Advances in Mathematics最新文献

Generalized rank functions and quilts of alternating sign matrices 交替符号矩阵的广义秩函数和矩阵

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-24 DOI: 10.1016/j.aim.2026.110863

Sara C. Billey , Matjaž Konvalinka

引用次数: 0

Minimal slopes and bubbling for complex Hessian equations 复Hessian方程的最小斜率和冒泡

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-18 DOI: 10.1016/j.aim.2026.110865

Ved Datar , Ramesh Mete , Jian Song

{"title":"Minimal slopes and bubbling for complex Hessian equations","authors":"Ved Datar , Ramesh Mete , Jian Song","doi":"10.1016/j.aim.2026.110865","DOIUrl":"10.1016/j.aim.2026.110865","url":null,"abstract":"<div><div>The existence of smooth solutions to a broad class of complex Hessian equations is related to nonlinear Nakai type criteria on intersection numbers on Kähler manifolds. Such a Nakai criteria can be interpreted as a slope stability condition analogous to the slope stability for Hermitian vector bundles over Kähler manifolds. In the present work, we initiate a program to find canonical solutions to such equations in the unstable case when the Nakai criteria fails. Conjecturally such solutions should arise as limits of natural parabolic flows and should be minimisers of the corresponding moment-map energy functionals. We implement our approach for the <em>J</em>-equation and the deformed Hermitian Yang-Mills equation on surfaces and some examples with symmetry. We prove that there always exist unique canonical solutions to these two equations on Kähler surfaces in the unstable cases. Such canonical solutions with singularities are also shown to be the limits of the corresponding J-flow and the cotangent flow on certain projective bundles. We further present the bubbling phenomena for the <em>J</em>-equation by constructing minimizing sequences of the moment-map energy functionals, whose Gromov-Hausdorff limits are singular algebraic spaces.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"491 ","pages":"Article 110865"},"PeriodicalIF":1.5,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386677","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

Nerves of generalized multicategories 广义多范畴神经

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-17 DOI: 10.1016/j.aim.2026.110862

Soichiro Fujii , Stephen Lack

{"title":"Nerves of generalized multicategories","authors":"Soichiro Fujii , Stephen Lack","doi":"10.1016/j.aim.2026.110862","DOIUrl":"10.1016/j.aim.2026.110862","url":null,"abstract":"<div><div>For any category <span><math><mi>E</mi></math></span> and monad <em>T</em> thereon, we introduce the notion of <em>T</em>-simplicial object in <span><math><mi>E</mi></math></span>. Any <em>T</em>-category in the sense of Burroni induces a <em>T</em>-simplicial object as its nerve. This nerve construction defines a fully faithful functor from the category <span><math><msub><mrow><mi>Cat</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo></math></span> of <em>T</em>-categories to the category <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>T</mi></mrow></msub><mi>E</mi></math></span> of <em>T</em>-simplicial objects, whose essential image is characterized by a simple condition. We show that the category <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>T</mi></mrow></msub><mi>E</mi></math></span> is enriched over the category of simplicial sets, and that this induces the usual 2-category structure on <span><math><msub><mrow><mi>Cat</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo></math></span>. We also study enriched limits and colimits in <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>T</mi></mrow></msub><mi>E</mi></math></span> and <span><math><msub><mrow><mi>Cat</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo></math></span>, and show that if <span><math><mi>E</mi></math></span> is locally finitely presentable and <em>T</em> is finitary, then <span><math><msub><mrow><mi>Cat</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo></math></span> is locally finitely presentable as a 2-category and <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>T</mi></mrow></msub><mi>E</mi></math></span> is locally finitely presentable as a simplicially-enriched category.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"491 ","pages":"Article 110862"},"PeriodicalIF":1.5,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386676","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

Explicit Hilbert spaces for the unitary dual of rank one orthogonal groups and applications 秩一正交群的酉对偶的显式Hilbert空间及其应用

