Memoirs of the American Mathematical Society最新文献

{"title":"Unipotent Representations, Theta Correspondences, and Quantum Induction","authors":"Hongyu He","doi":"10.1090/memo/1496","DOIUrl":"https://doi.org/10.1090/memo/1496","url":null,"abstract":"In this paper, we construct unipotent representations for the real orthagonal groups and the metaplectic groups in the sense of Vogan. Our construction is based on quantum induction which involves the compositions of even number of theta correspondences. In particular, our results imply that there are irreducible unitary representations attached to each special nilpotent orbit.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141699406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On 𝑝-adic 𝐿-functions for Hilbert modular forms","authors":"John Bergdall, David Hansen","doi":"10.1090/memo/1489","DOIUrl":"https://doi.org/10.1090/memo/1489","url":null,"abstract":"We construct \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-adic \u0000\u0000 \u0000 L\u0000 L\u0000 \u0000\u0000-functions associated with \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-adic families, and does not require any small slope or non-criticality assumptions on the \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-refinement. The main new ingredients are an adelic definition of a canonical map from overconvergent cohomology to a space of locally analytic distributions on the relevant Galois group, and a smoothness theorem for certain eigenvarieties at critically refined points.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141408679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simple Supercuspidal 𝐿-Packets of Quasi-Split Classical Groups","authors":"Masao Oi","doi":"10.1090/memo/1483","DOIUrl":"https://doi.org/10.1090/memo/1483","url":null,"abstract":"<p>In this memoir, for quasi-split classical groups over <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\u0000 <mml:semantics>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-adic fields, we determine the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\">\u0000 <mml:semantics>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">L</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-packets consisting of simple supercuspidal representations and their corresponding <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\">\u0000 <mml:semantics>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">L</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-parameters, under the assumption that <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\u0000 <mml:semantics>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is not equal to <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\">\u0000 <mml:semantics>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. The key is an explicit computation of characters of simple supercuspidal representations and the endoscopic character relation, which is a characterization of the local Langlands correspondence for quasi-split classical groups.</p>","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141034417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cubical Models of (∞,1)-Categories","authors":"Brandon Doherty, Krzysztof Kapulkin, Zachery Lindsey, Christian Sattler","doi":"10.1090/memo/1484","DOIUrl":"https://doi.org/10.1090/memo/1484","url":null,"abstract":"We construct a model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical analogue of inner horns. We show that this model structure is Quillen equivalent to the Joyal model structure on simplicial sets via the triangulation functor. As an application, we show that cubical quasicategories admit a convenient notion of a mapping space, which we use to characterize the weak equivalences between fibrant objects in our model structure as DK-equivalences.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141033393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Plethora of Cluster Structures on 𝐺𝐿_{𝑛}","authors":"M. Gekhtman, M. Shapiro, A. Vainshtein","doi":"10.1090/memo/1486","DOIUrl":"https://doi.org/10.1090/memo/1486","url":null,"abstract":"We continue the study of multiple cluster structures in the rings of regular functions on \u0000\u0000 \u0000 \u0000 G\u0000 \u0000 L\u0000 n\u0000 \u0000 \u0000 GL_n\u0000 \u0000\u0000, \u0000\u0000 \u0000 \u0000 S\u0000 \u0000 L\u0000 n\u0000 \u0000 \u0000 SL_n\u0000 \u0000\u0000 and \u0000\u0000 \u0000 \u0000 M\u0000 a\u0000 \u0000 t\u0000 n\u0000 \u0000 \u0000 Mat_n\u0000 \u0000\u0000 that are compatible with Poisson–Lie and Poisson-homogeneous structures. According to our initial conjecture, each class in the Belavin–Drinfeld classification of Poisson–Lie structures on a semisimple complex group \u0000\u0000 \u0000 \u0000 G\u0000 \u0000 mathcal {G}\u0000 \u0000\u0000 corresponds to a cluster structure in \u0000\u0000 \u0000 \u0000 \u0000 O\u0000 \u0000 (\u0000 \u0000 G\u0000 \u0000 )\u0000 \u0000 mathcal {O}(mathcal {G})\u0000 \u0000\u0000. Here we prove this conjecture for a large subset of Belavin–Drinfeld (BD) data of \u0000\u0000 \u0000 \u0000 A\u0000 n\u0000 \u0000 A_n\u0000 \u0000\u0000 type, which includes all the previously known examples. Namely, we subdivide all possible \u0000\u0000 \u0000 \u0000 A\u0000 n\u0000 \u0000 A_n\u0000 \u0000\u0000 type BD data into oriented and non-oriented kinds. We further single out BD data