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Higher homotopy groups of Cuntz classes Adv. Math. (IF 1.7) Pub Date : 2024-03-12 Andrew S. Toms
Let be a unital simple separable exact C-algebra which is approximately divisible and of real rank zero. We prove that the set of positive elements in with a fixed non-compact Cuntz class has vanishing homotopy groups. Combined with work of S. Zhang for the case of compact elements, this gives a complete calculation of the homotopy groups of Cuntz classes for these algebras. Examples covered include
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Multiple ergodic averages along functions from a Hardy field: Convergence, recurrence and combinatorial applications Adv. Math. (IF 1.7) Pub Date : 2024-03-08 Vitaly Bergelson, Joel Moreira, Florian K. Richter
We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in and obtain combinatorial applications which contain, as rather special cases, several previously known (polynomial and non-polynomial) extensions of Szemerédi's theorem on arithmetic progressions
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Batalin-Vilkovisky structures on moduli spaces of flat connections Adv. Math. (IF 1.7) Pub Date : 2024-03-08 Anton Alekseev, Florian Naef, Ján Pulmann, Pavol Ševera
Let Σ be a compact oriented 2-manifold (possibly with boundary), and let be the linear span of free homotopy classes of closed oriented curves on Σ equipped with the Goldman Lie bracket defined in terms of intersections of curves. A theorem of Goldman gives rise to a Lie homomorphism from to functions on the moduli space of flat connections for , equipped with the Atiyah-Bott Poisson bracket.
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On the Čech cohomology of Morse boundaries Adv. Math. (IF 1.7) Pub Date : 2024-03-07 Elia Fioravanti, Annette Karrer, Alessandro Sisto, Stefanie Zbinden
We consider cusped hyperbolic –manifolds, and compute Čech cohomology groups of the Morse boundaries of their fundamental groups. In particular, we show that the reduced Čech cohomology with real coefficients vanishes in dimension at most and does not vanish in dimension . A similar result holds for relatively hyperbolic groups with virtually nilpotent peripherals and Bowditch boundary homeomorphic
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On hypergeometric duality conjecture Adv. Math. (IF 1.7) Pub Date : 2024-03-04 Lev Borisov, Zengrui Han
We give an explicit formula for the duality, previously conjectured by Horja and Borisov, of two systems of GKZ hypergeometric PDEs. We prove that in the appropriate limit this duality can be identified with the inverse of the Euler characteristics pairing on cohomology of certain toric Deligne-Mumford stacks, by way of Γ-series cohomology valued solutions to the equations.
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A factorisation theory for generalised power series and omnific integers Adv. Math. (IF 1.7) Pub Date : 2024-03-04 Sonia L'Innocente, Vincenzo Mantova
We prove that in every ring of generalised power series with non-positive real exponents and coefficients in a field of characteristic zero, every series admits a factorisation into finitely many irreducibles with infinite support, the number of which can be bounded in terms of the order type of the series, and a unique product, up to multiplication by a unit, of factors with finite support.
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Rigidity and flexibility of polynomial entropy Adv. Math. (IF 1.7) Pub Date : 2024-03-04 Samuel Roth, Zuzana Roth, Ľubomír Snoha
We introduce the notion of a one-way horseshoe for topological dynamical systems and show that, quite surprisingly, it plays the same role in the theory of polynomial entropy as the notion of a horseshoe plays in the theory of topological entropy. Indeed, we show that the existence of a one-way horseshoe gives a lower bound for polynomial entropy and for maps of the interval also conversely, polynomial
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The fields of values of the height zero characters Adv. Math. (IF 1.7) Pub Date : 2024-03-04 Gabriel Navarro, Lucas Ruhstorfer, Pham Huu Tiep, Carolina Vallejo
We determine what are the fields of values of the irreducible -height zero characters of all finite groups for ; we conjecture what they should be for odd primes, and reduce this statement to a problem on blocks of quasi-simple groups.
