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Getting a handle on the Conway knot 掌握康威结
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-07-19 DOI: 10.1090/bull/1745
Jennifer Hom
{"title":"Getting a handle on the Conway knot","authors":"Jennifer Hom","doi":"10.1090/bull/1745","DOIUrl":"https://doi.org/10.1090/bull/1745","url":null,"abstract":"A knot is said to be slice if it bounds a smooth disk in the 4-ball. For 50 years, it was unknown whether a certain 11 crossing knot, called the Conway knot, was slice or not, and until recently, this was the only one of the thousands of knots with fewer than 13 crossings whose slice-status remained a mystery. We will describe Lisa Piccirillo's proof that the Conway knot is not slice. The main idea of her proof is given in the title of this article.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44351700","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
Michael Atiyah’s work in algebraic topology Michael Atiyah在代数拓扑方面的工作
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-07-15 DOI: 10.1090/BULL/1746
G. Segal
{"title":"Michael Atiyah’s work in algebraic topology","authors":"G. Segal","doi":"10.1090/BULL/1746","DOIUrl":"https://doi.org/10.1090/BULL/1746","url":null,"abstract":"In 1960 algebraic topology was at the centre of the mathematical stage, but Michael Atiyah burst into the field and changed its focus and its language. I describe his work of the following decade and its influence, keeping to the themes of \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-theory and generalized cohomology to minimise the overlap with Dan Freed’s account of Atiyah’s work on index theory, which also appears in this issue.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46287941","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
Book Review: Group actions in ergodic theory, geometry, and topology: Selected papers 书评：遍历理论、几何和拓扑中的群作用：论文选集
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-07-06 DOI: 10.1090/BULL/1741
David Kerr
{"title":"Book Review: Group actions in ergodic theory, geometry, and topology: Selected papers","authors":"David Kerr","doi":"10.1090/BULL/1741","DOIUrl":"https://doi.org/10.1090/BULL/1741","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48455671","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: Wigner-type theorems for Hilbert Grassmannians 书评：希尔伯特-格拉斯曼的Wigner型定理
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-06-21 DOI: 10.1090/bull/1743
G. P. Gehér
{"title":"Book Review: Wigner-type theorems for Hilbert Grassmannians","authors":"G. P. Gehér","doi":"10.1090/bull/1743","DOIUrl":"https://doi.org/10.1090/bull/1743","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49566937","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
On Katznelson’s Question for skew-product systems 关于斜积系统的卡兹尼尔森问题
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-06-21 DOI: 10.1090/bull/1764
Daniel Glasscock, Andreas Koutsogiannis, F. Richter
{"title":"On Katznelson’s Question for skew-product systems","authors":"Daniel Glasscock, Andreas Koutsogiannis, F. Richter","doi":"10.1090/bull/1764","DOIUrl":"https://doi.org/10.1090/bull/1764","url":null,"abstract":"Katznelson’s Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics and harmonic analysis. In this article, we give a positive answer to Katznelson’s Question for certain towers of skew-product extensions of equicontinuous systems, including systems of the form \u0000\u0000 \u0000 \u0000 (\u0000 x\u0000 ,\u0000 t\u0000 )\u0000 ↦\u0000 (\u0000 x\u0000 +\u0000 α\u0000 ,\u0000 t\u0000 +\u0000 h\u0000 (\u0000 x\u0000 )\u0000 )\u0000 \u0000 (x,t) mapsto (x + alpha , t + h(x))\u0000 \u0000\u0000. We describe which frequencies must be controlled for in order to ensure recurrence in such systems, and we derive combinatorial corollaries concerning the difference sets of syndetic subsets of the natural numbers.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47938623","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: 4
Book Review: Invitation to partial differential equations 书评:偏微分方程的邀请
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-06-18 DOI: 10.1090/bull/1742
Y. Pinchover
{"title":"Book Review: Invitation to partial differential equations","authors":"Y. Pinchover","doi":"10.1090/bull/1742","DOIUrl":"https://doi.org/10.1090/bull/1742","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60549727","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: Extrinsic geometric flows 书评：外在几何流
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-06-17 DOI: 10.1090/bull/1740
L. Ni
{"title":"Book Review: Extrinsic geometric flows","authors":"L. Ni","doi":"10.1090/bull/1740","DOIUrl":"https://doi.org/10.1090/bull/1740","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46478479","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
Dynamical versions of Hardy’s uncertainty principle: A survey 哈代测不准原理的动力学版本综述
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-06-03 DOI: 10.1090/bull/1729
Aingeru Fernández-Bertolin, E. Malinnikova
{"title":"Dynamical versions of Hardy’s uncertainty principle: A survey","authors":"Aingeru Fernández-Bertolin, E. Malinnikova","doi":"10.1090/bull/1729","DOIUrl":"https://doi.org/10.1090/bull/1729","url":null,"abstract":"The Hardy uncertainty principle says that no function is better localized together with its Fourier transform than the Gaussian. The textbook proof of the result, as well as one of the original proofs by Hardy, refers to the Phragmén–Lindelöf theorem. In this note we first describe the connection of the Hardy uncertainty to the Schrödinger equation, and give a new proof of Hardy’s result which is based on this connection and the Liouville theorem. The proof is related to the second proof of Hardy, which has been undeservedly forgotten. Then we survey the recent results on dynamical versions of Hardy’s theorem.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47301777","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
Geometry, analysis, and morphogenesis: Problems and prospects 几何、分析与形态发生:问题与展望
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-04-19 DOI: 10.1090/bull/1765
M. Lewicka, L. Mahadevan
{"title":"Geometry, analysis, and morphogenesis: Problems and prospects","authors":"M. Lewicka, L. Mahadevan","doi":"10.1090/bull/1765","DOIUrl":"https://doi.org/10.1090/bull/1765","url":null,"abstract":"The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics, and mathematics. How might these shapes be predicted, and how can they eventually be designed? We review our current understanding of this problem, which brings together analysis, geometry, and mechanics in the description of the morphogenesis of low-dimensional objects. Starting from the view that shape is the consequence of metric frustration in an ambient space, we examine the links between the classical Nash embedding problem and biological morphogenesis. Then, motivated by a range of experimental observations and numerical computations, we revisit known rigorous results on curvature-driven patterning of thin elastic films, especially the asymptotic behaviors of the solutions as the (scaled) thickness becomes vanishingly small and the local curvature can become large. Along the way, we discuss open problems that include those in mathematical modeling and analysis along with questions driven by the allure of being able to tame soft surfaces for applications in science and engineering.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41499695","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
In Memoriam: John H. Conway 纪念:约翰·h·康威
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2021-04-19 DOI: 10.1090/BULL/1702
M. Broué
{"title":"In Memoriam: John H. Conway","authors":"M. Broué","doi":"10.1090/BULL/1702","DOIUrl":"https://doi.org/10.1090/BULL/1702","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41606912","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
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