satisfying a certain combinatorial condition that we call aperiodicity and prove that for any oriented BD data of this kind there exists a regular cluster structure compatible with the corresponding Poisson–Lie bracket. In fact, we extend the aperiodicity condition to pairs of oriented BD data and prove a more general result that establishes an existence of a regular cluster structure on \u0000\u0000 \u0000 \u0000 S\u0000 \u0000 L\u0000 n\u0000 \u0000 \u0000 SL_n\u0000 \u0000\u0000 compatible with a Poisson bracket homogeneous with respect to the right and left action of two copies of \u0000\u0000 \u0000 \u0000 S\u0000 \u0000 L\u0000 n\u0000 \u0000 \u0000 SL_n\u0000 \u0000\u0000 equipped with two different Poisson-Lie brackets. Similar results hold for aperiodic non-oriented BD data, but the analysis of the corresponding regular cluster structure is more involved and not given here. If the aperiodicity condition is not satisfied, a compatible cluster structure has to be replaced with a generalized cluster structure. We will address these situations in future publications.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141036038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Transition Threshold for the 3D Couette Flow in a Finite Channel","authors":"Qi Chen, Dongyi Wei, Zhifei Zhang","doi":"10.1090/memo/1478","DOIUrl":"https://doi.org/10.1090/memo/1478","url":null,"abstract":"<p>In this paper, we study nonlinear stability of the 3D plane Couette flow <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis y comma 0 comma 0 right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>y</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(y,0,0)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> at high Reynolds number <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R e\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>R</mml:mi>\u0000 <mml:mi>e</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">{Re}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in a finite channel <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper T times left-bracket negative 1 comma 1 right-bracket times double-struck upper T\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">T</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">T</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {T}times [-1,1]times mathbb {T}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. It is well known that the plane Couette flow is linearly stable for any Reynolds number. However, it could become nonlinearly unstable and transition to turbulence for small but finite perturbations at high Reynolds number. This is so-called Sommerfeld paradox. One resolution of this paradox is to study the transition threshold problem, which is concerned with how much disturbance will lead to the instability of the flow and the dependence of disturbance on the Reynolds number. This work shows that if the initial velocity <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"v 0\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>v</mml:mi>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">v_0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> satisfies <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-vertical-bar v 0 minus left-parenthesis y comma 0 comma 0 right-parent","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140777519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Towers and the First-order Theories of Hyperbolic Groups","authors":"Vincent Guirardel, Gilbert Levitt, R. Sklinos","doi":"10.1090/memo/1477","DOIUrl":"https://doi.org/10.1090/memo/1477","url":null,"abstract":"This paper is devoted to the first-order theories of torsion-free hyperbolic groups. One of its purposes is to review some results and to provide precise and correct statements and definitions, as well as some proofs and new results.\u0000\u0000A key concept is that of a tower (Sela) or NTQ system (Kharlampovich-Myasnikov). We discuss them thoroughly.\u0000\u0000We state and prove a new general theorem which unifies several results in the literature: elementarily equivalent torsion-free hyperbolic groups have isomorphic cores (Sela); if \u0000\u0000 \u0000 H\u0000 H\u0000 \u0000\u0000 is elementarily embedded in a torsion-free hyperbolic group \u0000\u0000 \u0000 G\u0000 G\u0000 \u0000\u0000, then \u0000\u0000 \u0000 G\u0000 G\u0000 \u0000\u0000 is a tower over \u0000\u0000 \u0000 H\u0000 H\u0000 \u0000\u0000 relative to \u0000\u0000 \u0000 H\u0000 H\u0000 \u0000\u0000 (Perin); free groups (Perin-Sklinos, Ould-Houcine), and more generally free products of prototypes and free groups, are homogeneous.\u0000\u0000The converse to Sela and Perin’s results just mentioned is true. This follows from the solution to Tarski’s problem on elementary equivalence of free groups, due independently to Sela and Kharlampovich-Myasnikov, which we treat as a black box throughout the paper.\u0000\u0000We present many examples and counterexamples, and we prove some new model-theoretic results. We characterize prime models among torsion-free hyperbolic groups, and minimal models among elementarily free groups. Using Fraïssé’s method, we associate to every torsion-free hyperbolic group \u0000\u0000 \u0000 H\u0000 H\u0000 \u0000\u0000 a unique homogeneous countable group \u0000\u0000 \u0000 \u0000 \u0000 M\u0000 \u0000 \u0000 {mathcal {M}}\u0000 \u0000\u0000 in which any hyperbolic group \u0000\u0000 \u0000 \u0000 H\u0000 ′\u0000 \u0000 H’\u0000 \u0000\u0000 elementarily equivalent to \u0000\u0000 \u0000 H\u0000 H\u0000 \u0000\u0000 has an elementary embedding.