Advances in Mathematics最新文献_第8页

Conformal product structures on compact Kähler manifolds

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-27 DOI: 10.1016/j.aim.2025.110181

Andrei Moroianu , Mihaela Pilca

引用次数: 0

The Σ2-Potentialist Principle

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-27 DOI: 10.1016/j.aim.2025.110182

Omer Ben Neria , Gabriel Goldberg , Eyal Kaplan

{"title":"The Σ2-Potentialist Principle","authors":"Omer Ben Neria , Gabriel Goldberg , Eyal Kaplan","doi":"10.1016/j.aim.2025.110182","DOIUrl":"10.1016/j.aim.2025.110182","url":null,"abstract":"<div><div>We settle a question of Woodin motivated by the philosophy of potentialism in set theory. A sentence in the language of set theory is locally verifiable if it asserts the existence of a level <math><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub></math> of the cumulative hierarchy of sets with some first-order property; this is equivalent to being <math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math> in the Lévy hierarchy. A sentence is <math><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub></math>-satisfiable if it can be forced without changing <math><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub></math>, and V-satisfiable if it is <math><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub></math>-satisfiable for all ordinals α. The <math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-Potentialist Principle, introduced by Woodin, asserts that every V-satisfiable locally verifiable sentence is true. We show in Theorem 6.2 that the <math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-Potentialist Principle is consistent relative to a supercompact cardinal. We accomplish this by generalizing Gitik's method of iterating distributive forcings by embedding them into Príkry-type forcings [6, Section 6.4]; our generalization, Theorem 5.2, works for forcings that add no bounded subsets to a strongly compact cardinal, which requires a completely different proof. Finally, using the concept of mutual stationarity, we show in Theorem 7.5 that the <math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-Potentialist Principle implies the consistency of a Woodin cardinal.3</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110182"},"PeriodicalIF":1.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Symmetries of the cyclic nerve

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-26 DOI: 10.1016/j.aim.2025.110170

David Ayala, Aaron Mazel-Gee, Nick Rozenblyum

引用次数: 0

Large deviations of the empirical spectral measure of supercritical sparse Wigner matrices

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-24 DOI: 10.1016/j.aim.2025.110156

Fanny Augeri

{"title":"Large deviations of the empirical spectral measure of supercritical sparse Wigner matrices","authors":"Fanny Augeri","doi":"10.1016/j.aim.2025.110156","DOIUrl":"10.1016/j.aim.2025.110156","url":null,"abstract":"<div><div>Let Ξ be the adjacency matrix of an Erdős-Rényi graph on n vertices and with parameter p and consider A a <math><mi>n</mi><mo>×</mo><mi>n</mi></math> centred random symmetric matrix with bounded i.i.d. entries above the diagonal. When the mean degree np diverges, the empirical spectral measure of the normalized Hadamard product <math><mo>(</mo><mi>A</mi><mo>∘</mo><mi>Ξ</mi><mo>)</mo><mo>/</mo><msqrt><mrow><mi>n</mi><mi>p</mi></mrow></msqrt></math> converges weakly in probability to the semicircle law. In the regime where <math><mi>p</mi><mo>≪</mo><mn>1</mn></math> and <math><mi>n</mi><mi>p</mi><mo>≫</mo><mi>log</mi><mo>⁡</mo><mi>n</mi></math>, we prove a large deviations principle for the empirical spectral measure with speed <math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>p</mi></math> and with a good rate function solution of a certain variational problem. The rate function reveals in particular that the only possible deviations at the exponential scale <math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>p</mi></math> are around measures coming from Quadratic Vector Equations. As a byproduct, we obtain a large deviations principle for the empirical spectral measure of supercritical Erdős-Rényi graphs.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"466 ","pages":"Article 110156"},"PeriodicalIF":1.5,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143473995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Ortho-integral surfaces

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-20 DOI: 10.1016/j.aim.2025.110162

Nhat Minh Doan

引用次数: 0

Norm upper-semicontinuity of functions supported on open abelian isotropy in étale groupoids. Corrigendum to “Reconstruction of groupoids and C⁎-rigidity of dynamical systems” [Adv. Math. 390 (2021) 107923]

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-20 DOI: 10.1016/j.aim.2025.110150

Toke Meier Carlsen , Anna Duwenig , Efren Ruiz , Aidan Sims

引用次数: 0

On Jacobi–Weierstrass mock modular forms

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.aim.2025.110147

Claudia Alfes , Jens Funke , Michael H. Mertens , Eugenia Rosu

引用次数: 0

The length spectrum of random hyperbolic 3-manifolds

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.aim.2025.110158

Anna Roig-Sanchis

引用次数: 0

The constant term algebra of type A: The structure

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110154

Guoce Xin , Chen Zhang , Yue Zhou , Yueming Zhong

引用次数: 0

An adjunction inequality for the Bauer–Furuta type invariants, with applications to sliceness and 4-manifold topology

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110134

Nobuo Iida , Anubhav Mukherjee , Masaki Taniguchi

{"title":"An adjunction inequality for the Bauer–Furuta type invariants, with applications to sliceness and 4-manifold topology","authors":"Nobuo Iida , Anubhav Mukherjee , Masaki Taniguchi","doi":"10.1016/j.aim.2025.110134","DOIUrl":"10.1016/j.aim.2025.110134","url":null,"abstract":"<div><div>Our main result gives an adjunction inequality for embedded surfaces in certain 4-manifolds with contact boundary under a non-vanishing assumption on the Bauer–Furuta type invariants. Using this, we give infinitely many knots in <math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math> that are not smoothly H-slice (that is, bounding a null-homologous disk) in many 4-manifolds but they are topologically H-slice. In particular, we give such knots in the boundaries of the punctured elliptic surfaces <math><mi>E</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo></math>. In addition, we give obstructions to codimension-0 orientation-reversing embedding of weak symplectic fillings with <math><msub><mrow><mi>b</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn></math> into closed symplectic 4-manifolds with <math><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></math> and <math><msubsup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>≡</mo><mn>3</mn><mi>mod</mi><mspace></mspace><mn>4</mn></math>. From here we prove a Bennequin type inequality for strong symplectic caps of <math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>d</mi></mrow></msub><mo>)</mo></math>. We also show that any weakly symplectically fillable 3-manifold bounds a 4-manifold with at least two smooth structures.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"466 ","pages":"Article 110134"},"PeriodicalIF":1.5,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0