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Universality of free random variables: Atoms for non-commutative rational functions Adv. Math. (IF 1.7) Pub Date : 2024-03-04 Octavio Arizmendi, Guillaume Cébron, Roland Speicher, Sheng Yin
Consider a tuple of normal operators in a tracial operator algebra setting with prescribed sizes of the eigenspaces for each . We address the question what one can say about the sizes of the eigenspaces for any non-commutative polynomial in those operators? We show that for each polynomial there are unavoidable eigenspaces, which occur in for any with the prescribed eigenspaces for the marginals. We
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Hyperlogarithmic functional equations on del Pezzo surfaces Adv. Math. (IF 1.7) Pub Date : 2024-03-04 Ana-Maria Castravet, Luc Pirio
For any , we prove that the web of conics on a del Pezzo surface of degree carries a functional identity whose components are antisymmetric hyperlogarithms of weight . Our approach is uniform with respect to and relies on classical results about the action of the Weyl group on the set of lines on the del Pezzo surface. These hyperlogarithmic functional identities are natural generalizations of the
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Reflecting measures Adv. Math. (IF 1.7) Pub Date : 2024-03-04 Joan Bagaria, Gabriel Goldberg
We give new, purely combinatorial characterizations of several kinds of large cardinals, such as strongly -compact and -extendible, in terms of . We then study the key property of of elementary embeddings that witness strong -compactness, which prompts the introduction of the new large-cardinal notion of cardinal. Then we prove, assuming the Ultrapower Axiom, that a cardinal is tightly -compact if
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A family of exotic group C*-algebras Adv. Math. (IF 1.7) Pub Date : 2024-03-01 Maria Gerasimova, Nicolas Monod
We show that a large family of groups without non-abelian free subgroups satisfy the following strengthening of non-amenability: they each have a rich supply of irreducible representations defining exotic C*-algebras. The construction is explicit.
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On rank one log del Pezzo surfaces in characteristic different from two and three Adv. Math. (IF 1.7) Pub Date : 2024-03-01 Justin Lacini
We classify all log del Pezzo surfaces of Picard number one defined over algebraically closed fields of characteristic different from two and three. We also discuss some consequences of the classification. For example, we show that log del Pezzo surfaces of Picard number one defined over algebraically closed fields of characteristic larger than five admit a log resolution that lifts to characteristic
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On a smoothness characterization for good moduli spaces Adv. Math. (IF 1.7) Pub Date : 2024-03-01 Dan Edidin, Matthew Satriano, Spencer Whitehead
Let be a smooth Artin stack with properly stable good moduli space . The purpose of this paper is to prove that a simple geometric criterion can often characterize when the moduli space is smooth and the morphism is flat.
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The local categorical DT/PT correspondence Adv. Math. (IF 1.7) Pub Date : 2024-03-01 Tudor Pădurariu, Yukinobu Toda
In this paper, we prove the categorical wall-crossing formula for certain quivers containing the three loop quiver, which we call DT/PT quivers. These quivers appear as Ext-quivers for the wall-crossing of DT/PT moduli spaces on Calabi-Yau 3-folds. The resulting formula is a semiorthogonal decomposition which involves quasi-BPS categories studied in our previous papers, and we regard it as a categorical
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Homoclinic and heteroclinic intersections for lemon billiards Adv. Math. (IF 1.7) Pub Date : 2024-03-01 Xin Jin, Pengfei Zhang
We study the dynamical billiards on a symmetric lemon table , where is the intersection of two unit disks with center distance . We show that there exists such that for all (except possibly a discrete subset), the billiard map on the lemon table admits crossing homoclinic and heteroclinic intersections. In particular, such lemon billiards have positive topological entropy.