\u0000\u0000In an appendix we give a complete proof of the fact, due to Sela, that towers over a torsion-free hyperbolic group \u0000\u0000 \u0000 H\u0000 H\u0000 \u0000\u0000 are \u0000\u0000 \u0000 H\u0000 H\u0000 \u0000\u0000-limit groups.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140776116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mixed Hodge Structures on Alexander Modules","authors":"Eva Elduque, C. Geske, Moisés Herradón Cueto, L. Maxim, Botong Wang","doi":"10.1090/memo/1479","DOIUrl":"https://doi.org/10.1090/memo/1479","url":null,"abstract":"<p>Motivated by the limit mixed Hodge structure on the Milnor fiber of a hypersurface singularity germ, we construct a natural mixed Hodge structure on the torsion part of the Alexander modules of a smooth connected complex algebraic variety. More precisely, let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper U\">\u0000 <mml:semantics>\u0000 <mml:mi>U</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">U</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be a smooth connected complex algebraic variety and let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f colon upper U right-arrow double-struck upper C Superscript asterisk\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo>:<!-- : --></mml:mo>\u0000 <mml:mi>U</mml:mi>\u0000 <mml:mo stretchy=\"false\">→<!-- → --></mml:mo>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">C</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">fcolon Uto mathbb {C}^*</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be an algebraic map inducing an epimorphism in fundamental groups. The pullback of the universal cover of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper C Superscript asterisk\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">C</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {C}^*</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> by <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\">\u0000 <mml:semantics>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">f</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> gives rise to an infinite cyclic cover <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper U Superscript f\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>U</mml:mi>\u0000 <mml:mi>f</mml:mi>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">U^f</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper U\">\u0000 <mml:semantics>\u0000 <mml:mi>U</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">U</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. The action of the deck group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Z\">\u0000 <mm","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140795898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity","authors":"Filippo Giuliani, R. Feola","doi":"10.1090/memo/1471","DOIUrl":"https://doi.org/10.1090/memo/1471","url":null,"abstract":"We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the first existence result of quasi-periodic water waves solutions bifurcating from a completely resonant elliptic fixed point. The proof is based on a Nash–Moser scheme, Birkhoff normal form methods and pseudo differential calculus techniques. We deal with the combined problems of small divisors and the fully-nonlinear nature of the equations.\u0000\u0000The lack of parameters, like the capillarity or the depth of the ocean, demands a refined nonlinear bifurcation analysis involving several nontrivial resonant wave interactions, as the well-known “Benjamin-Feir resonances”. We develop a novel normal form approach to deal with that. Moreover, by making full use of the Hamiltonian structure, we are able to provide the existence of a wide class of solutions which are free from restrictions of parity in the time and space variables.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140085786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Classification of 𝒪_{∞}-Stable 𝒞*-Algebras","authors":"James Gabe","doi":"10.1090/memo/1461","DOIUrl":"https://doi.org/10.1090/memo/1461","url":null,"abstract":"<p>I present a proof of Kirchberg’s classification theorem: two separable, nuclear, <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper O Subscript normal infinity\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">O</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal O_infty</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-stable <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">C^ast</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-algebras are stably isomorphic if and only if they are ideal-related <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K upper K\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mi>K</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">KK</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-equivalent. In particular, this provides a more elementary proof of the Kirchberg–Phillips theorem which is isolated in the paper to increase readability of this important special case.</p>","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139391793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}