poly)stable.

  • On Fujita's freeness conjecture in dimension 5
    Adv. Math. (IF 1.494) Pub Date : 2020-06-02
    Fei Ye; Zhixian Zhu

    Let X be a smooth projective variety of dimension 5 and A an integral ample divisor on X. We show that |KX+kA| is basepoint-free for any integer k≥6.

  • Highly neighborly centrally symmetric spheres
    Adv. Math. (IF 1.494) Pub Date : 2020-06-01
    Isabella Novik; Hailun Zheng

    In 1995, Jockusch constructed an infinite family of centrally symmetric 3-dimensional simplicial spheres that are cs-2-neighborly. Here we generalize his construction and show that for all d≥3 and n≥d+1, there exists a centrally symmetric d-dimensional simplicial sphere with 2n vertices that is cs-⌈d/2⌉-neighborly. This result combined with work of Adin and Stanley completely resolves the upper bound

  • Higher order energy functionals
    Adv. Math. (IF 1.494) Pub Date : 2020-06-01
    V. Branding; S. Montaldo; C. Oniciuc; A. Ratto

    The study of higher order energy functionals was first proposed by Eells and Sampson in 1965 and, later, by Eells and Lemaire in 1983. These functionals provide a natural generalization of the classical energy functional. More precisely, Eells and Sampson suggested the investigation of the so-called ES−r-energy functionals ErES(φ)=(1/2)∫M|(d⁎+d)r(φ)|2dV, where φ:M→N is a map between two Riemannian

  • An index theory for asymptotic motions under singular potentials
    Adv. Math. (IF 1.494) Pub Date : 2020-05-29
    Vivina L. Barutello; Xijun Hu; Alessandro Portaluri; Susanna Terracini

    We develop an index theory for parabolic and collision solutions to the classical n-body problem and we prove sufficient conditions for the finiteness of the spectral index valid in a large class of trajectories ending with a total collapse or expanding with vanishing limiting velocities. Both problems suffer from a lack of compactness and can be brought in a similar form of a Lagrangian System on

  • Corrigendum to “Factorization homology I: Higher categories” [Adv. Math. 333 (2018) 1042–1177]
    Adv. Math. (IF 1.494) Pub Date : 2020-05-29
    David Ayala; John Francis; Nick Rozenblyum

    In our previous article [1], a functor was constructed from an ∞-category of (∞,n)-categories to space-valued invariants on vari-framed stratified n-manifolds. This functor was asserted to be fully-faithful, based on a calculation that a space of conically smooth diffeomorphisms of a hemispherically stratified n-disk that preserve a vari-framing is contractible. This core calculation is false in dimensions

  • Assouad dimension and local structure of self-similar sets with overlaps in Rd
    Adv. Math. (IF 1.494) Pub Date : 2020-05-29
    Ignacio García

    For a self-similar set in Rd that is the attractor of an iterated function system that does not verify the weak separation property, Fraser, Henderson, Olson and Robinson showed that its Assouad dimension is at least 1. In this paper, it is shown that the Assouad dimension of such a set is the sum of the dimension of the vector space spanned by the set of overlapping directions and the Assouad dimension

  • On partition identities of Capparelli and Primc
    Adv. Math. (IF 1.494) Pub Date : 2020-05-29
    Jehanne Dousse

    We show that, up to multiplication by a factor 1(cq;q)∞, the weighted words version of Capparelli's identity is a particular case of the weighted words version of Primc's identity. We prove this first using recurrences, and then bijectively. We also give finite versions of both identities.

  • Matching fields and lattice points of simplices
    Adv. Math. (IF 1.494) Pub Date : 2020-05-28
    Georg Loho; Ben Smith

    We show that the Chow covectors of a linkage matching field define a bijection between certain degree vectors and lattice points, and we demonstrate how one can recover the linkage matching field from this bijection. This resolves two open questions from Sturmfels and Zelevinsky (1993) [26] on linkage matching fields. For this, we give an explicit construction that associates a bipartite incidence

  • Hessian estimates for equations involving p-Laplacian via a fundamental inequality
    Adv. Math. (IF 1.494) Pub Date : 2020-05-28
    Hongjie Dong; Fa Peng; Yi Ru-Ya Zhang; Yuan Zhou