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-18 DOI: 10.1016/j.aim.2026.110868

Christian Arends, Frederik Bang-Jensen, Jan Frahm

{"title":"Explicit Hilbert spaces for the unitary dual of rank one orthogonal groups and applications","authors":"Christian Arends, Frederik Bang-Jensen, Jan Frahm","doi":"10.1016/j.aim.2026.110868","DOIUrl":"10.1016/j.aim.2026.110868","url":null,"abstract":"<div><div>We realize all irreducible unitary representations of the group <span><math><msub><mrow><mi>SO</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> on explicit Hilbert spaces of vector-valued <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-functions on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></math></span>. The key ingredient in our construction is an explicit expression for the standard Knapp–Stein intertwining operators between arbitrary principal series representations in terms of the Euclidean Fourier transform on a maximal unipotent subgroup isomorphic to <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</div><div>As an application, we describe the space of Whittaker vectors on all irreducible Casselman–Wallach representations. Moreover, the new realizations of the irreducible unitary representations immediately reveal their decomposition into irreducible representations of a parabolic subgroup, thus providing a simple proof of a recent result of Liu–Oshima–Yu.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"491 ","pages":"Article 110868"},"PeriodicalIF":1.5,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386526","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

A perturbative construction of primitive forms from log Landau-Ginzburg mirrors of toric manifolds 环流形log Landau-Ginzburg镜原始形式的微扰构造

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-24 DOI: 10.1016/j.aim.2026.110867

Kwokwai Chan , Ziming Nikolas Ma , Hao Wen

引用次数: 0

On the superadditivity of anticanonical Iitaka dimension 反正则Iitaka维的超可加性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-13 DOI: 10.1016/j.aim.2026.110860

Marta Benozzo , Iacopo Brivio , Chi-Kang Chang

引用次数: 0

(Co)Minuscule Hecke categories (Co)小类别

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-18 DOI: 10.1016/j.aim.2026.110866

Joseph Baine

引用次数: 0

Tropical thermodynamic formalism 热带热力学形式论

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-19 DOI: 10.1016/j.aim.2026.110864

Zhiqiang Li , Yiqing Sun

{"title":"Tropical thermodynamic formalism","authors":"Zhiqiang Li , Yiqing Sun","doi":"10.1016/j.aim.2026.110864","DOIUrl":"10.1016/j.aim.2026.110864","url":null,"abstract":"<div><div>We investigate the zero-temperature large deviation principle for equilibrium states in the context of distance-expanding maps. The logarithmic-type zero-temperature limit in the large deviation principle induces a tropical algebra structure, which motivates our study of the tropical adjoint Bousch operator <figure><img></figure> since the Bousch operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msub></math></span> is tropical linear and corresponds to the Ruelle operator <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>A</mi></mrow></msub></math></span>.</div><div>We extend tropical functional analysis, define the adjoint operator <figure><img></figure> as a tropical analog of the adjoint Ruelle operator <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math></span>, and establish the existence and generic uniqueness of tropical eigendensities of <figure><img></figure> associated with the maximal eigenvalue. The Aubry set and the Mañé potential, both originating from weak KAM theory, serve as important tools in the representations of tropical eigendensities. With our notion of tropical completeness and our tropical Riesz representation theorem, <figure><img></figure> can also be seen as a version of the tropical Koopman operator.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"491 ","pages":"Article 110864"},"PeriodicalIF":1.5,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386527","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

The monodromy divisor of an exact algebraic Lagrangian 精确代数拉格朗日的单除数

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-02-12 DOI: 10.1016/j.aim.2026.110851

Christopher Dodd

引用次数: 0

A simple proof of the Atkin-O'Brien partition Hecke congruence conjecture for powers of 13 13次幂的Atkin-O'Brien分合Hecke同余猜想的一个简单证明

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-01-30 DOI: 10.1016/j.aim.2026.110840

Frank Garvan, Zhumagali Shomanov

引用次数: 0