Advances in Mathematics最新文献

{"title":"Concave foliated flag structures and the SL3(R) Hitchin component","authors":"Alexander Nolte,&nbsp;J. Maxwell Riestenberg","doi":"10.1016/j.aim.2025.110504","DOIUrl":"10.1016/j.aim.2025.110504","url":null,"abstract":"<div><div>We give a geometric characterization of flag geometries associated to Hitchin representations in <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. Our characterization is based on distinguished invariant foliations, similar to those studied by Guichard-Wienhard in <span><math><msub><mrow><mi>PSL</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>.</div><div>We connect to the dynamics of Hitchin representations by constructing refraction flows for all positive roots in general <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> in our setting. One consequence is that the highest root flows are <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>α</mi></mrow></msup></math></span>. For <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>, leaves of our one-dimensional foliations are flow-lines.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110504"},"PeriodicalIF":1.5,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932291","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}

{"title":"Grothendieck shenanigans: Permutons from pipe dreams via integrable probability","authors":"A.H. Morales ,&nbsp;G. Panova ,&nbsp;L. Petrov ,&nbsp;D. Yeliussizov","doi":"10.1016/j.aim.2025.110510","DOIUrl":"10.1016/j.aim.2025.110510","url":null,"abstract":"<div><div>We study random permutations corresponding to pipe dreams. Our main model is motivated by the Grothendieck polynomials with parameter <span><math><mi>β</mi><mo>=</mo><mn>1</mn></math></span> arising in the <em>K</em>-theory of the flag variety. The probability weight of a permutation is proportional to the principal specialization (setting all variables to 1) of the corresponding Grothendieck polynomial. By mapping this random permutation to a version of TASEP (Totally Asymmetric Simple Exclusion Process), we describe the limiting permuton and fluctuations around it as the order <em>n</em> of the permutation grows to infinity. The fluctuations are of order <span><math><msup><mrow><mi>n</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup></math></span> and have the Tracy–Widom GUE distribution, which places this algebraic (<em>K</em>-theoretic) model into the Kardar–Parisi–Zhang universality class. As an application, we find the expected number of inversions in this random permutation, and contrast it with the case of non-reduced pipe dreams.</div><div>Inspired by Stanley's question for the maximal value of principal specializations of Schubert polynomials, we resolve the analogous question for <span><math><mi>β</mi><mo>=</mo><mn>1</mn></math></span> Grothendieck polynomials, and provide bounds for general <em>β</em>. This analysis uses a correspondence with the free fermion six-vertex model, and the frozen boundary of the Aztec diamond.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110510"},"PeriodicalIF":1.5,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932361","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}

{"title":"On decompositions for Fano schemes of intersections of two quadrics","authors":"Pieter Belmans ,&nbsp;Jishnu Bose ,&nbsp;Sarah Frei ,&nbsp;Benjamin Gould ,&nbsp;James Hotchkiss ,&nbsp;Alicia Lamarche ,&nbsp;Jack Petok ,&nbsp;Cristian Rodriguez Avila ,&nbsp;Saket Shah","doi":"10.1016/j.aim.2025.110506","DOIUrl":"10.1016/j.aim.2025.110506","url":null,"abstract":"<div><div>We propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelliptic (resp. stacky) curve. When the intersection is odd-dimensional, we moreover conjecture an identity in the Grothendieck ring of varieties and other motivic contexts. The evidence for these conjectures is given by upgrading recent results of Chen–Vilonen–Xue, to obtain formulae for the Hodge numbers of these Fano schemes. This allows us to numerically verify the conjecture in the hyperelliptic case, and establish a combinatorial identity as evidence for the stacky case.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110506"},"PeriodicalIF":1.5,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932290","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}

{"title":"An integral formula for Lie groups, and the Mathieu conjecture reduced to Abelian non-Lie conjectures","authors":"Michael Müger ,&nbsp;Lars Tuset","doi":"10.1016/j.aim.2025.110500","DOIUrl":"10.1016/j.aim.2025.110500","url":null,"abstract":"<div><div>We present an explicit integration formula for the Haar integral on a compact connected Lie group. This formula relies on a known decomposition of a compact connected simple Lie group into symplectic leaves, when one views the group as a Poisson Lie group. In this setting the Haar integral is constructed using the Kostant harmonic volume form on the corresponding flag manifold, and explicit coordinates are known for these invariant differential forms. The formula obtained is related to one found by Reshetikhin-Yakimov.</div><div>Using our integration formula, we reduce the Mathieu conjecture to two stronger conjectures about Laurent polynomials in several complex variables with polynomial coefficients in several real variable polynomials. In these stronger conjectures there is no reference to Lie group theory.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110500"},"PeriodicalIF":1.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925212","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}