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On some conjectures of the unitary dual of U(p,q) Adv. Math. (IF 1.7) Pub Date : 2024-03-01 Kayue Daniel Wong
In this manuscript, we introduce the notion of fundamental cases to study the unitary dual of . As applications, we prove of a conjecture of Salamanca-Riba and Vogan stated in 1998, as well as the fundamental parallelepiped (FPP) conjecture of Vogan in 2023 for .
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Spectral self-similar measures with alternate contraction ratios and consecutive digits Adv. Math. (IF 1.7) Pub Date : 2024-03-01 Hai-Hua Wu
Let be an iterated function system defined by , , where and is a positive integer. Let be a self-similar measure defined by . We show that is a spectral measure if and only if for some nature number and 2 divides . Moreover, we introduce a useful way to determine the spectrality of the convolution of two infinitely supported measures.
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Maximal and Borel Anosov representations into Sp(4,R) Adv. Math. (IF 1.7) Pub Date : 2024-02-29 Colin Davalo
We prove that any Borel Anosov representation of a surface group into that has maximal Toledo invariant must be Hitchin. We also prove that a representation of a surface group into that is -Anosov is maximal if and only if it satisfies the hyperconvexity property .
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A dichotomy for the dimension of SRB measure Adv. Math. (IF 1.7) Pub Date : 2024-02-29 Haojie Ren
We study dynamical systems generated by skew products: where integer , and is a real analytic -periodic function. We prove the following dichotomy for the SRB measure for : Either the support of is a graph of real analytic function, or the dimension of is equal to . Furthermore, given and , the former alternative only happens for finitely many unless is constant.
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Automorphisms of the quantum cohomology of the Springer resolution and applications Adv. Math. (IF 1.7) Pub Date : 2024-02-29 Changzheng Li, Changjian Su, Rui Xiong
In this paper, we introduce quantum Demazure–Lusztig operators acting by ring automorphisms on the equivariant quantum cohomology of the Springer resolution. Our main application is a presentation of the torus-equivariant quantum cohomology in terms of generators and relations. We provide explicit descriptions for the classical types. We also recover Kim's earlier results for the complete flag varieties
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Minor identities for Sklyanin determinants Adv. Math. (IF 1.7) Pub Date : 2024-02-29 Naihuan Jing, Jian Zhang
We explore the invariant theory of quantum symmetric spaces of orthogonal and symplectic types by employing R-matrix techniques. Our focus involves establishing connections among the quantum determinant, Sklyanin determinants associated with the orthogonal and symplectic cases, and the quantum Pfaffians over the symplectic quantum space. Drawing inspiration from twisted Yangians, we not only demonstrate
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K-rings of wonderful varieties and matroids Adv. Math. (IF 1.7) Pub Date : 2024-02-28 Matt Larson, Shiyue Li, Sam Payne, Nicholas Proudfoot
We study the -ring of the wonderful variety of a hyperplane arrangement and give a combinatorial presentation that depends only on the underlying matroid. We use this combinatorial presentation to define the -ring of an arbitrary loopless matroid. We construct an exceptional isomorphism, with integer coefficients, to the Chow ring of the matroid that satisfies a Hirzebruch–Riemann–Roch-type formula
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L2-Dolbeault resolution of the lowest Hodge piece of a Hodge module Adv. Math. (IF 1.7) Pub Date : 2024-02-27 Junchao Shentu, Chen Zhao
In this paper, we introduce a coherent subsheaf of Saito's -sheaf, which combines the -sheaf and the multiplier ideal sheaf. We construct its -Dolbeault resolution, which generalizes MacPherson's conjecture on the resolution of the Grauert-Riemenschneider sheaf. We also prove various transcendentally-based vanishing theorems for the -sheaf, including Saito's vanishing theorem, Kawamata-Viehweg vanishing
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Invariants for Gromov's pyramids and their applications Adv. Math. (IF 1.7) Pub Date : 2024-02-27 Syota Esaki, Daisuke Kazukawa, Ayato Mitsuishi
Pyramids introduced by Gromov are generalized objects of metric spaces with Borel probability measures. We study non-trivial pyramids, where non-trivial means that they are not represented as metric measure spaces. In this paper, we establish general theory of invariants of pyramids and construct several invariants. Using them, we distinguish concrete pyramids. Furthermore, we study a space consisting
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On the equality of test ideals Adv. Math. (IF 1.7) Pub Date : 2024-02-27 Ian Aberbach, Craig Huneke, Thomas Polstra
We provide a natural criterion that implies equality of the test ideal and big test ideal in local rings of prime characteristic. Most notably, we show that the criterion is met by every local weakly -regular ring whose anti-canonical algebra is Noetherian on the punctured spectrum.