    In this paper, we prove a fundamental inequality for the algebraic structure of ΔvΔ∞v: for every v∈C∞,||D2vDv|2−ΔvΔ∞v−12[|D2v|2−(Δv)2]|Dv|2|≤n−22[|D2v|2|Dv|2−|D2vDv|2], where Δ is the Laplacian and Δ∞ is the ∞-Laplacian. Based on this, we prove the following results: (i) For any p-harmonic functions u with p∈(1,2)∪(2,∞), we have|Du|p−γ2Du∈Wloc1,2with γ2. (ii) When n≥2 and p∈(1,2)∪(2,3+2n−2), the viscosity

  • Beurling integers with RH and large oscillation
    Adv. Math. (IF 1.494) Pub Date : 2020-05-28
    Frederik Broucke; Gregory Debruyne; Jasson Vindas

    We construct a Beurling generalized number system satisfying the Riemann hypothesis and whose integer counting function displays extremal oscillation in the following sense. The prime counting function of this number system satisfies π(x)=Li(x)+O(x), while its integer counting function satisfies the oscillation estimate N(x)=ρx+Ω±(xexp⁡(−clog⁡xlog⁡log⁡x)) for some c>0, where ρ>0 is its asymptotic density

  • A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics
    Adv. Math. (IF 1.494) Pub Date : 2020-05-28
    Tobias Fritz

    We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions

  • A bound on the number of rationally invisible repelling orbits
    Adv. Math. (IF 1.494) Pub Date : 2020-05-27
    Anna Miriam Benini; Núria Fagella

    We consider entire transcendental maps with bounded set of singular values such that periodic rays exist and land. For such maps, we prove a refined version of the Fatou-Shishikura inequality which takes into account rationally invisible periodic orbits, that is, repelling cycles which are not landing points of any periodic ray. More precisely, if there are q<∞ singular orbits, then the sum of the

  • Moment maps, strict linear precision, and maximum likelihood degree one
    Adv. Math. (IF 1.494) Pub Date : 2020-05-27
    Patrick Clarke; David A. Cox

    We study the moment maps of a smooth projective toric variety. In particular, we characterize when the moment map coming from the quotient construction is equal to a weighted Fubini-Study moment map. This leads to an investigation into polytopes with strict linear precision, and in the process we use results from and find remarkable connections between Symplectic Geometry, Geometric Modeling, Algebraic

  • Periodic Jacobi matrices on trees
    Adv. Math. (IF 1.494) Pub Date : 2020-05-27
    Nir Avni; Jonathan Breuer; Barry Simon

    We begin the systematic study of the spectral theory of periodic Jacobi matrices on trees including a formal definition. The most significant result that appears here for the first time is that these operators have no singular continuous spectrum. We review important previous results of Sunada and Aomoto and present several illuminating examples. We present many open problems and conjectures that we

  • On the behavior of modules of m-integrable derivations in the sense of Hasse-Schmidt under base change
    Adv. Math. (IF 1.494) Pub Date : 2020-05-27
    María de la Paz Tirado Hernández

    We study the behavior of modules of m-integrable derivations of a commutative finitely generated algebra in the sense of Hasse-Schmidt under base change. We focus on the case of separable ring extensions over a field of positive characteristic and on the case where the extension is a polynomial ring in an arbitrary number of variables.

  • The C0 estimate for the quaternionic Calabi conjecture
    Adv. Math. (IF 1.494) Pub Date : 2020-05-27
    Marcin Sroka

    We prove the C0 estimate for the quaternionic Monge-Ampère equation on compact hyperKähler with torsion manifolds. Our goal is to provide a simpler proof than the one presented in [3].

  • Continued fractions and orderings on the Markov numbers
    Adv. Math. (IF 1.494) Pub Date : 2020-05-27
    Michelle Rabideau; Ralf Schiffler

    Markov numbers are integers that appear in the solution triples of the Diophantine equation, x2+y2+z2=3xyz, called the Markov equation. A classical topic in number theory, these numbers are related to many areas of mathematics such as combinatorics, hyperbolic geometry, approximation theory and cluster algebras. There is a natural map from the rational numbers between zero and one to the Markov numbers

  • On large values of Weyl sums
    Adv. Math. (IF 1.494) Pub Date : 2020-05-25
    Changhao Chen; Igor E. Shparlinski

