{"title":"Book Review: Modern analysis of automorphic forms by example. Vol. 1; Modern analysis of automorphic forms by example. Vol. 2","authors":"M. Young","doi":"10.1090/bull/1788","DOIUrl":"https://doi.org/10.1090/bull/1788","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44801380","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":"Book Review: The distribution of prime numbers","authors":"Maksym Radziwill","doi":"10.1090/bull/1784","DOIUrl":"https://doi.org/10.1090/bull/1784","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46373153","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":"Book Review: Potential theory and geometry on Lie groups","authors":"L. Saloff‐Coste","doi":"10.1090/bull/1785","DOIUrl":"https://doi.org/10.1090/bull/1785","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60549746","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}
Black holes are important objects in our understanding of the universe, as they represent the extreme nature of General Relativity. The mathematics behind them has surprising geometric properties, and their dynamics is governed by hyperbolic partial differential equations. A basic question one may ask is whether these solutions to the Einstein equation are stable under small perturbations, which is a typical requirement to be physically meaningful. We illustrate the main conjectures regarding the stability problem of known black hole solutions and present some recent theorems regarding the fully nonlinear evolution of black holes in the case of vacuum and their interaction with matter fields.
{"title":"Stable black holes: in vacuum and beyond","authors":"Elena Giorgi","doi":"10.1090/bull/1781","DOIUrl":"https://doi.org/10.1090/bull/1781","url":null,"abstract":"Black holes are important objects in our understanding of the universe, as they represent the extreme nature of General Relativity. The mathematics behind them has surprising geometric properties, and their dynamics is governed by hyperbolic partial differential equations. A basic question one may ask is whether these solutions to the Einstein equation are stable under small perturbations, which is a typical requirement to be physically meaningful. We illustrate the main conjectures regarding the stability problem of known black hole solutions and present some recent theorems regarding the fully nonlinear evolution of black holes in the case of vacuum and their interaction with matter fields.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44532520","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}
We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering toward a weighted average heading. We consider the class of so-called p p -alignment hydrodynamics, based on 2 p 2p -Laplacians and weighted by a general family of symmetric communication kernels. The main new aspect here is the long-time emergence behavior for a general class of pressure tensors without a closure assumption, beyond the mere requirement that they form an energy dissipative process. We refer to such pressure laws as “entropic”, and prove the flocking of p p -alignment hydrodynamics, driven by singular kernels with a general class of entropic pressure tensors. These results indicate the rigidity of alignment in driving long-time flocking behavior despite the lack of thermodynamic closure.
研究了流体动力对准的群体行为。对中反映了向加权平均航向的转向。我们考虑一类所谓的p - p -取向流体力学，它基于2p2p -拉普拉斯算子，并由一般的对称通信核族加权。这里的主要新方面是一般类型的压力张量在没有闭合假设的情况下的长时间涌现行为，而不仅仅是要求它们形成能量耗散过程。我们将这种压力定律称为“熵”，并用一类广义的熵压力张量证明了由奇异核驱动的p - p -取向流体力学的群集。这些结果表明，尽管缺乏热力学闭合，但在驱动长时间群集行为时，对准的刚性。
{"title":"Swarming: hydrodynamic alignment with pressure","authors":"E. Tadmor","doi":"10.1090/bull/1793","DOIUrl":"https://doi.org/10.1090/bull/1793","url":null,"abstract":"We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering toward a weighted average heading. We consider the class of so-called \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-alignment hydrodynamics, based on \u0000\u0000 \u0000 \u0000 2\u0000 p\u0000 \u0000 2p\u0000 \u0000\u0000-Laplacians and weighted by a general family of symmetric communication kernels. The main new aspect here is the long-time emergence behavior for a general class of pressure tensors without a closure assumption, beyond the mere requirement that they form an energy dissipative process. We refer to such pressure laws as “entropic”, and prove the flocking of \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-alignment hydrodynamics, driven by singular kernels with a general class of entropic pressure tensors. These results indicate the rigidity of alignment in driving long-time flocking behavior despite the lack of thermodynamic closure.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43634100","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":"Book Review: Continuous semigroups of holomorphic self-maps of the unit disc","authors":"D. Shoikhet","doi":"10.1090/bull/1780","DOIUrl":"https://doi.org/10.1090/bull/1780","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46523331","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}
We observe that the group of all lifts of elements of Thompson’s group TT to the real line is finitely presented and contains the additive group Qmathbb {Q} of the rational numbers. This gives an explicit realization of the Higman embedding theorem for Qmathbb {Q}, answering a Kourovka notebook question of Martin Bridson and Pierre de la Harpe.
