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

{"title":"Estimates of the Kobayashi metric and Gromov hyperbolicity on convex domains of finite type","authors":"Hongyu Wang","doi":"10.1112/jlms.12966","DOIUrl":"https://doi.org/10.1112/jlms.12966","url":null,"abstract":"<p>In this paper, we give a local estimate for the Kobayashi distance on a bounded convex domain of finite type, which relates to a local pseudodistance near the boundary. The estimate is precise up to a bounded additive term. Also, we conclude that the domain equipped with the Kobayashi distance is Gromov hyperbolic that gives another proof of the result of Zimmer.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736848","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":"Applying projective functors to arbitrary holonomic simple modules","authors":"Marco Mackaay,&nbsp;Volodymyr Mazorchuk,&nbsp;Vanessa Miemietz","doi":"10.1112/jlms.12965","DOIUrl":"https://doi.org/10.1112/jlms.12965","url":null,"abstract":"<p>We prove that applying a projective functor to a holonomic simple module over a semisimple finite-dimensional complex Lie algebra produces a module that has an essential semisimple submodule of finite length. This implies that holonomic simple supermodules over certain Lie superalgebras are quotients of modules that are induced from simple modules over the even part. We also provide some further insight into the structure of Lie algebra modules that are obtained by applying projective functors to simple modules.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12965","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639500","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":"P. Jones' interpolation theorem for noncommutative martingale Hardy spaces II","authors":"Narcisse Randrianantoanina","doi":"10.1112/jlms.12968","DOIUrl":"https://doi.org/10.1112/jlms.12968","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math> be a semifinite von Neumann algebra equipped with an increasing filtration <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$(mathcal {M}_n)_{ngeqslant 1}$</annotation>\u0000 </semantics></math> of (semifinite) von Neumann subalgebras of <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math>. For <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>⩽</mo>\u0000 <mi>p</mi>\u0000 <mo>⩽</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1leqslant p leqslant infty$</annotation>\u0000 </semantics></math>, let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>H</mi>\u0000 <mi>p</mi>\u0000 <mi>c</mi>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {H}_p^c(mathcal {M})$</annotation>\u0000 </semantics></math> denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$(mathcal {M}_n)_{ngeqslant 1}$</annotation>\u0000 </semantics></math> and the index <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. We prove the following real interpolation identity: If <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>θ</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>1</mn>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639563","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":"Subrank and optimal reduction of scalar multiplications to generic tensors","authors":"Harm Derksen,&nbsp;Visu Makam,&nbsp;Jeroen Zuiddam","doi":"10.1112/jlms.12963","DOIUrl":"https://doi.org/10.1112/jlms.12963","url":null,"abstract":"<p>The subrank of a tensor measures how much a tensor can be diagonalized. We determine this parameter precisely for essentially all (i.e., generic) tensors. Namely, we prove for generic tensors in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mo>⊗</mo>\u0000 <mi>V</mi>\u0000 <mo>⊗</mo>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation>$V otimes V otimes V$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>dim</mo>\u0000 <mo>(</mo>\u0000 <mi>V</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$dim (V) = n$</annotation>\u0000 </semantics></math> that the subrank is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Θ</mi>\u0000 <mo>(</mo>\u0000 <msqrt>\u0000 <mi>n</mi>\u0000 </msqrt>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Theta (sqrt {n})$</annotation>\u0000 </semantics></math>. Our result significantly improves on the previous upper bound from the work of Strassen (1991) and Bürgisser (1990) which was <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>/</mo>\u0000 <mn>3</mn>\u0000 <mo>+</mo>\u0000 <mi>o</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$n^{2/3+o(1)}$</annotation>\u0000 </semantics></math>. Our result is tight up to an additive constant. Our full result covers not only 3-tensors but also <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-tensors, for which we find that the generic subrank is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Θ</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Thet","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12963","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141608101","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":"Intersection matrices for the minimal regular model of \u0000 \u0000 \u0000 \u0000 X\u0000 0\u0000 \u0000 \u0000 (\u0000 N\u0000 )\u0000 \u0000 \u0000 ${X}_0(N)$\u0000 and applications to the Arakelov canonical sheaf","authors":"Paolo Dolce,&nbsp;Pietro Mercuri","doi":"10.1112/jlms.12964","DOIUrl":"https://doi.org/10.1112/jlms.12964","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$N&amp;gt;1$</annotation>\u0000 </semantics></math> be an integer coprime to 6 such