Advances in Mathematics最新文献

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Totally nonnegative matrices, chain enumeration and zeros of polynomials 全非负矩阵，链枚举和多项式的零

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-06 DOI: 10.1016/j.aim.2025.110760

Petter Brändén, Leonardo Saud Maia Leite

We prove that every lower unitriangular and totally nonnegative matrix gives rise to a family of polynomials with only real zeros. This has consequences for problems in several areas of mathematics. We use it to develop a general theory for chain enumeration in posets and zeros of chain polynomials. The results obtained extend and unify results of the first author, Brenti, Welker and Athanasiadis. In the process we define a notion of h-vector for a large class of posets which generalize the notions of h-vectors associated to simplicial and cubical complexes. A consequence of our methods is a characterization of the convex hull of all characteristic polynomials of hyperplane arrangements of fixed dimension and over a fixed finite field. This may be viewed as a refinement of the Critical Problem of Crapo and Rota.

We also use the methods developed to solve an open problem posed by Forgács and Tran on the real-rootedness of polynomials arising from certain bivariate rational functions.

我们证明了每一个下单角完全非负矩阵都能产生一个只有实零的多项式族。这对几个数学领域的问题产生了影响。我们利用它发展了链多项式的零和偏集链枚举的一般理论。结果得到了第一作者Brenti， Welker和Athanasiadis结果的推广和统一。在此过程中，我们定义了一大类偏序集的h向量概念，这些偏序集推广了与简单复形和立方复形相关的h向量概念。我们的方法的一个结果是对固定维数和固定有限域上的超平面排列的所有特征多项式的凸包进行了表征。这可以看作是对Crapo和Rota关键问题的改进。我们还使用开发的方法来解决由Forgács和Tran提出的关于由某些二元有理函数引起的多项式的实根性的开放问题。

引用次数: 0

Topological Hochschild homology of the image of J 象J的拓扑Hochschild同调

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-02 DOI: 10.1016/j.aim.2025.110759

David Jongwon Lee , Ishan Levy

We compute the mod

(p, v_{1})

and mod

(2, η, v_{1})

THH of many variants of the image-of-J spectrum. In particular, we do this for

j_{ζ}

, whose TC is closely related to the K-theory of the

K (1)

-local sphere. We find in particular that the failure for THH to satisfy

Z_{p}

-Galois descent for the extension

j_{ζ} \to ℓ_{p}

corresponds to the failure of the p-adic circle to be its own free loop space. For

p > 2

, we also prove the Segal conjecture for

j_{ζ}

, and we compute the K-theory of the

K (1)

-local sphere in degrees

\leq 4 p - 6

我们计算了j光谱像的许多变体的mod （p,v1）和mod (2,η,v1) THH。特别地，我们对jζ这样做，它的TC与K(1)局部球的K理论密切相关。特别地，我们发现THH不能满足扩展jζ→∑p的zp -伽罗瓦下降，对应于p进圆不能成为它自己的自由环空间。对于p>；2，我们也证明了jζ的Segal猜想，并计算了K(1)-局部球在度≤4p−6的K-理论。

引用次数: 0

The equifibered approach to ∞-properads 对∞属性的配置方法

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-02 DOI: 10.1016/j.aim.2025.110755

Shaul Barkan, Jan Steinebrunner

We define a notion of ∞-properads that generalizes ∞-operads by allowing operations with multiple outputs. Specializing to the case where each operation has a single output provides a simple new perspective on ∞-operads, but at the same time the extra generality allows for examples such as bordism categories. We also give an interpretation of our ∞-properads as Segal presheaves on a category of graphs by comparing them to the Segal ∞-properads of Hackney–Robertson–Yau. Combining these two approaches yields a flexible tool for doing higher algebra with operations that have multiple inputs and outputs. Crucially, this allows for a definition of algebras over an ∞-properad such that, for example, topological field theories are algebras over the bordism ∞-properad.

The key ingredient to this paper is the notion of an equifibered map between

E_{\infty}

-monoids, which is a well-behaved generalization of free maps. We also use this to prove facts about free

E_{\infty}

-monoids, for example that free

E_{\infty}

-monoids are closed under pullbacks along arbitrary maps.

我们定义了一个∞属性的概念，它通过允许具有多个输出的操作来推广∞操作。对于每个操作都有一个输出的情况，特殊化提供了对∞操作的一个简单的新视角，但同时，额外的通用性允许诸如边界类别之类的示例。通过与Hackney-Robertson-Yau的Segal∞-性质的比较，我们也给出了我们的∞-性质作为一类图上的Segal预束的解释。结合这两种方法，可以产生一种灵活的工具，用于处理具有多个输入和输出的操作的高等代数。至关重要的是，这允许代数在∞属性上的定义，例如，拓扑场论是在bordism∞属性上的代数。本文的关键内容是E∞-模群之间的配纤维映射的概念，它是自由映射的一个很好的推广。我们也用它证明了关于自由E∞-monoids的一些事实，例如自由E∞-monoids在沿任意映射的回拉下是闭合的。

