Journal of the London Mathematical Society-Second Series最新文献

{"title":"Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings","authors":"Michelle Delcourt, Luke Postle","doi":"10.1112/jlms.70660","DOIUrl":"https://doi.org/10.1112/jlms.70660","url":null,"abstract":"<p>In 1973, Erdős conjectured the existence of high girth <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(n,3,2)$</annotation>\u0000 </semantics></math>-Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős' conjecture. Recently, Kwan, Sah, Sawhney, and Simkin proved Erdős' conjecture. As for Steiner systems with more general parameters, Glock, Kühn, Lo, and Osthus conjectured the existence of high girth <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 <mo>,</mo>\u0000 <mi>r</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(n,q,r)$</annotation>\u0000 </semantics></math>-Steiner systems. We prove the approximate version of their conjecture. This result follows from our general main results that concern finding perfect or almost perfect matchings in a hypergraph <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> avoiding a given set of submatchings (which we view as a hypergraph <span></span><math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>E</mi>\u0000 <mo>(</mo>\u0000 <mi>G</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$V(H)=E(G)$</annotation>\u0000 </semantics></math>). Our first main result is a common generalization of the classical theorems of Pippenger (for finding an almost perfect matching) and Ajtai, Komlós, Pintz, Spencer, and Szemerédi (for finding an independent set in girth five hypergraphs). More generally, we prove this for coloring and even list coloring, and also generalize this further to when <span></span><math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> is a hypergraph with small codegrees (for which high girth designs is a specific instance). Indeed, the coloring version of our result even yields an almost partition of <span></span><math>\u0000 <semantics>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70660","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Link patterns and elliptic Hecke algebra","authors":"Andrzej Weber","doi":"10.1112/jlms.70648","DOIUrl":"https://doi.org/10.1112/jlms.70648","url":null,"abstract":"<p>We compare three families of geometric objects: Schubert varieties in flag manifolds, matrix Schubert varieties, and Borel orbits of 2-nilpotent matrices. The first family is indexed by permutations, the second by partial permutations, and the third, the most general, by link patterns. Each of the geometric objects mentioned above carries a characteristic class in equivariant elliptic cohomology, defined in the framework provided by Borisov and Libgober. We introduce a Hecke-type algebra that gives inductive formulae for computing the equivariant elliptic classes of link patterns. This requires extending the action of the Hecke algebra to menage partial permutations and link patterns. In studying the extended action, an important role is played by the associated quadratic forms and by the action of reflections on forms. Also, we analyze the specialization of equivariant elliptic classes of link patterns to the corresponding classes of Schubert varieties.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fundamental solution for higher-order homogeneous hypoelliptic operators structured on Hörmander vector fields","authors":"Stefano Biagi,&nbsp;Marco Bramanti","doi":"10.1112/jlms.70655","DOIUrl":"https://doi.org/10.1112/jlms.70655","url":null,"abstract":"<p>We introduce and study a new class of higher-order differential operators defined on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{n}$</annotation>\u0000 </semantics></math>, which are built with Hörmander vector fields, homogeneous w.r.t. a family of dilations (but not left-invariant w.r.t. any structure of Lie group) and have a structure such that a suitably lifted version of the operator is hypoelliptic. We call these operators “generalized Rockland operators.” We prove that these operators are themselves hypoelliptic and, under a natural condition on the homogeneity degree, possess a global fundamental solution <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 <mfenced>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 </mfenced>\u0000 </mrow>\u0000 <annotation>$Gamma left(x,yright)$</annotation>\u0000 </semantics></math> which is jointly homogeneous in <span></span><math>\u0000 <semantics>\u0000 <mfenced>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 </mfenced>\u0000 <annotation>$left(x,yright)$</annotation>\u0000 </semantics></math> and satisfies sharp pointwise estimates. Our theory can be applied also to some higher-order heat-type operators and their fundamental solutions.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-isometric rigidity of extended admissible groups","authors":"Alex Margolis,&nbsp;Hoang Thanh Nguyen","doi":"10.1112/jlms.70657","DOIUrl":"https://doi.org/10.1112/jlms.70657","url":null,"abstract":"<p>We introduce the class of extended admissible groups, which include both fundamental groups of nongeometric 3-manifolds and Croke–Kleiner admissible groups. We show that the class of extended admissible groups is quasi-isometrically rigid.