Bulletin of the London Mathematical Society最新文献

{"title":"On some exotic cylindrical algebraic decompositions and cells","authors":"Lucas Michel","doi":"10.1112/blms.70512","DOIUrl":"https://doi.org/10.1112/blms.70512","url":null,"abstract":"<p>Cylindrical algebraic decompositions (CADs) endowed with additional topological properties have found applications beyond their original logical setting, including algorithmic optimizations in CAD construction, robot motion planning, and the algorithmic study of the topology of semi-algebraic sets. In this paper, we construct explicit examples of CADs and CAD cells that refute several conjectures and open questions of J. H. Davenport, A. Locatelli, and G. K. Sankaran concerning these topological assumptions.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Curved RUM spectra of periodic frameworks","authors":"Antonio Acuaviva,&nbsp;Jack Esson,&nbsp;Eleftherios Kastis,&nbsp;Bernd Schulze","doi":"10.1112/blms.70513","DOIUrl":"https://doi.org/10.1112/blms.70513","url":null,"abstract":"<p>The rigid unit mode (RUM) spectrum records the phases at which a periodic (or crystal) framework admits a phase-periodic infinitesimal motion. This plays a central role in the geometric rigidity of crystal frameworks, with applications in crystallography and materials science. In this paper, we prove that there exists a crystal framework with a non-zero vanishing infinitesimal motion but no non-zero finitely supported infinitesimal motion. To exhibit such a vanishing infinitesimal motion, we integrate over the framework's RUM spectrum, for which the logarithmic plot forms a pair of curves. By considering alternative periodic configurations of the same periodic graph, we also show that having a trivial RUM spectrum is not a generic property of a periodic graph.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70513","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Syzygies of the residue field over Golod rings","authors":"Đoàn Trung Cường,&nbsp;Hailong Dao,&nbsp;David Eisenbud,&nbsp;Toshinori Kobayashi,&nbsp;Claudia Polini,&nbsp;Bernd Ulrich","doi":"10.1112/blms.70498","DOIUrl":"https://doi.org/10.1112/blms.70498","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>k</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(R,mathfrak {m},k)$</annotation>\u0000 </semantics></math> be a Golod ring. We give a recurrence formula for the high syzygies of <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> in terms of the previous ones. When <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> has embedding dimension at most 2, we explicitly determine the indecomposable summands of all syzygies of <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global dimension of dg algebras via compact silting objects","authors":"Panagiotis Kostas","doi":"10.1112/blms.70497","DOIUrl":"https://doi.org/10.1112/blms.70497","url":null,"abstract":"<p>We introduce a notion of global dimension for a triangulated category relative to a compact silting object. We prove that the finiteness of this dimension is an intrinsic property of the triangulated category itself and, therefore, independent of the choice of the silting object. Focusing on the setup of connective differential graded (dg) algebras, we analyse the behaviour of global dimension under dg algebra homomorphisms and establish explicit bounds. This allows us to deduce a bound for the global dimension of certain dg quiver algebras. We also relate the regularity of the big singularity category of a proper connective dg algebra to the finiteness of its global dimension.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70497","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Transitivity of mutation of \u0000 \u0000 τ\u0000 $tau$\u0000 -exceptional sequences in the \u0000 \u0000 τ\u0000 $tau$\u0000 -tilting finite case","authors":"Aslak B. Buan,&nbsp;Eric J. Hanson,&nbsp;Bethany R. Marsh","doi":"10.1112/blms.70499","DOIUrl":"https://doi.org/10.1112/blms.70499","url":null,"abstract":"<p>We prove that mutation of complete <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-exceptional sequences is transitive for <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-tilting finite algebras.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70499","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New discretised polynomial expander and incidence estimates","authors":"Ciprian Demeter,&nbsp;William O'Regan","doi":"10.1112/blms.70504","DOIUrl":"https://doi.org/10.1112/blms.70504","url":null,"abstract":"<p>We present two applications of recent developments in incidence geometry. One is a <span></span><math>\u0000 <semantics>\u0000 <mi>δ</mi>\u0000 <annotation>$delta$</annotation>\u0000 </semantics></math>-discretised version of a particular ‘Elekes–Rónyai’ expander problem. The second is an incidence estimate addressing the scenario in which both tubes, squares and their shadings satisfy non-concentration assumptions.