that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>∉</mo>\u0000 <mo>{</mo>\u0000 <mn>5</mn>\u0000 <mo>,</mo>\u0000 <mn>7</mn>\u0000 <mo>,</mo>\u0000 <mn>13</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$Nnotin lbrace 5,7,13rbrace$</annotation>\u0000 </semantics></math> and let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>=</mo>\u0000 <mi>g</mi>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$g=g(N)$</annotation>\u0000 </semantics></math> be the genus of the modular curve <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$X_0(N)$</annotation>\u0000 </semantics></math>. We compute the intersection matrices relative to special fibres of the minimal regular model of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$X_0(N)$</annotation>\u0000 </semantics></math>. Moreover, we prove that the self-intersection of the Arakelov canonical sheaf of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$X_0(N)$</annotation>\u0000 </semantics></math> is asymptotic to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 <mi>g</mi>\u0000 <mi>log</mi>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$3glog N$</annotation>\u0000 </semantics></math>, for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597079","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":"Spectral constant rigidity of warped product metrics","authors":"Xiaoxiang Chai,&nbsp;Juncheol Pyo,&nbsp;Xueyuan Wan","doi":"10.1112/jlms.12958","DOIUrl":"https://doi.org/10.1112/jlms.12958","url":null,"abstract":"<p>A theorem of Llarull says that if a smooth metric <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> on the <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-sphere <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {S}^n$</annotation>\u0000 </semantics></math> is bounded below by the standard round metric and the scalar curvature <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <annotation>$R_g$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> is bounded below by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$n (n - 1)$</annotation>\u0000 </semantics></math>, then the metric <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> must be the standard round metric. We prove a spectral Llarull theorem by replacing the bound <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <mo>⩾</mo>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$R_g geqslant n (n - 1)$</annotation>\u0000 </semantics></math> by a lower bound on the first eigenvalue of an elliptic operator involving the Laplacian and the scalar curvature <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <annotation>$R_g$</annotation>\u0000 </semantics></math>. We utilize two methods: spinor and spacetime harmonic function.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12958","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141488322","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":"Spectral large deviations of sparse random matrices","authors":"Shirshendu Ganguly,&nbsp;Ella Hiesmayr,&nbsp;Kyeongsik Nam","doi":"10.1112/jlms.12954","DOIUrl":"https://doi.org/10.1112/jlms.12954","url":null,"abstract":"<p>Eigenvalues of Wigner matrices has been a major topic of investigation. A particularly important subclass of such random matrices, useful in many applications, are what are known as sparse or diluted random matrices, where each entry in a Wigner matrix is multiplied by an independent Bernoulli random variable with mean <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. Alternatively, such a matrix can be viewed as the adjacency matrix of an Erdős–Rényi graph <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathcal {G}_{n,p}$</annotation>\u0000 </semantics></math> equipped with independent and identically distributed (i.i.d.) edge-weights. An observable of particular interest is the largest eigenvalue. In this paper, we study the large deviations behavior of the largest eigenvalue of such matrices, a topic that has received considerable attention over the years. While certain techniques have been devised for the case when <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> is fixed or perhaps going to zero not too fast with the matrix size, we focus on the case <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mfrac>\u0000 <mi>d</mi>\u0000 <mi>n</mi>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$p = frac{d}{n}$</annotation>\u0000 </semantics></math>, that is, constant average degree regime of sparsity, which is a central example due to its connections to many models in statistical mechanics and other applications. Most known techniques break down in this regime and even the typical behavior of the spectrum of such random matrices is not very well understood. So far, results were known only for the Erdős–Rényi graph <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mfrac>\u0000 <mi>d</mi>\u0000 <mi>n</mi>\u0000 </mfrac>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathcal {G}_{n,frac{d}{n}}$</annotation>\u0000 </semantics></math> <i>without</i> edge-weights and with <i>Gaussian</i> edge-weights. In the present article, we consider the effect of general weight distributions. More specifically, we consider entry distributions whose tail probabilities decay at rate <span></span><math>\u0000 <semantics>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141489020","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":"Discontinuous homomorphisms on C(X) with the negation of CH and a weak forcing axiom","authors":"Yushiro