    A special case of the Menshov–Rademacher theorem implies for almost all polynomials x1Z+…+xdZd∈R[Z] of degree d for the Weyl sums satisfy the upper bound|∑n=1Nexp⁡(2πi(x1n+…+xdnd))|⩽N1/2+o(1),N→∞. Here we investigate the exceptional sets of coefficients (x1,…,xd) with large values of Weyl sums for infinitely many N, and show that in terms of the Baire categories and Hausdorff dimension they are quite

  • Blowup stability at optimal regularity for the critical wave equation
    Adv. Math. (IF 1.494) Pub Date : 2020-05-22
    Roland Donninger; Ziping Rao

    We establish Strichartz estimates for the radial energy-critical wave equation in 5 dimensions in similarity coordinates. Using these, we prove the nonlinear asymptotic stability of the ODE blowup in the energy space.

  • Representations of simple Jordan superalgebras
    Adv. Math. (IF 1.494) Pub Date : 2020-05-22
    Iryna Kashuba; Vera Serganova

    This paper completes description of categories of representations of finite-dimensional simple unital Jordan superalgebras over algebraically closed field of characteristic zero.

  • Elliptic extension of Gustafson's q-integral of type G2
    Adv. Math. (IF 1.494) Pub Date : 2020-05-21
    Masahiko Ito; Masatoshi Noumi

    The evaluation formula for an elliptic beta integral of type G2 is proved. The integral is expressed by a product of Ruijsenaars' elliptic gamma functions, and the formula includes that of Gustafson's q-beta integral of type G2 as a special limiting case as p→0. The elliptic beta integral of type BC1 by van Diejen and Spiridonov is effectively used in the proof of the evaluation formula.

  • Motivic zeta functions on Q-Gorenstein varieties
    Adv. Math. (IF 1.494) Pub Date : 2020-05-19
    Edwin León-Cardenal; Jorge Martín-Morales; Willem Veys; Juan Viu-Sos

    We study motivic zeta functions for Q-divisors in a Q-Gorenstein variety. By using a toric partial resolution of singularities we reduce this study to the local case of two normal crossing divisors where the ambient space is an abelian quotient singularity. For the latter we provide a closed formula which is worked out directly on the quotient singular variety. As a first application we provide a family

  • Brunn-Minkowski type inequalities for the lattice point enumerator
    Adv. Math. (IF 1.494) Pub Date : 2020-05-19
    David Iglesias; Jesús Yepes Nicolás; Artem Zvavitch

    Geometric and functional Brunn-Minkowski type inequalities for the lattice point enumerator Gn(⋅) are provided. In particular, we show thatGn((1−λ)K+λL+(−1,1)n)1/n≥(1−λ)Gn(K)1/n+λGn(L)1/n for any non-empty bounded sets K,L⊂Rn and all λ∈(0,1). We also show that these new discrete versions imply the classical results, and discuss some links with other related inequalities.

  • The FFRT property of two-dimensional normal graded rings and orbifold curves
    Adv. Math. (IF 1.494) Pub Date : 2020-05-19
    Nobuo Hara; Ryo Ohkawa

    We study the finite F-representation type (abbr. FFRT) property of a two-dimensional normal graded ring R in characteristic p>0, using notions from the theory of algebraic stacks. Given a graded ring R, we consider an orbifold curve C, which is a root stack over the smooth curve C=ProjR, such that R is the section ring associated with a line bundle L on C. The FFRT property of R is then rephrased with

  • A finite-tame-wild trichotomy theorem for tensor diagrams
    Adv. Math. (IF 1.494) Pub Date : 2020-05-18
    Jacob Turner

    In this paper, we consider the problem of determining when two tensor networks are equivalent under a heterogeneous change of basis. In particular, to a tensor (or string) diagram in a certain monoidal category (which we call tensor diagrams), we formulate an associated abelian category of representations. Each representation corresponds to a tensor network on that diagram. We then classify which tensor

  • Breaking the 12-barrier for the twisted second moment of Dirichlet L-functions
    Adv. Math. (IF 1.494) Pub Date : 2020-05-15
    Hung M. Bui; Kyle Pratt; Nicolas Robles; Alexandru Zaharescu

    We study the second moment of Dirichlet L-functions to a large prime modulus q twisted by the square of an arbitrary Dirichlet polynomial. We break the 12-barrier in this problem, and obtain an asymptotic formula provided that the length of the Dirichlet polynomial is less than q51/101=q1/2+1/202. As an application, we obtain an upper bound of the correct order of magnitude for the third moment of