{"title":"Arakelov geometry on flag varieties over function fields and related topics","authors":"Yangyu Fan ,&nbsp;Wenbin Luo ,&nbsp;Binggang Qu","doi":"10.1016/j.aim.2025.110508","DOIUrl":"10.1016/j.aim.2025.110508","url":null,"abstract":"<div><div>Let <strong>k</strong> be an algebraically closed field of characteristic zero. Let <em>G</em> be a connected reductive group over <strong>k</strong>, <span><math><mi>P</mi><mo>⊆</mo><mi>G</mi></math></span> be a parabolic subgroup and <span><math><mi>λ</mi><mo>:</mo><mi>P</mi><mo>⟶</mo><mi>G</mi></math></span> be a strictly antidominant character. Let <em>C</em> be a projective smooth curve over <strong>k</strong> with function field <span><math><mi>K</mi><mo>=</mo><mi>k</mi><mo>(</mo><mi>C</mi><mo>)</mo></math></span> and <em>F</em> be a principal <em>G</em>-bundle on <em>C</em>. Then <span><math><mi>F</mi><mo>/</mo><mi>P</mi><mo>⟶</mo><mi>C</mi></math></span> is a flag bundle and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>=</mo><mi>F</mi><msub><mrow><mo>×</mo></mrow><mrow><mi>P</mi></mrow></msub><msub><mrow><mi>k</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> on <span><math><mi>F</mi><mo>/</mo><mi>P</mi></math></span> is a relatively ample line bundle.</div><div>We compute the height filtration, successive minima, and the Boucksom-Chen concave transform of the height function <span><math><msub><mrow><mi>h</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>λ</mi></mrow></msub></mrow></msub><mo>:</mo><mi>X</mi><mo>(</mo><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover><mo>)</mo><mo>⟶</mo><mi>R</mi></math></span> over the flag variety <span><math><mi>X</mi><mo>=</mo><msub><mrow><mo>(</mo><mi>F</mi><mo>/</mo><mi>P</mi><mo>)</mo></mrow><mrow><mi>K</mi></mrow></msub></math></span>. An interesting application is that the height of <em>X</em> equals to a weighted average of successive minima, and one may view this as a refinement of Zhang's inequality of successive minima.</div><div>Let <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>F</mi><mo>/</mo><mi>P</mi><mo>)</mo></math></span> be the numerical class of a vertical fiber. We compute the augmented base loci <span><math><msub><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>−</mo><mi>t</mi><mi>f</mi><mo>)</mo></math></span> for any <span><math><mi>t</mi><mo>∈</mo><mi>R</mi></math></span>, and it turns out that they are almost the same as the height filtration. As a corollary, we compute the <em>k</em>-th movable cones of flag bundles over curves for all <em>k</em>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110508"},"PeriodicalIF":1.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925214","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}

{"title":"N-best adaptive Fourier decomposition for slice hyperholomorphic functions","authors":"Ming Jin ,&nbsp;Tao Qian ,&nbsp;Irene Sabadini ,&nbsp;Jinxun Wang","doi":"10.1016/j.aim.2025.110498","DOIUrl":"10.1016/j.aim.2025.110498","url":null,"abstract":"<div><div>The purpose of this article is to establish the <em>N</em>-best adaptive Fourier decomposition for slice hyperholomorphic functions in the slice hyperholomorphic quaternionic Hardy space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>B</mi><mo>)</mo></math></span>, where <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> is the right half space and <span><math><mi>B</mi></math></span> is the Euclidean unit ball of quaternions. We prove the existence of the <em>N</em>-best approximation problem for <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> functions which requires considering multiple parameters of the slice Takenaka-Malmquist system simultaneously. In the non-commutative quaternion field our proof relies on the limit behavior for the slice Takenaka-Malmquist system which is obtained through separating quaternionic Blaschke factors from elements of the system, that is quite different to the complex variable and several complex variables cases. Technically, it is more subtle for the right half space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110498"},"PeriodicalIF":1.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925210","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}

