Bulletin of the London Mathematical Society最新文献

{"title":"Coloured shuffle compatibility, Hadamard products, and ask zeta functions","authors":"Angela Carnevale,&nbsp;Vassilis Dionyssis Moustakas,&nbsp;Tobias Rossmann","doi":"10.1112/blms.70081","DOIUrl":"https://doi.org/10.1112/blms.70081","url":null,"abstract":"<p>We devise an explicit method for computing combinatorial formulae for Hadamard products of certain rational generating functions. The latter arise naturally when studying so-called ask zeta functions of direct sums of modules of matrices or class- and orbit-counting zeta functions of direct products of nilpotent groups. Our method relies on shuffle compatibility of coloured permutation statistics and coloured quasisymmetric functions, extending recent work of Gessel and Zhuang.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2132-2154"},"PeriodicalIF":0.8,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70081","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681128","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":"Semibrick-cosilting correspondence","authors":"Ramin Ebrahimi,&nbsp;Alireza Nasr-Isfahani","doi":"10.1112/blms.70076","DOIUrl":"https://doi.org/10.1112/blms.70076","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>Λ</mi>\u0000 <annotation>$Lambda$</annotation>\u0000 </semantics></math> be a finite-dimensional algebra. In this paper, we show that there is a natural bijection between cosilting modules in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>Mod</mo>\u0000 <mi>Λ</mi>\u0000 </mrow>\u0000 <annotation>$operatorname{Mod}Lambda$</annotation>\u0000 </semantics></math> and semibricks in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>Mod</mo>\u0000 <mi>Λ</mi>\u0000 </mrow>\u0000 <annotation>$operatorname{Mod}Lambda$</annotation>\u0000 </semantics></math> satisfying some condition. Also this bijection restricts to a bijection between all semibricks in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mi>Λ</mi>\u0000 </mrow>\u0000 <annotation>$operatorname{mod}Lambda$</annotation>\u0000 </semantics></math> and a certain subclass of cosilting modules. These bijections are generalizations of Asai's correspondence (<i>Int. Math. Res. Not</i>. 16 (2020) 4993–5054) between support <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>τ</mi>\u0000 <mo>−</mo>\u0000 </msup>\u0000 <annotation>$tau ^-$</annotation>\u0000 </semantics></math>-tilting modules and right finite semibricks.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2018-2032"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681366","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":"Noncompact surfaces, triangulations and rigidity","authors":"Stephen C. Power","doi":"10.1112/blms.70083","DOIUrl":"https://doi.org/10.1112/blms.70083","url":null,"abstract":"<p>Every noncompact surface is shown to have a (3,6)-tight triangulation, and applications are given to the generic rigidity of countable bar-joint frameworks in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>${mathbb {R}}^3$</annotation>\u0000 </semantics></math>. In particular, every noncompact surface has a (3,6)-tight triangulation that is minimally 3-rigid. A simplification of Richards' proof of Kerékjártó's classification of noncompact surfaces is also given.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2097-2115"},"PeriodicalIF":0.8,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681282","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":"Constructing strictly sign regular matrices of all sizes and sign patterns","authors":"Projesh Nath Choudhury,&nbsp;Shivangi Yadav","doi":"10.1112/blms.70080","DOIUrl":"https://doi.org/10.1112/blms.70080","url":null,"abstract":"<p>The class of strictly sign regular (SSR) matrices has been extensively studied by many authors over the past century, notably by Schoenberg, Motzkin, Gantmacher, and Krein. A classical result of Gantmacher–Krein assures the existence of SSR matrices for any dimension and sign pattern. In this article, we provide an algorithm to explicitly construct an SSR matrix of any given size and sign pattern. (We also provide in the Appendix, a Python code implementing our algorithm.) To develop this algorithm, we show that one can extend an SSR matrix by adding an extra row (column) to its border, resulting in a higher order SSR matrix. Furthermore, we show how inserting a suitable new row/column between any two successive rows/columns of an SSR matrix results in a matrix that remains SSR. We also establish analogous results for SSR <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>×</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$m times n$</annotation>\u0000 </semantics></math> matrices of order <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> for any <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>[</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>min</mi>\u0000 <mo>{</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>}</mo>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$p in [1, min lbrace m,nrbrace]$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2077-2096"},"PeriodicalIF":0.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681234","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 new proof of the Bondal–Orlov reconstruction using Matsui spectra","authors":"Daigo Ito,&nbsp;Hiroki Matsui","doi":"10.1112/blms.70079","DOIUrl":"https://doi.org/10.1112/blms.70079","url":null,"abstract":"&lt;p&gt;In 2005, Balmer defined the ringed space &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;Spec&lt;/mo&gt;\u0000 &lt;mo&gt;⊗&lt;/mo&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{Spec}_otimes mathcal {T}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for a given tensor triangulated category, while in 2023, the second author introduced the ringed space &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;Spec&lt;/mo&gt;\u0000 &lt;mi&gt;▵&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{Spec}_vartriangle mathcal {T}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for a given triangulated category. In the algebro-geometric context, these spectra provided several reconstruction theorems using derived categories. In this paper, we prove that &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;Spec&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mo&gt;⊗&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;Perf&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{Spec}_{otimes _X^mathbb {L}} operatorname{Perf} X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an open ringed subspace of &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;Spec&lt;/mo&gt;\u0000 &lt;mi&gt;▵&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;Perf&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{Spec}_vartriangle operatorname{Perf} X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for a quasi-projective variety &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. As an application, we provide a new proof of the Bondal–Orlov and Ballard reconstruction theorems in terms of these spectra. Recently, the first author introduced the Fourier–Mukai locus &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mo&gt;Spec&lt;/mo&gt;\u0000 &lt;mi&gt;FM&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;Perf&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{Spec}^mathsf {FM} operatorname{Perf} X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for a smooth projective variety &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, which is constructed by gluing Fourier–Mukai partners of &lt;span&gt;&lt;/span","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2058-2076"},"PeriodicalIF":0.8,"publicationDate":"2025-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681263","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 the injective dimension of unit Cartier and unit Frobenius modules","authors":"Manuel Blickle,&nbsp;Daniel Fink,&nbsp;Alexandria Wheeler,&nbsp;Wenliang Zhang","doi":"10.1112/blms.70075","DOIUrl":"https://doi.org/10.1112/blms.70075","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> be a regular <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-finite ring of prime characteristic <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. We prove that the injective dimension of every unit Frobenius module <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> in the category of unit Frobenius modules is at most <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>dim</mo>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mo>Supp</mo>\u0000 <mi>R</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$dim (operatorname{Supp}_R(M))+1$</annotation>\u0000 </semantics></math>. We further show that for unit Cartier modules the same bound holds over any noetherian <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-finite ring <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> of prime characteristic <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. This shows that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>dim</mo>\u0000 <mi>A</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$dim A+1$</annotation>\u0000 </semantics></math> is a uniform upper bound for the injective dimension of any unit Cartier module over a noetherian <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-finite ring <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2006-2017"},"PeriodicalIF":0.8,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70075","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681525","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":"Spectra of subrings of cohomology generated by characteristic classes for fusion systems","authors":"Ian J. Leary,&nbsp;Jason Semeraro","doi":"10.1112/blms.70074","DOIUrl":"https://doi.org/10.1112/blms.70074","url":null,"abstract":"&lt;p&gt;If &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;$mathcal {F}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a saturated fusion system on a finite &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;-group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we define the Chern subring &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;Ch&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${operatorname{Ch}}(mathcal {F})$&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;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {F}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to be the subring of &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;H&lt;/mi&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;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$H^*(S;{mathbb {F}}_p)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; generated by Chern classes of &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;$mathcal {F}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-stable representations of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We show that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;Ch&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${operatorname{Ch}}(mathcal {F})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is contained 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;H&lt;/mi&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;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"1990-2005"},"PeriodicalIF":0.8,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70074","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681526","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 classical solutions and canonical transformations for Hamilton–Jacobi–Bellman equations","authors":"Mohit Bansil,&nbsp;Alpár R. Mészáros","doi":"10.1112/blms.70078","DOIUrl":"https://doi.org/10.1112/blms.70078","url":null,"abstract":"<p>In this note, we show how canonical transformations reveal hidden convexity properties for deterministic optimal control problems, which in turn result in global existence of <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mi>l</mi>\u0000 <mi>o</mi>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <annotation>$C^{1,1}_{loc}$</annotation>\u0000 </semantics></math> solutions to first-order Hamilton–Jacobi–Bellman equations.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2045-2057"},"PeriodicalIF":0.8,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70078","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681114","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":"The birational geometry of GIT quotients","authors":"Ruadhaí Dervan,&nbsp;Rémi Reboulet","doi":"10.1112/blms.70072","DOIUrl":"https://doi.org/10.1112/blms.70072","url":null,"abstract":"<p>Geometric invariant theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by work of Dolgachev–Hu and Thaddeus, it is known that two quotients of the same variety using different polarisations are related by birational transformations. Only finitely many birational varieties arise in this way: variation of GIT fails to capture the entirety of the birational geometry of GIT quotients. We construct a space parametrising all possible GIT quotients of all birational models of the variety in a simple and natural way, which captures the entirety of the birational geometry of GIT quotients in a precise sense. It yields in particular a compactification of a birational analogue of the set of stable orbits of the variety.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"1952-1967"},"PeriodicalIF":0.8,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70072","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681298","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":"Existence and regularity for integro-differential free transmission problem","authors":"Sun-Sig Byun,&nbsp;Seunghyun Kim","doi":"10.1112/blms.70070","DOIUrl":"https://doi.org/10.1112/blms.70070","url":null,"abstract":"<p>We study an integro-differential free transmission problem associated with the Bellman–Isaacs-type operator that is solution-dependent. The existence of a viscosity solution is proved by constructing solutions of suitable auxiliary problems for such a nonlocal problem. We also identify circumstances under which the gradient of the solution enjoys an interior Hölder regularity whose estimates remain uniform as the degree of the equation approaches 2.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"1923-1937"},"PeriodicalIF":0.8,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70070","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681297","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}