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引用次数: 0

A relative Nash-Tognoli theorem over Q and application to the Q-algebraicity problem Q上的一个相对纳什-托格诺里定理及其在Q-代数问题中的应用

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-31 DOI: 10.1016/j.aim.2025.110757

Enrico Savi

We prove a relative version over

Q

of Nash-Tognoli theorem, that is: Let M be a compact smooth manifold with closed smooth submanifolds

M_{1}, \dots, M_{ℓ}

in general position, then there exists a nonsingular real algebraic set

M^{'} \subset R^{n}

with nonsingular algebraic subsets

M_{1}^{'}, \dots, M_{ℓ}^{'}

and a diffeomorphism

h : M \to M^{'}

such that

h (M_{i}) = M_{i}^{'}

for all

i = 1, \dots, ℓ

such that

M^{'}, M_{1}^{'}, \dots, M_{ℓ}^{'}

are described, both globally and locally, by polynomial equations with rational coefficients. In addition, if

M, M_{1}, \dots, M_{ℓ}

are nonsingular algebraic sets, then we prove the diffeomorphism

h : M \to M^{'}

can be chosen semialgebraic and the result can be extended to the noncompact case. In the proof we describe also the

Z / 2 Z

-homological cycles of real embedded Grassmannian manifolds by nonsingular algebraic representatives over

Q

via the Bott-Samelson resolution of Schubert varieties.

我们证明一个相对版本在问Nash-Tognoli定理,即:让M是一个紧凑的光滑流形与封闭光滑流形中的M1,…,Mℓ一般位置,那么存在一组非奇异的真正的代数M与非奇异的代数子集⊂Rn M1,…,Mℓ“和微分同胚映射h: M→M”这样h (Mi) = Mi的所有我= 1,…,ℓ这样M’,M1,…,Mℓ描述,全球和本地与有理系数多项式方程。此外，如果M，M1，…，M，M是非奇异代数集，则证明了微分同态h:M→M '可以是半代数的，并将结果推广到非紧情况。在证明中，我们还通过Schubert变分的bot - samelson解析，描述了Q上由非奇异代数表示的实嵌入Grassmannian流形的Z/ 2z同调循环。

引用次数: 0

Quasisymmetric geometry of low-dimensional random spaces 低维随机空间的拟对称几何

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-31 DOI: 10.1016/j.aim.2025.110758

Gefei Cai , Wen-Bo Li, Tim Mesikepp

We investigate several naturally-arising random fractals from the perspective of quasisymmetric geometry, and show that they fall outside the realm of quasisymmetric uniformization to simple canonical spaces. We begin with Brownian motion and various forms of the Schramm-Loewner evolution

{SLE}_{κ}

for

κ > 0

, showing that a.s. neither is a quasisymmetric to a straight line. We also study the conformal loop ensemble

{CLE}_{κ}

for

κ \in (\frac{8}{3}, 4]

, and show that the collection of all points outside the loops is a.s. homeomorphic to the standard Sierpiński carpet, but not quasisymmetrically equivalent to a round carpet.

从拟对称几何的角度研究了几种自然产生的随机分形，并证明了它们不属于拟对称均匀化到简单正则空间的范畴。我们从布朗运动和各种形式的Schramm-Loewner演化slek （κ>0）开始，表明两者都不是直线的准对称。我们还研究了k∈(83,4)的共形环系CLEκ，并证明环外所有点的集合与标准Sierpiński地毯同胚，但不拟对称地等效于圆形地毯。

引用次数: 0

Stability of the favorable Falkner-Skan profiles for the stationary Prandtl equations 平稳Prandtl方程有利的Falkner-Skan型的稳定性

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-30 DOI: 10.1016/j.aim.2025.110749

Sameer Iyer

The (favorable) Falkner-Skan boundary layer profiles are a one parameter (

β \in [0, 2]

) family of self-similar solutions to the stationary Prandtl system which describes the flow over a wedge with angle

β \frac{π}{2}

. The most famous member of this family is the endpoint Blasius profile,

β = 0

, which exhibits pressureless flow over a flat plate. In contrast, the

β > 0

profiles are physically expected to exhibit a favorable pressure gradient, a common adage in the physics literature. In this work, we prove quantitative scattering estimates as

x \to \infty

which precisely captures the effect of this favorable gradient through the presence of new “CK” (Cauchy-Kovalevskaya) terms that appear in a quasilinear energy cascade.