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A birational description of the minimal exponent","authors":"Qianyu Chen,&nbsp;Mircea Mustaţă","doi":"10.1112/jlms.70645","DOIUrl":"https://doi.org/10.1112/jlms.70645","url":null,"abstract":"<p>We give a description of the minimal exponent of a hypersurface using higher direct images of suitably twisted sheaves of log forms on a log resolution.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70645","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cluster scattering diagrams via quiver moduli and tight gradings","authors":"Amanda Burcroff,&nbsp;Kyungyong Lee,&nbsp;Lang Mou,&nbsp;Gregg Musiker,&nbsp;Markus Reineke","doi":"10.1112/jlms.70642","DOIUrl":"https://doi.org/10.1112/jlms.70642","url":null,"abstract":"<p>We study rank-2 cluster scattering diagrams through moduli spaces of quiver representations and a recently developed combinatorial framework of tight gradings. Combining quiver-theoretic and combinatorial methods, we prove and extend a collection of conjectures posed by Elgin–Reading–Stella concerning the structural and enumerative properties of the wall-function coefficients. The tight grading perspective also provides a new proof of the Weyl group symmetry of the scattering diagram.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70642","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blow-up analysis and energy identities for super-sinh-Gordon-type equation","authors":"Lei Liu,&nbsp;Miaomiao Zhu","doi":"10.1112/jlms.70659","DOIUrl":"https://doi.org/10.1112/jlms.70659","url":null,"abstract":"<p>We study blow-up analysis for the super-sinh-Gordon-type equation,\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Derivations as algebras","authors":"Jean-Simon Pacaud Lemay,&nbsp;Chiara Sava","doi":"10.1112/jlms.70650","DOIUrl":"https://doi.org/10.1112/jlms.70650","url":null,"abstract":"<p>Differential categories provide the categorical foundations for the algebraic approaches to differentiation. They have been successful in formalizing various important concepts related to differentiation, such as, in particular, derivations. In this paper, we show that the differential modality of a differential category lifts to a monad on the arrow category and, moreover, that the algebras of this monad are precisely derivations. Furthermore, in the presence of finite byproducts, the differential modality, in fact, lifts to a differential modality on the arrow category. In other words, the arrow category of a differential category is again a differential category. As a consequence, derivations also form a tangent category, and derivations on free algebras form a cartesian differential category.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70650","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The quaternionic Maass Spezialschar on split \u0000 \u0000 \u0000 SO\u0000 (\u0000 8\u0000 )\u0000 \u0000 $operatorname{SO}(8)$","authors":"Jennifer Johnson-Leung,&nbsp;Finn McGlade,&nbsp;Isabella Negrini,&nbsp;Aaron Pollack,&nbsp;Manami Roy","doi":"10.1112/jlms.70652","DOIUrl":"https://doi.org/10.1112/jlms.70652","url":null,"abstract":"<p>The classical Maass Spezialschar is a Hecke-stable subspace of the space of holomorphic Siegel modular forms of genus two and level 1 cut out by certain linear relations among Fourier coefficients. We define an analogous quaternionic Maass Spezialschar, which consists of the quaternionic modular forms of level 1 on split <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>SO</mo>\u0000 <mo>(</mo>\u0000 <mn>8</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{SO}(8)$</annotation>\u0000 </semantics></math> whose Fourier coefficients satisfy certain linear relations. We characterize this space in terms of a theta lift from the space of holomorphic Siegel modular forms on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>Sp</mo>\u0000 <mo>(</mo>\u0000 <mn>4</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{Sp}(4)$</annotation>\u0000 </semantics></math>, and in terms of periods. We also give a conjecture for the Dirichlet series of the standard <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-function of quaternionic modular eigenforms on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>SO</mo>\u0000 <mo>(</mo>\u0000 <mn>8</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{SO}(8)$</annotation>\u0000 </semantics></math> and verify our conjecture on the quaternionic Maass Spezialschar.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Damping-diffusion-noise interactions in the stochastic Camassa–Holm equation","authors":"Diego Alonso-Orán,&nbsp;Peter H. C. Pang,&nbsp;Hao Tang","doi":"10.1112/jlms.70634","DOIUrl":"https://doi.org/10.1112/jlms.70634","url":null,"abstract":"<p>In this paper, we investigate the effects of the interaction between time-inhomogeneous damping, non-local diffusion and noise on classical solutions to the Camassa–Holm equation incorporating these features. First, a local-in-time theory is established, covering the existence, uniqueness and a blow-up criterion under relatively general conditions for these interacting mechanisms. Subsequently, we identify different conditions on the interactions between damping, diffusion and noise that guarantee the global regularity and long-time behaviour of classical solutions. Notably, we demonstrate the existence of an evolution system of measures, which generalises the concept of invariant measures to the time-inhomogeneous setting.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}