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Brackets and products from centres in extension categories Adv. Math. (IF 1.7) Pub Date : 2024-02-27 Domenico Fiorenza, Niels Kowalzig
Building on Retakh's approach to Ext groups through categories of extensions, Schwede reobtained the well-known Gerstenhaber algebra structure on Ext groups over bimodules of associative algebras both from splicing extensions (leading to the cup product) and from a suitable loop in the categories of extensions (leading to the Lie bracket). We show how Schwede's construction admits a vast generalisation
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Critical points of arbitrary energy for the Trudinger-Moser functional in planar domains Adv. Math. (IF 1.7) Pub Date : 2024-02-27 Andrea Malchiodi, Luca Martinazzi, Pierre-Damien Thizy
Given a smoothly bounded non-contractible domain , we prove the existence of positive critical points of the Trudinger-Moser embedding for arbitrary Dirichlet energies. This is done via degree theory, sharp compactness estimates and a topological argument relying on the Poincaré-Hopf theorem.
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Lagrangian multi-sections and their toric equivariant mirror Adv. Math. (IF 1.7) Pub Date : 2024-02-27 Yong-Geun Oh, Yat-Hin Suen
The SYZ conjecture suggests a folklore that “Lagrangian multi-sections are mirror to holomorphic vector bundles”. In this paper, we prove this folklore for Lagrangian multi-sections inside the cotangent bundle of a vector space, which are equivariantly mirror to complete toric varieties by the work of Fang-Liu-Treumann-Zaslow. We also introduce the , which asks whether one can construct an unobstructed
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Construction of Kuranishi structures on the moduli spaces of pseudo-holomorphic disks: II Adv. Math. (IF 1.7) Pub Date : 2024-02-27 Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono
This is the second of a series of two articles in which we provide detailed and self-contained account of the construction of a system of Kuranishi structures on the moduli spaces of pseudo-holomorphic disks. Using the notion of obstruction bundle data introduced in , we give a systematic way of constructing a system of Kuranishi structures on the moduli spaces of pseudo-holomorphic disks which are
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Minimal heights and defect groups with two character degrees Adv. Math. (IF 1.7) Pub Date : 2024-02-27 Gunter Malle, Alexander Moretó, Noelia Rizo
Conjecture A of predicts the equality between the smallest positive height of the irreducible characters in a -block of a finite group and the smallest positive height of the irreducible characters in its defect group. Hence, it can be seen as a generalization of Brauer's famous height zero conjecture. One inequality was shown to be a consequence of Dade's Projective Conjecture. We prove the other
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The Brown measure of a sum of two free random variables, one of which is triangular elliptic Adv. Math. (IF 1.7) Pub Date : 2024-02-26 Serban Belinschi, Zhi Yin, Ping Zhong
The triangular elliptic operators are natural extensions of the elliptic deformation of circular operators. We obtain a Brown measure formula for the sum of a triangular elliptic operator with a random variable , which is ⁎-free from with amalgamation over certain unital subalgebra. Let be a circular operator. We prove that the Brown measure of is the push-forward measure of the Brown measure of by
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Geometric realisations of the unipotent enveloping algebra of a quiver Adv. Math. (IF 1.7) Pub Date : 2024-02-23 Lucien Hennecart