（有利的）Falkner-Skan边界层轮廓是描述角为βπ2的楔形流动的平稳Prandtl系统的单参数（β∈[0,2]）自相似解族。这个家族中最著名的成员是终点Blasius剖面，β=0，它显示了平板上的无压流动。相反，β>；0剖面在物理上被期望表现出有利的压力梯度，这是物理文献中常见的格言。在这项工作中，我们证明了定量散射估计为x→∞，它通过出现在拟线性能量级联中的新“CK”（Cauchy-Kovalevskaya）项的存在精确地捕获了这种有利梯度的影响。

引用次数: 0

Solution to Lawvere's first problem: A Grothendieck topos that has proper class many quotient topoi Lawvere第一个问题的解：一类具有适当类多商拓扑的Grothendieck拓扑

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-30 DOI: 10.1016/j.aim.2025.110751

Yuhi Kamio, Ryuya Hora

This paper solves the first of the open problems in topos theory posted by William Lawvere, concerning the existence of a Grothendieck topos that has proper class many quotient topoi. This paper concretely constructs such Grothendieck topoi, including the presheaf topos on the free monoid generated by countably infinitely many elements

PSh (M_{ω})

. Utilizing the combinatorics of the classifying topos of the theory of inhabited objects and with the help of a system of pairing functions, the problem is reduced to a theorem of Vopěnka, Pultr, and Hedrlín, which states that any set admits a rigid relational structure.

本文解决了William Lawvere在拓扑理论中提出的第一个开放问题，即具有适当类多商拓扑的Grothendieck拓扑的存在性问题。本文具体构造了这样的Grothendieck拓扑，包括由可数无穷多元PSh（Mω）生成的自由模阵上的preshef拓扑。利用居住对象理论分类拓扑的组合学，在配对函数系统的帮助下，该问题被简化为vopovinka， Pultr和Hedrlín的定理，该定理指出任何集合都承认刚性关系结构。

引用次数: 0

Hyperelliptic curves mapping to abelian varieties and applications to Beilinson's conjecture for zero-cycles 超椭圆曲线映射到阿贝尔变体及零环Beilinson猜想的应用

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-30 DOI: 10.1016/j.aim.2025.110746

Evangelia Gazaki , Jonathan Love

Let A be an abelian surface over an algebraically closed field

\overline{k}

with an embedding

\overline{k} ↪ C

. When A is isogenous to a product of elliptic curves, we describe a large collection of pairwise non-isomorphic hyperelliptic curves mapping birationally into A. For infinitely many integers

g \geq 2

, this collection has infinitely many curves of genus g, and no two curves in the collection have the same image under any isogeny from A. Using these hyperelliptic curves, we find many rational equivalences in the Chow group of zero-cycles

{CH}_{0} (A)

. We use these results to give some progress towards Beilinson's conjecture for zero-cycles, which predicts that for a smooth projective variety X over

\overline{Q}

the kernel of the Albanese map of X is zero.

设A是一个嵌入k´´“C”的代数闭域k面上的一个阿贝尔曲面。当A与椭圆曲线的乘积同构时，我们描述了一个大的两两非同构超椭圆曲线的集合，它们分别映射到A上。对于无穷多个整数g≥2，这个集合有无穷多条g属曲线，并且集合中没有两条曲线在A的任何同构下具有相同的像。利用这些超椭圆曲线，我们发现了零环CH0(A)的Chow群中的许多有理等价。我们用这些结果给出了零环的Beilinson猜想的一些进展，该猜想预测了对于Q上的光滑投影变体X， X的Albanese映射的核是零。

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引用次数: 0

Symplectic fillings of unit cotangent bundles of spheres and applications 球面单位余切束的辛填充及其应用

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-29 DOI: 10.1016/j.aim.2025.110748

Myeonggi Kwon , Takahiro Oba

We prove the uniqueness, up to diffeomorphism, of symplectically aspherical fillings of the unit cotangent bundle of odd-dimensional spheres. As applications, we first show the non-existence of exact symplectic cobordisms between some 5-dimensional Brieskorn manifolds. We also determine the diffeomorphism types of closed symplectic 6-manifolds with certain codimension 2 symplectic submanifolds.

证明了奇维球的单位余切束辛非球填充的唯一性，直至微分同胚。作为应用，我们首先证明了某些5维Brieskorn流形之间不存在精确辛配合。我们还确定了具有一定余维数的2辛子流形的闭辛6流形的微分同态类型。

引用次数: 0

Unified theory on V-states structures for active scalar equations 有源标量方程v态结构的统一理论

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-29 DOI: 10.1016/j.aim.2025.110750

Taoufik Hmidi , Liutang Xue , Zhilong Xue

This paper revolves around the existence of V-states close to Rankine vortices for active scalar equations with completely monotone kernels. This allows to unify various results on this topic related to geophysical flows. A key ingredient is a new factorization formula for the spectrum using a universal function which is independent of the model. This function admits several interesting properties allowing to track the spectrum distribution.

本文讨论了具有完全单调核的有源标量方程在朗肯涡附近的v态的存在性。这样就可以统一与地球物理流动有关的这个主题的各种结果。其中一个关键因素是利用独立于模型的通用函数对光谱进行新的因子分解公式。这个函数有几个有趣的特性，可以用来跟踪频谱分布。

引用次数: 0

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