  • Modular operads and the nerve theorem
    Adv. Math. (IF 1.494) Pub Date : 2020-05-15
    Philip Hackney; Marcy Robertson; Donald Yau

    We describe a category of undirected graphs which comes equipped with a faithful functor into the category of (colored) modular operads. The associated singular functor from modular operads to presheaves is fully faithful, and its essential image can be classified by a Segal condition. This theorem can be used to recover a related statement, due to André Joyal and Joachim Kock, concerning a larger

  • On bifibrations of model categories
    Adv. Math. (IF 1.494) Pub Date : 2020-05-13
    Pierre Cagne; Paul-André Melliès

    In this article, we develop a notion of Quillen bifibration whose purpose is to combine the two notions of Grothendieck bifibration and of Quillen model structure. In particular, given a bifibration p:E→B, we describe when a family of model structures on the fibers EA and on the basis category B combines into a model structure on the total category E, such that the functor p preserves cofibrations

  • Two-row W-graphs in affine type A
    Adv. Math. (IF 1.494) Pub Date : 2020-05-13
    Dongkwan Kim; Pavlo Pylyavskyy

    For affine symmetric groups we construct finite W-graphs corresponding to two-row shapes, and prove their uniqueness. This gives the first non-trivial family of purely combinatorial constructions of finite W-graphs in an affine type. We compare our construction with quotients of periodic W-graphs defined by Lusztig. Under certain positivity assumption on the latter the two are shown to be isomorphic

  • Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature
    Adv. Math. (IF 1.494) Pub Date : 2020-05-08
    D. Cushing; S. Kamtue; J. Koolen; S. Liu; F. Münch; N. Peyerimhoff

    We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers sharp graphs (hypercubes, cocktail party graphs, even-dimensional demi-cubes, Johnson graphs J(2n,n), the Gosset graph and suitable Cartesian products). We also present a purely combinatorial reformulation of this result. We

  • Topological generation of exceptional algebraic groups
    Adv. Math. (IF 1.494) Pub Date : 2020-05-07
    Timothy C. Burness; Spencer Gerhardt; Robert M. Guralnick

    Let G be a simple algebraic group over an algebraically closed field k and let C1,…,Ct be non-central conjugacy classes in G. In this paper, we consider the problem of determining whether there exist gi∈Ci such that 〈g1,…,gt〉 is Zariski dense in G. First we establish a general result, which shows that if Ω is an irreducible subvariety of Gt, then the set of tuples in Ω generating a dense subgroup of

  • Amalgamation and Ramsey properties of Lp spaces
    Adv. Math. (IF 1.494) Pub Date : 2020-05-07
    V. Ferenczi; J. Lopez-Abad; B. Mbombo; S. Todorcevic

    We study the dynamics of the group of isometries of Lp-spaces. In particular, we study the canonical actions of these groups on the space of δ-isometric embeddings of finite dimensional subspaces of Lp(0,1) into itself, and we show that for every real number 1≤p<∞ with p≠4,6,8,… they are ε-transitive provided that δ is small enough. We achieve this by extending the classical equimeasurability principle

  • Higher dimensional generalizations of the Thompson groups
    Adv. Math. (IF 1.494) Pub Date : 2020-05-07
    Mark V. Lawson; Alina Vdovina

    Motivated by the goal of generalizing the Cuntz-Krieger algebras, and making heavy use of the pioneering work of Robertson and Steger, Kumjian and Pask generalized the notion of a directed graph to what they termed a ‘higher rank graph’. The C⁎-algebras constructed from such higher rank graphs have proved to be highly interesting. Higher rank graphs are, in fact, a class of cancellative categories

  • Archimedean non-vanishing, cohomological test vectors, and standard L-functions of GL2n: Complex case
    Adv. Math. (IF 1.494) Pub Date : 2020-05-07
    Bingchen Lin; Fangyang Tian

    The purpose of this paper is to study the local zeta integrals of Friedberg-Jacquet at complex place and to establish similar results to the recent work [4] joint with C. Chen and D. Jiang. In this paper, we will (1) give a necessary and sufficient condition on an irreducible essentially tempered cohomological representation π of GL2n(C) with a non-zero Shalika model; (2) construct a new twisted linear

  • Higher Steenrod squares for Khovanov homology
    Adv. Math. (IF 1.494) Pub Date : 2020-05-06
    Federico Cantero Morán

    We describe stable cup-i products on the cochain complex with F2 coefficients of any augmented semi-simplicial object in the Burnside category. An example of such an object is the Khovanov functor of Lawson, Lipshitz and Sarkar. Thus we obtain explicit formulas for cohomology operations on the Khovanov homology of any link.

  • Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations
    Adv. Math. (IF 1.494) Pub Date : 2020-05-05
    Kurusch Ebrahimi-Fard; Loïc Foissy; Joachim Kock; Frédéric Patras

    We establish and explore a relationship between two approaches to moment-cumulant relations in free probability theory: on one side the main approach, due to Speicher, given in terms of Möbius inversion on the lattice of noncrossing partitions, and on the other side the more recent non-commutative shuffle-algebra approach, where the moment-cumulant relations take the form of certain exponential-logarithm

  • Overdetermined systems of equations on toric, spherical, and other algebraic varieties
    Adv. Math. (IF 1.494) Pub Date : 2020-05-05
    Leonid Monin

    Let E1,…,Ek be a collection of linear series on an irreducible algebraic variety X over C which is not assumed to be complete or affine. That is, Ei⊂H0(X,Li) is a finite dimensional subspace of the space of regular sections of line bundles Li. Such a collection is called overdetermined if the generic systems1=…=sk=0, with si∈Ei does not have any roots on X. In this paper we study consistent systems

  • With respect to whom are you critical?
    Adv. Math. (IF 1.494) Pub Date : 2020-05-05
    Jin-ichi Itoh; Costin Vîlcu; Tudor Zamfirescu

    For any compact Riemannian surface S and any point y in S, Qy−1 denotes the set of all points in S for which y is a critical point, and |Qy−1| its cardinality. We proved [2] together with Imre Bárány that |Qy−1|≥1, and that equality for all y∈S characterizes the surfaces homeomorphic to the sphere. Here we show, for any orientable surface S and any point y∈S, the following two main results. There exists

  • On the strength of Ramsey's theorem for trees
    Adv. Math. (IF 1.494) Pub Date : 2020-05-05
    C.T. Chong; Wei Li; Wei Wang; Yue Yang

    Let TT1 denote the principle that every finite coloring of the full binary tree has a homogeneous isomorphic subtree, i.e. one that is monochromatic. We show that over the system RCA0, the inductive strength of TT1 is weaker than Σ20-induction. This follows from the main theorem that over the same system, TT1 is Π11-conservative over Σ20-bounding plus the principle of the totality of the Ackermann

  • n-level density of the low-lying zeros of primitive Dirichlet L-functions
    Adv. Math. (IF 1.494) Pub Date : 2020-05-05
    Vorrapan Chandee; Yoonbok Lee

    Katz and Sarnak conjectured that the statistics of low-lying zeros of various family of L-functions matched with the scaling limit of eigenvalues from the random matrix theory. In this paper we confirm this statistic for a family of primitive Dirichlet L-functions matches up with corresponding statistic in the random unitary ensemble, in a range that includes the off-diagonal contribution. To estimate

  • Fundamental solutions of a class of ultra-hyperbolic operators on pseudo H-type groups
    Adv. Math. (IF 1.494) Pub Date : 2020-05-05
    Wolfram Bauer; André Froehly; Irina Markina

    Pseudo H-type Lie groups Gr,s of signature (r,s) are defined via a module action of the Clifford algebra Cℓr,s on a vector space V≅R2n. They form a subclass of all 2-step nilpotent Lie groups. Based on their algebraic structure they can be equipped with a left-invariant pseudo-Riemannian metric. Let Nr,s denote the Lie algebra corresponding to Gr,s. In the case s>0 a choice of left-invariant vector

  • Polyhedral parametrizations of canonical bases & cluster duality
    Adv. Math. (IF 1.494) Pub Date : 2020-05-04
    Volker Genz; Gleb Koshevoy; Bea Schumann

    We establish the relation of Berenstein–Kazhdan's decoration function and Gross–Hacking–Keel–Kontsevich's potential on the open double Bruhat cell in the base affine space G/N of a simple, simply connected, simply laced algebraic group G. As a byproduct we derive explicit identifications of polyhedral parametrization of canonical bases of the ring of regular functions on G/N arising from the tropicalizations

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