We compare and generalise the various geometric constructions (due to Ringel, Lusztig, Schofield, Bozec, Davison...) of the unipotent generalised Kac–Moody algebra associated with an arbitrary quiver. These constructions are interconnected through several geometric operations, including the stalk Euler characteristic of constructible complexes, the characteristic cycle, the Euler obstruction map, and
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Disk counting statistics near hard edges of random normal matrices: The multi-component regime Adv. Math. (IF 1.7) Pub Date : 2024-02-23 Yacin Ameur, Christophe Charlier, Joakim Cronvall, Jonatan Lenells
We consider a two-dimensional point process whose points are separated into two disjoint components by a hard wall, and study the multivariate moment generating function of the corresponding disk counting statistics. We investigate the “hard edge regime” where all disk boundaries are a distance of order away from the hard wall, where is the number of points. We prove that as , the asymptotics of the
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On the Duflo-Serganova functor for the queer Lie superalgebra Adv. Math. (IF 1.7) Pub Date : 2024-02-23 M. Gorelik, A. Sherman
We study the Duflo-Serganova functor for the queer Lie superalgebra and for all odd with semisimple. For the case when the rank of is 1 we give a formula for multiplicities in terms of the arc diagram attached to a dominant weight . Further, we prove that is semisimple if is a simple finite-dimensional module and is of rank 1 satisfying .
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Non-uniqueness times for the maximizer of the KPZ fixed point Adv. Math. (IF 1.7) Pub Date : 2024-02-23 Duncan Dauvergne
Let be the KPZ fixed point started from any initial condition that guarantees has a maximum at every time almost surely. For any fixed , almost surely is uniquely attained. However, there are exceptional times when is achieved at multiple points. Let denote the set of times when is achieved at exactly points. We show that almost surely has Hausdorff dimension 2/3 and is dense, has Hausdorff dimension
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Euler characteristics of homogeneous and weighted-homogeneous hypersurfaces Adv. Math. (IF 1.7) Pub Date : 2024-02-22 Marc Levine, Simon Pepin Lehalleur, Vasudevan Srinivas
Let be a perfect field and let be the Grothendieck-Witt ring of (virtual) non-degenerate symmetric bilinear forms over . We develop methods for computing the quadratic Euler characteristic for a smooth hypersurface in a projective space and in a weighted projective space. We raise the question of a quadratic refinement of classical conductor formulas and find such a formula for the degeneration of
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Non-diagonal critical central sections of the cube Adv. Math. (IF 1.7) Pub Date : 2024-02-22 Gergely Ambrus, Barnabás Gárgyán
We study the -dimensional volume of central hyperplane sections of the -dimensional cube . Our main goal is two-fold: first, we provide an alternative, simpler argument for proving that the volume of the section perpendicular to the main diagonal of the cube is strictly locally maximal for every , which was shown before by L. Pournin . Then, we prove that non-diagonal critical central sections of exist
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Semi-modules and crystal bases via affine Deligne-Lusztig varieties Adv. Math. (IF 1.7) Pub Date : 2024-02-22 Ryosuke Shimada
There are two combinatorial ways of parameterizing the -orbits of the irreducible components of affine Deligne-Lusztig varieties for and superbasic . One way is to use the extended semi-modules introduced by Viehmann. The other way is to use the crystal bases introduced by Kashiwara and Lusztig. In this paper, we give an explicit correspondence between them using the crystal structure.
