Proceedings of the American Mathematical Society, Series B最新文献

{"title":"The strong Lefschetz property for quadratic reverse lexicographic ideals","authors":"Filip Jonsson Kling","doi":"10.1090/bproc/234","DOIUrl":"https://doi.org/10.1090/bproc/234","url":null,"abstract":"<p>Consider ideals <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I\">\u0000 <mml:semantics>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">I</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of the form <disp-formula content-type=\"math/mathml\">\u0000[\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I equals left-parenthesis x 1 squared comma ellipsis comma x Subscript n Superscript 2 Baseline right-parenthesis plus upper R upper L e x left-parenthesis x Subscript i Baseline x Subscript j Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msubsup>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mo>…</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msubsup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>RLex</mml:mi>\u0000 <mml:mo>⁡</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>i</mml:mi>\u0000 </mml:msub>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>j</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">I=(x_1^2,dots , x_n^2)+operatorname {RLex}(x_ix_j)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000]\u0000</disp-formula> where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R upper L e x left-parenthesis x Subscript i Baseline x Subscript j Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>RLex</mml:mi>\u0000 <mml:mo>⁡</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>i</mml:mi>\u0000 </mml:msub>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>j</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">operatorname {RLex}(x_ix_j)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is the ideal generated by all the square-free monomials which are greater than or equal to <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x Subscript i Baseline x Subscript j\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>i</mml:mi>\u0000 </mml:msub>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>j</mml:mi>\u0000 </mml:msub>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">x_ix_j</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in the reverse lexicographic o","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"90 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141657642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new proof of the Gagliardo–Nirenberg and Sobolev inequalities: Heat semigroup approach","authors":"Tohru Ozawa, Taiki Takeuchi","doi":"10.1090/bproc/211","DOIUrl":"https://doi.org/10.1090/bproc/211","url":null,"abstract":"We give a new proof of the Gagliardo–Nirenberg and Sobolev inequalities based on the heat semigroup. Concerning the Gagliardo–Nirenberg inequality, we simplify the previous proof by relying only on the \u0000\u0000 \u0000 \u0000 L\u0000 p\u0000 \u0000 L^p\u0000 \u0000\u0000-\u0000\u0000 \u0000 \u0000 L\u0000 q\u0000 \u0000 L^q\u0000 \u0000\u0000 estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"113 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141657167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonergodicity of the geodesic flow on a special class of Cantor tree surfaces","authors":"Michael Pandazis","doi":"10.1090/bproc/228","DOIUrl":"https://doi.org/10.1090/bproc/228","url":null,"abstract":"A Riemann surface equipped with its conformal hyperbolic metric is parabolic if and only if the geodesic flow on its unit tangent bundle is ergodic. Let \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 be a Cantor tree or a blooming Cantor tree Riemann surface. Fix a geodesic pants decomposition of \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 and call the boundary geodesics in the decomposition cuffs. Basmajian, Hakobyan, and Šarić proved that if the lengths of cuffs are rapidly converging to zero, then \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 is parabolic. More recently, Šarić proved a slightly slower convergence of lengths of cuffs to zero implies \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 is not parabolic. In this paper, we interpolate between the two rates of convergence of the cuffs to zero and find that these surfaces are not parabolic, thus completing the picture.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"65 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141693636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Explicit bounds on the coefficients of modular polynomials for the elliptic 𝑗-invariant","authors":"Florian Breuer, Fabien Pazuki","doi":"10.1090/bproc/179","DOIUrl":"https://doi.org/10.1090/bproc/179","url":null,"abstract":"<p>We obtain an explicit upper bound on the size of the coefficients of the elliptic modular polynomials <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Phi Subscript upper N\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi mathvariant=\"normal\">Φ</mml:mi>\u0000 <mml:mi>N</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">Phi _N</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> for any <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N greater-than-or-equal-to 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo>≥</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Ngeq 1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. These polynomials vanish at pairs of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"j\">\u0000 <mml:semantics>\u0000 <mml:mi>j</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">j</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-invariants of elliptic curves linked by cyclic isogenies of degree <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\">\u0000 <mml:semantics>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">N</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. The main term in the bound is asymptotically optimal as <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\">\u0000 <mml:semantics>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">N</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> tends to infinity.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"42 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonexistence of nontrivial solutions to Kirchhoff-like equations","authors":"Christopher Goodrich","doi":"10.1090/bproc/224","DOIUrl":"https://doi.org/10.1090/bproc/224","url":null,"abstract":"<p>Subject to given boundary data, nonexistence of solution to the one-dimensional Kirchhoff-like equation <disp-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"minus upper M left-parenthesis left-parenthesis a asterisk StartAbsoluteValue u EndAbsoluteValue Superscript q Baseline right-parenthesis left-parenthesis 1 right-parenthesis right-parenthesis u left-parenthesis t right-parenthesis equals lamda f left-parenthesis t comma u left-parenthesis t right-parenthesis right-parenthesis comma 0 greater-than t greater-than 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo>−</mml:mo>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">(</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mi>a</mml:mi>\u0000 <mml:mo>∗</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">|</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">|</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>q</mml:mi>\u0000 </mml:msup>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi>λ</mml:mi>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mtext> </mml:mtext>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">begin{equation*} -MBig (big (a*|u|^qbig )(1)Big )u(t)=lambda fbig (t,u(t)big ), 0>t>1 end{equation*}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</dis","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"87 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141699361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Examples of étale extensions of Green functors","authors":"A. Lindenstrauss, Birgit Richter, Foling Zou","doi":"10.1090/bproc/189","DOIUrl":"https://doi.org/10.1090/bproc/189","url":null,"abstract":"<p>We provide new examples of étale extensions of Green functors by transferring classical examples of