Aoki","doi":"10.1112/jlms.12956","DOIUrl":"https://doi.org/10.1112/jlms.12956","url":null,"abstract":"<p>In this paper, I introduce the properties <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>EPC</mi>\u0000 <msub>\u0000 <mi>ℵ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </msub>\u0000 <annotation>$mathrm{EPC}_{aleph _1}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ProjCes</mi>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{ProjCes}(E)$</annotation>\u0000 </semantics></math> for forcing notions and show that it is consistent that the forcing axiom for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>EPC</mi>\u0000 <msub>\u0000 <mi>ℵ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <mi>ProjCes</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{EPC}_{aleph _1}+ mathrm{ProjCes}(E)$</annotation>\u0000 </semantics></math> forcing notions holds, the continuum hypothesis fails, and an ultrapower of the field of reals has the property <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>β</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$beta _1$</annotation>\u0000 </semantics></math>. This provides a partial solution to H. Woodin's question concerning the existence of discontinuous homomorphisms on the Banach algebra of all complex-valued continuous functions on a compact space. Furthermore, we prove that the uniformization of a coloring of a ladder system on a stationary–costationary set <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math> is an example of an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>EPC</mi>\u0000 <msub>\u0000 <mi>ℵ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <mi>ProjCes</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>ω</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>∖</mo>\u0000 <mi>E</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{EPC}_{aleph _1}+ mathrm{ProjCes}(omega _1 setminus E)$</annotation>\u0000 </se","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141488323","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":"Full Souslin trees at small cardinals","authors":"Assaf Rinot,&nbsp;Shira Yadai,&nbsp;Zhixing You","doi":"10.1112/jlms.12957","DOIUrl":"https://doi.org/10.1112/jlms.12957","url":null,"abstract":"<p>A <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa$</annotation>\u0000 </semantics></math>-tree is <i>full</i> if each of its limit levels omits no more than one potential branch. Kunen asked whether a full <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa$</annotation>\u0000 </semantics></math>-Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa $</annotation>\u0000 </semantics></math>. Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℵ</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <annotation>$aleph _3$</annotation>\u0000 </semantics></math> many full <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℵ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$aleph _2$</annotation>\u0000 </semantics></math>-trees such that the product of any countably many of them is an <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℵ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$aleph _2$</annotation>\u0000 </semantics></math>-Souslin tree.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12957","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141488977","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":"Sarnak's conjecture in quantum computing, cyclotomic unitary group coranks, and Shimura curves","authors":"Colin Ingalls,&nbsp;Bruce W. Jordan,&nbsp;Allan Keeton,&nbsp;Adam Logan,&nbsp;Yevgeny Zaytman","doi":"10.1112/jlms.12952","DOIUrl":"https://doi.org/10.1112/jlms.12952","url":null,"abstract":"<p>Sarnak's conjecture in quantum computing concerns when the groups <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>PU</mo>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$operatorname{PU}_{2}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>PSU</mo>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$operatorname{PSU}_{2}$</annotation>\u0000 </semantics></math> over cyclotomic rings <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Z</mi>\u0000 <mo>[</mo>\u0000 <msub>\u0000 <mi>ζ</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>${mathbb {Z}}[zeta _{n}, 1/2]$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>ζ</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mi>e</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>π</mi>\u0000 <mi>i</mi>\u0000 <mo>/</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$zeta _n=e^{2pi i/n}$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mo>|</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$4|n$</annotation>\u0000 </semantics></math>, are generated by the Clifford-cyclotomic gate set. We previously settled this using Euler–Poincaré characteristics. A generalization of Sarnak's conjecture is to ask when these groups are generated by torsion elements. An obstruction to this is provided by the corank: a group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> has <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>corank</mo>\u0000 <mi>G</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$operatorname{corank}G&amp;gt;0$</annotation>\u0000 </semantics></math> only if <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is not generated by torsion elements. In this paper, we study the corank of these cyclotomic unitary grou","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141488427","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}