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Essence of independence: Hodge theory of matroids since June Huh 独立的本质：六月以来的拟阵Hodge理论
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-11-10 DOI: 10.1090/bull/1803
C. Eur
{"title":"Essence of independence: Hodge theory of matroids since June Huh","authors":"C. Eur","doi":"10.1090/bull/1803","DOIUrl":"https://doi.org/10.1090/bull/1803","url":null,"abstract":"Matroids are combinatorial abstractions of independence, a ubiquitous notion that pervades many branches of mathematics. June Huh and his collaborators recently made spectacular breakthroughs by developing a Hodge theory of matroids that resolved several long-standing conjectures in matroid theory. We survey the main results in this development and ideas behind them.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41704786","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}
引用次数: 1
Book Review: Modern analysis of automorphic forms by example. Vol. 1; Modern analysis of automorphic forms by example. Vol. 2 书评:自同构形式的现代实例分析。卷1;自同构形式的现代实例分析。2卷。
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-11-03 DOI: 10.1090/bull/1788
M. Young
{"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":" ","pages":""},"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}
引用次数: 1
Book Review: The distribution of prime numbers 书评:质数的分布
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-10-24 DOI: 10.1090/bull/1784
Maksym Radziwill
{"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":" ","pages":""},"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}
引用次数: 0
Book Review: Potential theory and geometry on Lie groups 书评:李群的势理论和几何
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-10-24 DOI: 10.1090/bull/1785
L. Saloff‐Coste
{"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":"1 1","pages":""},"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}
引用次数: 0
Stable black holes: in vacuum and beyond 稳定的黑洞：在真空中和更远的地方
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-09-07 DOI: 10.1090/bull/1781
Elena Giorgi
{"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":" ","pages":""},"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}
引用次数: 2
Swarming: hydrodynamic alignment with pressure 蜂群:有压力的流体动力对准
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-08-24 DOI: 10.1090/bull/1793
E. Tadmor
{"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":" ","pages":""},"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}
引用次数: 6
Book Review: Continuous semigroups of holomorphic self-maps of the unit disc 书评：单位圆盘的全纯自映射的连续半群
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-08-16 DOI: 10.1090/bull/1780
D. Shoikhet
{"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":" ","pages":""},"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}
引用次数: 0
Embedding ℚ into a finitely presented group 将π嵌入到有限表示群中
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-08-11 DOI: 10.1090/bull/1762
James M. Belk, J. Hyde, Francesco Matucci
{"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":" ","pages":""},"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}
引用次数: 8
Local well-posedness for quasi-linear problems: A primer 拟线性问题的局部适定性：一个引子
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-07-27 DOI: 10.1090/bull/1775
M. Ifrim, D. Tataru
{"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":" ","pages":""},"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}
引用次数: 6
The algebro-geometric method: Solving algebraic differential equations by parametrizations 代数-几何方法:用参数化法求解代数微分方程
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2022-07-11 DOI: 10.1090/bull/1773
Sebastian Falkensteiner, Johann J. Mitteramskogler, J. Sendra, F. Winkler
{"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":" ","pages":""},"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}
引用次数: 2
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