我们观察到Thompson群T的元素到实数的所有提升的群是有限的，并且包含有理数的加法群Qmathbb｛Q｝。这给出了Qmathbb｛Q｝的Higman嵌入定理的显式实现，回答了Martin Bridson和Pierre de la Harpe的Kourovka笔记本问题。
{"title":"Embedding ℚ into a finitely presented group","authors":"James M. Belk, J. Hyde, Francesco Matucci","doi":"10.1090/bull/1762","DOIUrl":"https://doi.org/10.1090/bull/1762","url":null,"abstract":"<p>We observe that the group of all lifts of elements of Thompson’s group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T\">\u0000 <mml:semantics>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">T</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> to the real line is finitely presented and contains the additive group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Q\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Q</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {Q}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of the rational numbers. This gives an explicit realization of the Higman embedding theorem for <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Q\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Q</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {Q}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, answering a Kourovka notebook question of Martin Bridson and Pierre de la Harpe.</p>","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45768586","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}
Proving local well-posedness for quasi-linear problems in partial differential equations presents a number of difficulties, some of which are universal and others of which are more problem specific. On one hand, a common standard for what well-posedness should mean has existed for a long time, going back to Hadamard. On the other hand, in terms of getting there, there are by now both many variations—and also many misconceptions. The aim of these expository notes is to collect a number of both classical and more recent ideas in this direction, and to assemble them into a cohesive roadmap that can be then adapted to the reader’s problem of choice.
{"title":"Local well-posedness for quasi-linear problems: A primer","authors":"M. Ifrim, D. Tataru","doi":"10.1090/bull/1775","DOIUrl":"https://doi.org/10.1090/bull/1775","url":null,"abstract":"Proving local well-posedness for quasi-linear problems in partial differential equations presents a number of difficulties, some of which are universal and others of which are more problem specific. On one hand, a common standard for what well-posedness should mean has existed for a long time, going back to Hadamard. On the other hand, in terms of getting there, there are by now both many variations—and also many misconceptions.\u0000\u0000The aim of these expository notes is to collect a number of both classical and more recent ideas in this direction, and to assemble them into a cohesive roadmap that can be then adapted to the reader’s problem of choice.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46596543","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}
Sebastian Falkensteiner, Johann J. Mitteramskogler, J. Sendra, F. Winkler
We present a survey of the algebro-geometric method for solving algebraic ordinary differential equations by means of parametrizations of the associated algebraic sets. In particular, we deal with equations of order one, and also systems of algebro-geometric dimension one. Various classes of solutions are treated symbolically, such as rational, algebraic, and power series solutions. We also consider classes of algebraic transformations of the associated algebraic sets preserving the solutions of the differential equations. Two Maple packages, implementing some of these solution methods, are presented.
{"title":"The algebro-geometric method: Solving algebraic differential equations by parametrizations","authors":"Sebastian Falkensteiner, Johann J. Mitteramskogler, J. Sendra, F. Winkler","doi":"10.1090/bull/1773","DOIUrl":"https://doi.org/10.1090/bull/1773","url":null,"abstract":"We present a survey of the algebro-geometric method for solving algebraic ordinary differential equations by means of parametrizations of the associated algebraic sets. In particular, we deal with equations of order one, and also systems of algebro-geometric dimension one. Various classes of solutions are treated symbolically, such as rational, algebraic, and power series solutions. We also consider classes of algebraic transformations of the associated algebraic sets preserving the solutions of the differential equations. Two Maple packages, implementing some of these solution methods, are presented.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45869226","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":"About the Cover: Eduard Helly","authors":"H. Hauser","doi":"10.1090/bull/1778","DOIUrl":"https://doi.org/10.1090/bull/1778","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44574157","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}
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