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Quantitative rigidity of almost maximal volume entropy for both [formula omitted] spaces and integral Ricci curvature bound Adv. Math. (IF 1.7) Pub Date : 2024-02-22 Lina Chen, Shicheng Xu
The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian -manifold with a negative lower Ricci curvature bound and a upper diameter bound, it was known that it admits an almost maximal volume entropy if and only if it is diffeomorphic and Gromov-Hausdorff close to a hyperbolic space
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Commensurability of lattices in right-angled buildings Adv. Math. (IF 1.7) Pub Date : 2024-02-22 Sam Shepherd
Let Γ be a graph product of finite groups, with finite underlying graph, and let Δ be the associated right-angled building. We prove that a uniform lattice Λ in the cubical automorphism group is weakly commensurable to Γ if and only if all convex subgroups of Λ are separable. As a corollary, any two finite special cube complexes with universal cover Δ have a common finite cover. An important special
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Non-simplicial quantum toric varieties Adv. Math. (IF 1.7) Pub Date : 2024-02-21 Antoine Boivin
This paper defines quantum toric varieties associated with an arbitrary fan in a finitely generated subgroup of some . This is a generalization of the results of the article of Katzarkov, Lupercio, Meersseman and Verjovsky.
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Operator algebras of free wreath products Adv. Math. (IF 1.7) Pub Date : 2024-02-21 Pierre Fima, Arthur Troupel
We give a description of operator algebras of free wreath products in terms of fundamental algebras of graphs of operator algebras as well as an explicit formula for the Haar state. This allows us to deduce stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity and K-amenability. We study qualitative properties of the associated von Neumann algebra:
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On minimal non-σ-scattered linear orders Adv. Math. (IF 1.7) Pub Date : 2024-02-21 James Cummings, Todd Eisworth, Justin Tatch Moore
The purpose of this article is to give new constructions of linear orders which are with respect to being . Specifically, we will show that Jensen's principle ⋄ implies that there is a minimal Countryman line, answering a question of Baumgartner . We also produce the first consistent examples of minimal non--scattered linear orders of cardinality greater than , as given a successor cardinal , we obtain
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Open Gromov-Witten invariants from the Fukaya category Adv. Math. (IF 1.7) Pub Date : 2024-02-21 Kai Hugtenburg
This paper proposes a framework to show that the Fukaya category of a symplectic manifold determines the open Gromov-Witten invariants of Lagrangians . We associate to an object in an -category an extension of the negative cyclic homology, called . We extend the Getzler-Gauss-Manin connection to relative cyclic homology. Then, we construct (under simplifying technical assumptions) a relative cyclic
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t-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras Adv. Math. (IF 1.7) Pub Date : 2024-02-21 Masaki Kashiwara, Se-jin Oh
As every simple module of a quiver Hecke algebra appears as the image of the R-matrix defined on the convolution product of certain cuspidal modules, knowing the -invariants of the R-matrices between cuspidal modules is quite significant. In this paper, we prove that the -Cartan matrix specialized at of finite type, called the , inform us of the invariants of R-matrices. To prove this, we use combinatorial
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A relative Yau-Tian-Donaldson conjecture and stability thresholds Adv. Math. (IF 1.7) Pub Date : 2024-02-21 Antonio Trusiani
Generalizing Fujita-Odaka invariant, we define a function on a set of -divisors over a smooth Fano variety. This allows us to provide a new characterization of uniform -stability. A key role is played by a new Riemann-Zariski formalism for -stability.
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On shadowing and chain recurrence in linear dynamics Adv. Math. (IF 1.7) Pub Date : 2024-02-21 Nilson C. Bernardes Jr., Alfred Peris
In the present work we study the concepts of shadowing and chain recurrence in the setting of linear dynamics. We prove that shadowing and finite shadowing always coincide for operators on Banach spaces, but we exhibit operators on the Fréchet space of entire functions that have the finite shadowing property but do not have the shadowing property. We establish a characterization of mixing for continuous
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Actions on positively curved manifolds and boundary in the orbit space Adv. Math. (IF 1.7) Pub Date : 2024-02-21 Claudio Gorodski, Andreas Kollross, Burkhard Wilking
We study isometric actions of compact Lie groups on complete orientable positively curved -manifolds whose orbit spaces have non-empty boundary in the sense of Alexandrov geometry. In particular, we classify quotients of the unit sphere by actions of compact simple Lie groups with non-empty boundary. We deduce from this the list of representations of compact simple Lie groups that admit non-trivial
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Rigidity for piecewise smooth circle homeomorphisms and certain GIETs Adv. Math. (IF 1.7) Pub Date : 2024-02-20 Przemysław Berk, Frank Trujillo
In this article, we prove a rigidity property for a class of generalized interval exchange transformations (GIETs), which contains the class of piecewise smooth circle homeomorphisms.