{"title":"On the evolution of structure in triangle-free graphs","authors":"Matthew Jenssen ,&nbsp;Will Perkins ,&nbsp;Aditya Potukuchi","doi":"10.1016/j.aim.2025.110499","DOIUrl":"10.1016/j.aim.2025.110499","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We study the typical structure and the number of triangle-free graphs with &lt;em&gt;n&lt;/em&gt; vertices and &lt;em&gt;m&lt;/em&gt; edges where &lt;em&gt;m&lt;/em&gt; is large enough so that a typical triangle-free graph has a cut containing nearly all of its edges, but may not be bipartite.&lt;/div&gt;&lt;div&gt;Erdős, Kleitman, and Rothschild showed that almost every triangle-free graph is bipartite, which leads to an asymptotic formula for the number of triangle-free graphs on &lt;em&gt;n&lt;/em&gt; vertices. Osthus, Prömel, and Taraz later showed that for &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/span&gt;, almost every triangle-free graph on &lt;em&gt;n&lt;/em&gt; vertices and &lt;em&gt;m&lt;/em&gt; edges is bipartite, which likewise leads to an asymptotic formula for their number. Here we give a precise characterization of the distribution of edges within each part of the max cut of a uniformly chosen triangle-free graph &lt;em&gt;G&lt;/em&gt; on &lt;em&gt;n&lt;/em&gt; vertices and &lt;em&gt;m&lt;/em&gt; edges, for a larger range of densities with &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Using this characterization, we describe the evolution of the structure of typical triangle-free graphs as the density changes. We show that as the number of edges decreases below &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/span&gt;, the following structural changes occur in &lt;em&gt;G&lt;/em&gt;:&lt;ul&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;Isolated edges, then trees, then more complex subgraphs emerge as ‘defect edges’, the edges within the parts of a max cut of &lt;em&gt;G&lt;/em&gt;. In fact, the distribution of defect edges is first that of independent Erdős-Rényi random graphs inside the parts, then that of independent exponential random graphs, conditioned on a small maximum degree and no triangles.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;There is a sharp threshold for 3-colorability at &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;∼&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/span&gt; and a sharp threshold between 4-colorability and unbounded chromatic number at &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;∼&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110499"},"PeriodicalIF":1.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925211","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}

{"title":"The anti-spherical Hecke categories for Hermitian symmetric pairs","authors":"Chris Bowman ,&nbsp;Maud De Visscher ,&nbsp;Amit Hazi ,&nbsp;Emily Norton","doi":"10.1016/j.aim.2025.110501","DOIUrl":"10.1016/j.aim.2025.110501","url":null,"abstract":"<div><div>We calculate the <em>p</em>-Kazhdan–Lusztig polynomials for Hermitian symmetric pairs and prove that the corresponding anti-spherical Hecke categories are standard Koszul. We prove that the combinatorial invariance conjecture can be lifted to the level of graded Morita equivalences between subquotients of these Hecke categories.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110501"},"PeriodicalIF":1.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925292","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}

{"title":"Profinite almost rigidity in 3-manifolds","authors":"Xiaoyu Xu","doi":"10.1016/j.aim.2025.110505","DOIUrl":"10.1016/j.aim.2025.110505","url":null,"abstract":"<div><div>We prove that any compact, orientable 3-manifold with empty or toral boundary is profinitely almost rigid among all compact, orientable 3-manifolds. In other words, the profinite completion of its fundamental group determines its homeomorphism type to finitely many possibilities. Moreover, the profinite completion of the fundamental group of a mixed 3-manifold together with the peripheral structure uniquely determines the homeomorphism type of its Seifert part, i.e. the maximal graph manifold components in the JSJ-decomposition. On the other hand, without assigning the peripheral structure, the profinite completion of a mixed 3-manifold group may not uniquely determine the fundamental group of its Seifert part. The proof is based on JSJ-decomposition.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110505"},"PeriodicalIF":1.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925213","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}

{"title":"Central charges in local mirror symmetry via hypergeometric duality","authors":"Zengrui Han","doi":"10.1016/j.aim.2025.110502","DOIUrl":"10.1016/j.aim.2025.110502","url":null,"abstract":"<div><div>We apply the better-behaved GKZ hypergeometric systems to study toric Calabi-Yau Deligne-Mumford stacks and their Hori-Vafa mirrors given by affine hypersurfaces in <span><math><msup><mrow><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>d</mi></mrow></msup></math></span>. We show that the integral structures of A-branes and B-branes coincide. This confirms a local version of a conjecture of Hosono and can be seen as a generalization of the Gamma conjecture for local mirror symmetry.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110502"},"PeriodicalIF":1.5,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144913273","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}