Advances in Mathematics最新文献_第7页

Motivic cohomology of cyclic coverings 循环覆盖的动机上同调

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2026-01-07 DOI: 10.1016/j.aim.2025.110767

Tariq Syed

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

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-30 DOI: 10.1016/j.aim.2025.110751

Yuhi Kamio, Ryuya Hora

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Formal multiple Eisenstein series and their derivations 形式多重爱森斯坦级数及其推导

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-29 DOI: 10.1016/j.aim.2025.110739

Henrik Bachmann , Jan-Willem van Ittersum

{"title":"Formal multiple Eisenstein series and their derivations","authors":"Henrik Bachmann , Jan-Willem van Ittersum","doi":"10.1016/j.aim.2025.110739","DOIUrl":"10.1016/j.aim.2025.110739","url":null,"abstract":"<div><div>We introduce the algebra of formal multiple Eisenstein series and study its derivations. This algebra is motivated by the classical multiple Eisenstein series, introduced by Gangl–Kaneko–Zagier as a hybrid of classical Eisenstein series and multiple zeta values. In depth one, we obtain formal versions of the Eisenstein series satisfying the same algebraic relations as the classical Eisenstein series. In particular, they generate an algebra whose elements we call formal quasimodular forms. We show that the algebra of formal multiple Eisenstein series is an <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-algebra by formalizing the usual derivations for quasimodular forms and extending them naturally to the whole algebra. Additionally, we introduce some families of derivations for general quasi-shuffle algebras, providing a broader context for these derivations. Further, we prove that a quotient of this algebra is isomorphic to the algebra of formal multiple zeta values. This gives a novel and purely formal approach to classical (quasi)modular forms and builds a new link between (formal) multiple zeta values and modular forms.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"487 ","pages":"Article 110739"},"PeriodicalIF":1.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145847578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Nuclear dimension and virtually polycyclic groups 核维度和几乎多环基团

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2026-01-13 DOI: 10.1016/j.aim.2025.110768

Caleb Eckhardt , Jianchao Wu

引用次数: 0

Hölder regularity of harmonic functions on metric measure spaces Hölder度量度量空间上调和函数的正则性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2026-01-22 DOI: 10.1016/j.aim.2026.110797

Jin Gao , Meng Yang

引用次数: 0

The weighted ambient metric for manifolds with density 带密度流形的加权环境度规

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2026-01-19 DOI: 10.1016/j.aim.2026.110787

Ayush Khaitan

引用次数: 0

On the invariant surface area functionals in 3-dimensional CR geometry 三维CR几何中的不变表面积泛函

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2026-01-19 DOI: 10.1016/j.aim.2026.110790

Pak Tung Ho

{"title":"On the invariant surface area functionals in 3-dimensional CR geometry","authors":"Pak Tung Ho","doi":"10.1016/j.aim.2026.110790","DOIUrl":"10.1016/j.aim.2026.110790","url":null,"abstract":"<div><div>Cheng, Yang, and Zhang have studied two invariant surface area functionals in 3-dimensional CR manifolds. They deduced the Euler–Lagrange equations of the associated energy functionals when the 3-dimensional CR manifold has constant Webster curvature and vanishing torsion. In this paper, we deduce the Euler–Lagrange equations of the energy functionals in a more general 3-dimensional CR manifold. Moreover, we study the invariant area functionals on the disk bundle, on the Rossi sphere, and on 3-dimensional tori. In particular, we show that the Clifford torus is a minimizer for <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> on the Rossi sphere <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>t</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> when <span><math><mi>t</mi><mo>=</mo><mo>−</mo><mn>4</mn><mo>+</mo><msqrt><mrow><mn>15</mn></mrow></msqrt></math></span>. Also, by computing the second variation formula, we show that the Clifford torus is not a minimizer for <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> on the Rossi sphere <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>t</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> when <span><math><mi>t</mi><mo>></mo><mo>−</mo><mn>4</mn><mo>+</mo><msqrt><mrow><mn>15</mn></mrow></msqrt></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"488 ","pages":"Article 110790"},"PeriodicalIF":1.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Expander graphs are globally synchronizing 扩展器图是全局同步的

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2026-01-19 DOI: 10.1016/j.aim.2025.110773

Pedro Abdalla , Afonso S. Bandeira , Martin Kassabov , Victor Souza , Steven H. Strogatz , Alex Townsend

{"title":"Expander graphs are globally synchronizing","authors":"Pedro Abdalla , Afonso S. Bandeira , Martin Kassabov , Victor Souza , Steven H. Strogatz , Alex Townsend","doi":"10.1016/j.aim.2025.110773","DOIUrl":"10.1016/j.aim.2025.110773","url":null,"abstract":"<div><div>The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively with vertices and edges of a graph. In this paper, we show that a graph with sufficient expansion must be globally synchronizing, meaning that a homogeneous Kuramoto model of identical oscillators on such a graph will converge to the fully synchronized state with all the oscillators having the same phase, for every initial state up to a set of measure zero. In particular, we show that for any <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> and <span><math><mi>p</mi><mo>⩾</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>ε</mi><mo>)</mo><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo><mo>/</mo><mi>n</mi></math></span>, the homogeneous Kuramoto model on the Erdős–Rényi random graph <span><math><mi>G</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></span> is globally synchronizing with probability tending to one as <em>n</em> goes to infinity. This improves on a previous result of Kassabov, Strogatz, and Townsend and solves a conjecture of Ling, Xu, and Bandeira. We also show that the Kuramoto model is globally synchronizing on any <em>d</em>-regular Ramanujan graph, and on typical <em>d</em>-regular graphs, for <span><math><mi>d</mi><mo>⩾</mo><mn>600</mn></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"488 ","pages":"Article 110773"},"PeriodicalIF":1.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-31 DOI: 10.1016/j.aim.2025.110758

Gefei Cai , Wen-Bo Li, Tim Mesikepp

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

Advances in Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-30 DOI: 10.1016/j.aim.2025.110746

Evangelia Gazaki , Jonathan Love

{"title":"Hyperelliptic curves mapping to abelian varieties and applications to Beilinson's conjecture for zero-cycles","authors":"Evangelia Gazaki , Jonathan Love","doi":"10.1016/j.aim.2025.110746","DOIUrl":"10.1016/j.aim.2025.110746","url":null,"abstract":"<div><div>Let <em>A</em> be an abelian surface over an algebraically closed field <span><math><mover><mrow><mi>k</mi></mrow><mo>‾</mo></mover></math></span> with an embedding <span><math><mover><mrow><mi>k</mi></mrow><mo>‾</mo></mover><mo>↪</mo><mi>C</mi></math></span>. When <em>A</em> is isogenous to a product of elliptic curves, we describe a large collection of pairwise non-isomorphic hyperelliptic curves mapping birationally into <em>A</em>. For infinitely many integers <span><math><mi>g</mi><mo>≥</mo><mn>2</mn></math></span>, this collection has infinitely many curves of genus <em>g</em>, and no two curves in the collection have the same image under any isogeny from <em>A</em>. Using these hyperelliptic curves, we find many rational equivalences in the Chow group of zero-cycles <span><math><msub><mrow><mi>CH</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span>. We use these results to give some progress towards Beilinson's conjecture for zero-cycles, which predicts that for a smooth projective variety <em>X</em> over <span><math><mover><mrow><mi>Q</mi></mrow><mo>‾</mo></mover></math></span> the kernel of the Albanese map of <em>X</em> is zero.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"487 ","pages":"Article 110746"},"PeriodicalIF":1.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0