Bulletin of the London Mathematical Society最新文献

{"title":"Extremal behavior of ideals of minors","authors":"Trung Chau,&nbsp;Michael DeBellevue,&nbsp;Souvik Dey,&nbsp;Omkar Javadekar,&nbsp;Ganapathy Krishnamoorthy","doi":"10.1112/blms.70466","DOIUrl":"https://doi.org/10.1112/blms.70466","url":null,"abstract":"<p>Ideals of minors arising from minimal free resolutions—equivalently, the Fitting ideals of syzygy modules—are natural invariants of interest in commutative algebra and algebraic geometry. A surprising observation in recent years by Brown–Dao–Sridhar is that for many nice classes of rings, such as complete intersection rings and Golod rings, ideals of minors tend to become eventually periodic. In this article, we establish similar periodicity phenomena for further classes of rings, namely fiber products and artinian stretched Gorenstein rings. In fact, we show that when the embedding dimension is at least 3, under a mild characteristic assumption, the ideals of minors stabilize to powers of the maximal ideal, exhibiting extremal behavior. We also study the transfer of periodicity between rings. Specifically, we prove that for any local ring <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 </mrow>\u0000 <annotation>$(R,mbox{$mathfrak {m}$})$</annotation>\u0000 </semantics></math> and a super-regular element <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mo>∈</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$xin mbox{$mathfrak {m}$}$</annotation>\u0000 </semantics></math>, if the ideals of minors of an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>/</mo>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$R/(x)$</annotation>\u0000 </semantics></math>-module <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> have extremal behavior, then so do the ideals of minors of <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> over <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752429","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":"On deficit estimates of the logarithmic Sobolev inequality for the Tsallis entropy via nonlinear diffusion equations","authors":"Takeshi Suguro","doi":"10.1112/blms.70465","DOIUrl":"https://doi.org/10.1112/blms.70465","url":null,"abstract":"<p>We consider functional inequalities for the Tsallis entropy, a one-parameter extension of the Boltzmann–Shannon entropy. For the Boltzmann–Shannon entropy, the logarithmic Sobolev inequality is known as an upper bound estimate by the Fisher information. This inequality is related to the dissipative estimate for solutions to the heat equation and plays a crucial role in the study of its asymptotic behavior. In this paper, we focus on the Tsallis entropy associated with nonlinear diffusion equations and derive deficit estimates of the functional inequality for the Tsallis entropy.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752428","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":"Morita equivalences between cyclotomic KLR algebras in types \u0000 \u0000 \u0000 C\u0000 ∞\u0000 \u0000 ${C}_{infty}$\u0000 and \u0000 \u0000 \u0000 A\u0000 ∞\u0000 \u0000 ${A}_{infty}$","authors":"Chris Bowman,&nbsp;Robert Muth,&nbsp;Liron Speyer,&nbsp;Louise Sutton","doi":"10.1112/blms.70459","DOIUrl":"https://doi.org/10.1112/blms.70459","url":null,"abstract":"<p>We prove that level one cyclotomic Khovanov–Lauda–Rouquier (KLR) algebras in type <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>${C}_{infty}$</annotation>\u0000 </semantics></math> are graded Morita equivalent to level two cyclotomic KLR algebras in type <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>${A}_{infty}$</annotation>\u0000 </semantics></math>. We hence deduce the graded decomposition numbers and full submodule structures of all level one cyclotomic KLR algebras in type <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>${C}_{infty}$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148647823","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":"Self-improving property for certain degenerate functionals with generalized Orlicz growth","authors":"Vertti Hietanen,&nbsp;Mikyoung Lee","doi":"10.1112/blms.70453","DOIUrl":"https://doi.org/10.1112/blms.70453","url":null,"abstract":"<p>We investigate a self-improving property of variational integrals in a weighted framework under generalized Orlicz growth conditions. Assuming that the weight belongs to an appropriate Muckenhoupt class and the growth function satisfies standard structural conditions, we prove that the gradient of any local quasi-minimizer has local higher integrability. In addition, we establish the existence of minimizers for the associated functional.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70453","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616951","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":"Irrationality of rapidly converging series: A problem of Erdős and Graham","authors":"Kevin Barreto,&nbsp;Jiwon Kang,&nbsp;Sang-hyun Kim,&nbsp;Vjekoslav Kovač,&nbsp;Shengtong Zhang","doi":"10.1112/blms.70457","DOIUrl":"https://doi.org/10.1112/blms.70457","url":null,"abstract":"&lt;p&gt;Answering a question of Erdős and Graham, we show that the double-exponential growth condition &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;lim sup&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$limsup _{nrightarrow infty }a_n^{1/phi ^n}=infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for a strictly increasing sequence of positive integers &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$lbrace a_nrbrace _{n=1}^infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is sufficient for the series &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mo&gt;∑&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$sum _{n=1}^infty 1/(a_n a_{n+1})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to have an irrational sum; here &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;annotation&gt;$phi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denotes the golden ratio. We also provide a positive generalizat","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616953","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":"The number of regular simplices in higher dimensions","authors":"Felix Christian Clemen,&nbsp;Adrian Dumitrescu,&nbsp;Dingyuan Liu","doi":"10.1112/blms.70452","DOIUrl":"https://doi.org/10.1112/blms.70452","url":null,"abstract":"&lt;p&gt;We study the extremal function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$S^k_d(n)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, defined as the maximum number of regular &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(k-1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-simplices spanned by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; points in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathbb {R}^d$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. For any fixed &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;6&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$dgeqslant 2kgeqslant 6$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we determine the asymptotic behavior of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$S^k_d(n)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; up to a lower-order term. In particular, when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$k=3$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we determine the exact value of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70452","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615803","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":"Corrigendum to ‘Local mirror symmetry via SYZ'","authors":"Benjamin Gammage","doi":"10.1112/blms.70463","DOIUrl":"https://doi.org/10.1112/blms.70463","url":null,"abstract":"<p>This note corrects a faulty statement in the author's paper <i>Local mirror symmetry via SYZ</i>, Bull. Lond. Math. Soc. <b>56</b> (2024), no. 10, 3181–3195.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70463","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615839","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":"When is the graph of a random 0/1 polytope a clique?","authors":"Catherine Babecki,&nbsp;Tycho Elling,&nbsp;Asaf Ferber","doi":"10.1112/blms.70456","DOIUrl":"https://doi.org/10.1112/blms.70456","url":null,"abstract":"&lt;p&gt;We study graph-theoretic properties of random &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0/1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; polytopes. Specifically, let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;⊆&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Q_p^n subseteq lbrace 0,1rbrace ^n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a random subset where each point is included independently with probability &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and consider the graph &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$G_p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of the polytope &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;conv&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{conv}(Q_p^n)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We provide a short and combinatorial proof that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$p = 2^{-n/2}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a threshold for when the edge density of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$G_p$&lt;/annotation&gt;\u0000 &lt;/semantics","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70456","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615787","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":"Corrigendum II: Higher-dimensional analogs of Châtelet surfaces (Bull. London Math. Soc. 44 (2012) 125–135)","authors":"Anthony Várilly-Alvarado,&nbsp;Bianca Viray","doi":"10.1112/blms.70458","DOIUrl":"https://doi.org/10.1112/blms.70458","url":null,"abstract":"&lt;p&gt;A. Várilly-Alvarado and B. Viray, &lt;i&gt;Higher-dimensional analogs of Châtelet surfaces&lt;/i&gt;, Bull. London Math. Soc. &lt;b&gt;44&lt;/b&gt; (2012), no. 1, 125–135, https://doi.org/10.1112/blms/bdr075&lt;/p&gt;&lt;p&gt;When considering &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$X_{K/k, P(x)}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; up to birational equivalence, it suffices to consider the case when each field extension generated by a single root of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$P(x)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is linearly disjoint from &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$K/k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (see Lemma 2). In [&lt;span&gt;2&lt;/span&gt;], we implicitly reduced to this case, resulting in incorrect statements when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; has nontrivial intersection with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$k(alpha)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for some root &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;annotation&gt;$alpha$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$P(x)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In particular, [&lt;span&gt;2&lt;/span&gt;, Proposition 3.1] and [&lt;span&gt;2&lt;/span&gt;, Theorem 3.2] are incorrect as stated; these should be replaced by Corrected Proposition 3.1 and Corrected Theorem 3.2 below. In [&lt;span&gt;2&lt;/span&gt;, Proposition 3.1] was used only in the proof of [&lt;span&gt;2&lt;/span&gt;, Theorem 3.2], and [&lt;span&gt;2&lt;/span&gt;, Theorem 3.2] was used only in the proof of [&lt;span&gt;2&lt;/span&gt;, Corollary 3.3","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70458","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615788","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":"Convergence of Hermite expansions in modulation spaces","authors":"Philippe Jaming,&nbsp;Michael Speckbacher","doi":"10.1112/blms.70460","DOIUrl":"https://doi.org/10.1112/blms.70460","url":null,"abstract":"&lt;p&gt;The aim of this paper is to give an elementary proof that the Hermite expansion of a function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in the modulation space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M^p({mathbb {R}})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; converges to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M^p({mathbb {R}})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$1&lt;p&lt;infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and may diverge when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0&lt;pleqslant 1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, or when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$p=infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Although related results exist in the context of Fock spaces, their formulation and consequences for modulation spaces appear to have gone unnoticed in time–frequency analysis. More precisely, the result was previously established for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$1&lt;p&lt;i","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70460","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615790","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}