étale extensions to the equivariant setting. Our examples are Tambara functors, and we prove Green étaleness for them, which implies Tambara étaleness. We show that every <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">C_2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Galois extensions of fields gives rise to an étale extension of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">C_2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Green functors. Here we associate the constant Tambara functor to the base field and the fix-Tambara functor to the extension. We also prove that all <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Subscript n\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">C_n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Kummer extensions give rise to étale extensions for arbitrary finite <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:semantics>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Étale extensions of fields induce étale extension of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Green functors for any finite group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> by passing to the corresponding constant <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Tambara functors.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"74 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141714856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characters of logarithmic vertex operator algebras and coloured invariants of torus links","authors":"S. Kanade","doi":"10.1090/bproc/223","DOIUrl":"https://doi.org/10.1090/bproc/223","url":null,"abstract":"<p>We show that the characters of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German s German l Subscript r\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"fraktur\">s</mml:mi>\u0000 <mml:mi mathvariant=\"fraktur\">l</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>r</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathfrak {sl}_r</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> versions of the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis 1 comma p right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(1,p)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> singlet and the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis 1 comma p right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(1,p)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> triplet vertex operator algebras arise as limits of appropriately coloured <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German s German l Subscript r\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"fraktur\">s</mml:mi>\u0000 <mml:mi mathvariant=\"fraktur\">l</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>r</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathfrak {sl}_r</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> Jones invariants of certain torus links.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"2 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141266169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Holomorphic support functions for uniformly pseudoconvex hypersurfaces, with an application to CR maps","authors":"Josef Greilhuber","doi":"10.1090/bproc/222","DOIUrl":"https://doi.org/10.1090/bproc/222","url":null,"abstract":"We construct holomorphic support functions for smooth weakly pseudoconvex hypersurfaces with Levi form of constant rank. These are then applied to show that formal holomorphic curves which are tangential to infinite order to such a hypersurface must be formally contained in its Levi foliation. As a consequence, we obtain a holomorphic deformation theorem for nowhere smooth CR maps into smooth pseudoconvex hypersurfaces with one-dimensional Levi foliation, strengthening a very general result of Lamel and Mir about formal deformations in this particular case.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141267710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the (6,4)-problem of Brown, Erdős, and Sós","authors":"Stefan Glock, Felix Joos, Jaehoon Kim, Marcus Kühn, Lyuben Lichev, Oleg Pikhurko","doi":"10.1090/bproc/170","DOIUrl":"https://doi.org/10.1090/bproc/170","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f Superscript left-parenthesis r right-parenthesis Baseline left-parenthesis n semicolon s comma k right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>r</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>;</mml:mo>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">f^{(r)}(n;s,k)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be the maximum number of edges of an <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r\">\u0000 <mml:semantics>\u0000 <mml:mi>r</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">r</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-uniform hypergraph on <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:semantics>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> vertices not containing a subgraph with <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\">\u0000 <mml:semantics>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> edges and at most <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"s\">\u0000 <mml:semantics>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">s</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> vertices. In 1973, Brown, Erdős, and Sós conjectured that the limit <disp-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"limit Underscript n right-arrow normal infinity Endscripts n Superscript negative 2 f Superscript left-parenthesis 3 right-parenthesis Baseline left-parenthesis n semicolon k plus 2 comma k right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:munder>\u0000 <mml:mo movablelimits=\"true\" form=\"prefix\">lim</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo stretchy=\"false\">→</mml:mo>\u0000 <mml:mi mathvariant=\"normal\">∞</mml:mi>\u0000 </mml:mrow>\u0000 </mml:munder>\u0000 <mml:msup>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>−</mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:msup>\u0000 <mml:mi","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"87 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141267856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Completely continuous multilinear mappings on 𝐿₁","authors":"Raffaella Cilia, Joaquín Gutiérrez","doi":"10.1090/bproc/213","DOIUrl":"https://doi.org/10.1090/bproc/213","url":null,"abstract":"<p>A useful result of H. Rosenthal and J. Bourgain states that, given a Banach space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, an operator <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T colon upper L 1 left-bracket 0 comma 1 right-bracket right-arrow upper X\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mo>:</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 <mml:mo stretchy=\"false\">→</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">T:L_1[0,1]to X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is completely continuous if and only if its composition with the natural inclusion <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"i Subscript normal infinity Baseline colon upper L Subscript normal infinity Baseline left-bracket 0 comma 1 right-bracket right-arrow upper L 1 left-bracket 0 comma 1 right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>i</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">∞</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo>:</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">∞</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 <mml:mo stretchy=\"false\">→</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">i_infty :L_infty [0,1] to L_1[0,1]</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is compact. We extend this result to multilinear mappings on products of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L 1 left-bracket 0 comma 1 right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">L_1[0,1]</mml:annotation>\u0000 </mml:seman","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"136 38","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140976877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}