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New monotonicity for p-capacitary functions in 3-manifolds with nonnegative scalar curvature Adv. Math. (IF 1.7) Pub Date : 2024-02-20 Chao Xia, Jiabin Yin, Xingjian Zhou
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On separably integrable symmetric convex bodies Adv. Math. (IF 1.7) Pub Date : 2024-02-20 Vladyslav Yaskin, Bartłomiej Zawalski
An infinitely smooth symmetric convex body is called -separably integrable, , if its -dimensional isotropic volume function can be written as a finite sum of products in which the dependence on and is separated. In this paper, we will obtain a complete classification of such bodies. Namely, we will prove that if is even, then is an ellipsoid, and if is odd, then is a Euclidean ball. This generalizes
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Geometric Arveson-Douglas conjecture for the Drury-Arveson space: The case of one-dimensional variety Adv. Math. (IF 1.7) Pub Date : 2024-02-19 Jingbo Xia
We consider a class of analytic subsets of an open neighborhood of the closed unit ball in . Such an gives rise to a submodule and a quotient module of the Drury-Arveson module in variables. The geometric Arveson-Douglas conjecture predicts that the quotient module is -essentially normal for . We prove this conjecture for the case of dimension . In fact, we prove that if , then is 1-essentially normal
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The dg Leavitt algebra, singular Yoneda category and singularity category Adv. Math. (IF 1.7) Pub Date : 2024-02-15 Xiao-Wu Chen, Zhengfang Wang, Bernhard Keller, Yu Wang
For any finite dimensional algebra Λ given by a quiver with relations, we prove that its dg singularity category is quasi-equivalent to the perfect dg derived category of a dg Leavitt path algebra. The result might be viewed as a deformed version of the known description of the dg singularity category of a radical-square-zero algebra in terms of a Leavitt path algebra with trivial differential.
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Corrigendum to “Energy gap for Yang–Mills connections, II: Arbitrary closed Riemannian manifolds” [Adv. Math. 312 (2017) 547–587] Adv. Math. (IF 1.7) Pub Date : 2024-02-14 Paul M.N. Feehan
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A discrete framework for the interpolation of Banach spaces Adv. Math. (IF 1.7) Pub Date : 2024-02-14 Nick Lindemulder, Emiel Lorist
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Partial Hasse invariants for Shimura varieties of Hodge-type Adv. Math. (IF 1.7) Pub Date : 2024-02-14 Naoki Imai, Jean-Stefan Koskivirta
For a connected reductive group over a finite field, we define partial Hasse invariants on the stack of -zip flags. We obtain similar sections on the flag space of Shimura varieties of Hodge-type. They are mod automorphic forms which cut out a single codimension one stratum. We study their properties and show that such invariants admit a natural factorization through higher rank automorphic vector
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Poisson groupoids and moduli spaces of flat bundles over surfaces Adv. Math. (IF 1.7) Pub Date : 2024-02-13 Daniel Álvarez
Let Σ be a compact connected and oriented surface with nonempty boundary and let be a Lie group equipped with a bi-invariant pseudo-Riemannian metric. The moduli space of flat principal -bundles over Σ which are trivialized at a finite subset of ∂Σ carries a natural quasi-Hamiltonian structure which was introduced by Li-Bland and Ševera. By a suitable restriction of the holonomy over ∂Σ and of the
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