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70504","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the maximum likelihood degree of Gaussian graphical models","authors":"Carlos Améndola,&nbsp;Rodica Andreea Dinu,&nbsp;Mateusz Michałek,&nbsp;Martin Vodička","doi":"10.1112/blms.70507","DOIUrl":"https://doi.org/10.1112/blms.70507","url":null,"abstract":"<p>In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML-degree behaves monotonically on induced subgraphs. Furthermore, we complete a missing argument that the ML-degree of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mi>th</mi>\u0000 </mrow>\u0000 <annotation>$n{rm th}$</annotation>\u0000 </semantics></math> cycle is larger than 1 for any <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 4$</annotation>\u0000 </semantics></math>, therefore completing the characterization that the only Gaussian graphical models with rational maximum likelihood estimator are the ones corresponding to chordal (decomposable) graphs. Finally, we prove that the formula for the ML-degree of a cycle conjectured by Drton, Sturmfels and Sullivant provides a correct lower bound.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70507","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the convergence of boundary points for hyperbolic inner functions","authors":"Anna Jové,&nbsp;Mateo Mencía","doi":"10.1112/blms.70506","DOIUrl":"https://doi.org/10.1112/blms.70506","url":null,"abstract":"<p>Given a hyperbolic inner function <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <mi>D</mi>\u0000 <mo>→</mo>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$ fcolon mathbb {D}rightarrow mathbb {D}$</annotation>\u0000 </semantics></math> with Denjoy–Wolff point <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mi>∂</mi>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$ pin partial mathbb {D}$</annotation>\u0000 </semantics></math>, it is well-known that almost every point <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ζ</mi>\u0000 <mo>∈</mo>\u0000 <mi>∂</mi>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$ zeta in partial mathbb {D}$</annotation>\u0000 </semantics></math> converges to <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$ p$</annotation>\u0000 </semantics></math> under iteration of the radial extension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>f</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <mo>:</mo>\u0000 <mi>∂</mi>\u0000 <mi>D</mi>\u0000 <mo>→</mo>\u0000 <mi>∂</mi>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$ f^*colon partial mathbb {D}rightarrow partial mathbb {D}$</annotation>\u0000 </semantics></math>. We provide explicit bounds for the rate of this convergence in terms of the angular derivative, holding almost surely. Our results also cover the case where the Denjoy–Wolff point is a singularity.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148981423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A tropical version of Martens' theorem for metric graphs","authors":"Giusi Capobianco,&nbsp;Angelina Zheng","doi":"10.1112/blms.70505","DOIUrl":"https://doi.org/10.1112/blms.70505","url":null,"abstract":"<p>We study the conjecture stated by Jensen and Len on a tropical version on Martens' theorem via the Brill–Noether rank of a tropical curve. We recall Coppens' counterexample of Martens-special chain of cycles, and we generalize the construction defining another class of graphs, Martens-special trees of cycles, for which the conjecture does not hold in a similar setting. These are not the only counterexamples. However, we prove that the conjecture holds for all metric graphs with a stricter assumption on the degree in the Brill–Noether rank.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70505","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148981469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On locally distinguishing Sierpiński dynamical systems","authors":"Sergei Merenkov","doi":"10.1112/blms.70502","DOIUrl":"https://doi.org/10.1112/blms.70502","url":null,"abstract":"<p>We prove that there is no local quasiconformal map between the limit set of a convex-cocompact Kleinian group and the Julia set of a postcritically finite rational map, provided that both are Sierpiński carpets. This contrasts with the recent results by Y. Luo, D. Ntalampekos and Y. Luo, M. Mj, S. Mukherjee for gasket and tree-like spaces, respectively.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148981470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}