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About the cover: Quaste 关于封面：Quaste
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-08-14 DOI: 10.1090/BULL/1679
H. Hauser
{"title":"About the cover: Quaste","authors":"H. Hauser","doi":"10.1090/BULL/1679","DOIUrl":"https://doi.org/10.1090/BULL/1679","url":null,"abstract":"More instructive is the remark that the polynomial on the left-hand side is a generator of the ideal I = 〈y − (x− w), z − w − w〉 ∩ R[x, y, z]. This shows that quaste is the image of the surface P in R defined by the two equations C : y = x and N : z = w+w under the linear projection π : R → R sending (x, y, z, w) to (x + w, y, z). Note that P equals the product C ×N of the cusp and node defined in R by the first (resp., second) equation. We can therefore interpret quaste as a rather faithful representation in R of the Cartesian product surface P in R. If we pass to parametrizations, things become clearer. The cusp is parametrized by s → (s, s) and the node by t → (t−t, t−1); hence P has the parametrization (s, t) → (s, s, t − t, t − 1).","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49481881","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
Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra 特征值中的特征向量:线性代数中一个基本恒等式的综述
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-08-10 DOI: 10.1090/BULL/1722
P. Denton, S. Parke, T. Tao, Xining Zhang
{"title":"Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra","authors":"P. Denton, S. Parke, T. Tao, Xining Zhang","doi":"10.1090/BULL/1722","DOIUrl":"https://doi.org/10.1090/BULL/1722","url":null,"abstract":"If $A$ is an $n times n$ Hermitian matrix with eigenvalues $lambda_1(A),dots,lambda_n(A)$ and $i,j = 1,dots,n$, then the $j^{mathrm{th}}$ component $v_{i,j}$ of a unit eigenvector $v_i$ associated to the eigenvalue $lambda_i(A)$ is related to the eigenvalues $lambda_1(M_j),dots,lambda_{n-1}(M_j)$ of the minor $M_j$ of $A$ formed by removing the $j^{mathrm{th}}$ row and column by the formula $$ |v_{i,j}|^2prod_{k=1;kneq i}^{n}left(lambda_i(A)-lambda_k(A)right)=prod_{k=1}^{n-1}left(lambda_i(A)-lambda_k(M_j)right),.$$ We refer to this identity as the emph{eigenvector-eigenvalue identity}. Despite the simple nature of this identity and the extremely mature state of development of linear algebra, this identity was not widely known until very recently. In this survey we describe the many times that this identity, or variants thereof, have been discovered and rediscovered in the literature (with the earliest precursor we know of appearing in 1834). We also provide a number of proofs and generalizations of the identity.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43291447","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: 94
Book Review: Discrete harmonic analysis 书评：离散谐波分析
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-07-29 DOI: 10.1090/BULL/1674
R. Grigorchuk
{"title":"Book Review: Discrete harmonic analysis","authors":"R. Grigorchuk","doi":"10.1090/BULL/1674","DOIUrl":"https://doi.org/10.1090/BULL/1674","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46819319","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
Minimal surfaces and free boundaries: Recent developments 最小表面和自由边界:最近的发展
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-06-28 DOI: 10.1090/BULL/1673
L. Caffarelli, Y. Sire
{"title":"Minimal surfaces and free boundaries: Recent developments","authors":"L. Caffarelli, Y. Sire","doi":"10.1090/BULL/1673","DOIUrl":"https://doi.org/10.1090/BULL/1673","url":null,"abstract":"Free boundaries occur in a lot of physical phenomena and are of major interest both mathematically and physically. The aim of this contribution is to describe new ideas and results developed in the last 20 years or so that deal with some nonlocal (sometimes called anomalous) free boundary problems. Actually, such free boundary problems have been known for several decades, one of the main instances being the thin obstacle problem, the so-called (scalar) Signorini free boundary problem. We will describe in this survey some new techniques that allow to deal with long-range interactions. We will not try to be exhaustive since the literature on this type of problem has been flourishing substantially, but rather we give an overview of the main current directions of research. In particular, we want to emphasize the link, very much well-known in the community, between minimal surfaces, their “approximation” by the Allen–Cahn equation and free boundary problems.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/BULL/1673","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46584857","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: 5
Book Review: Combinatorics and random matrix theory; Dynamical approach to random matrix theory 书评：组合数学与随机矩阵理论；随机矩阵理论的动力学方法
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-06-25 DOI: 10.1090/BULL/1675
T. Tao
{"title":"Book Review: Combinatorics and random matrix theory; Dynamical approach to random matrix theory","authors":"T. Tao","doi":"10.1090/BULL/1675","DOIUrl":"https://doi.org/10.1090/BULL/1675","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43247115","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
Tangent developable surfaces and the equations defining algebraic curves 切线可展曲面与代数曲线方程
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-06-13 DOI: 10.1090/bull/1683
L. Ein, R. Lazarsfeld
{"title":"Tangent developable surfaces and the equations defining algebraic curves","authors":"L. Ein, R. Lazarsfeld","doi":"10.1090/bull/1683","DOIUrl":"https://doi.org/10.1090/bull/1683","url":null,"abstract":"This is an introduction, aimed at a general mathematical audience, to recent work of Aprodu, Farkas, Papadima, Raicu and Weyman. These authors established a long-standing folk conjecture concerning the equations defining the tangent developable surface of a rational normal curve. This in turn led to a new proof of a fundamental theorem of Voisin on the syzygies of a general canonical curve. The present note, which is the write-up of a talk given by the second author at the Current Events seminar at the 2019 JMM, surveys this circle of ideas.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/bull/1683","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41885366","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
A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces Mirzakhani关于Riemann曲面模空间的研究之旅
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-05-05 DOI: 10.1090/bull/1687
A. Wright
{"title":"A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces","authors":"A. Wright","doi":"10.1090/bull/1687","DOIUrl":"https://doi.org/10.1090/bull/1687","url":null,"abstract":"We survey Mirzakhani's work relating to Riemann surfaces, which spans about 20 papers. We target the discussion at a broad audience of non-experts.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/bull/1687","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43547372","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: 50
About the cover: Mathematicians in bronze 关于封面:数学家铜像
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-04-19 DOI: 10.1090/BULL/1669
G. Alexanderson, L. F. Klosinski
{"title":"About the cover: Mathematicians in bronze","authors":"G. Alexanderson, L. F. Klosinski","doi":"10.1090/BULL/1669","DOIUrl":"https://doi.org/10.1090/BULL/1669","url":null,"abstract":"From Robin Wilson’s column in The Mathematical Intelligencer [2] we regularly learn about mathematicians who have been immortalized by being pictured on a postage stamp from a country one is often quite unfamiliar with. But we know the mathematician. The stamp is usually on rather fragile paper and, if used and canceled, is really quite delicate. And rarely there are coins that portray the portrait of a mathematician. But a much more robust portrayal of the visage of a mathematician is often to be found on a bronze medal. These are usually issued by an appropriate academy of sciences or sometimes by a university proud of a well-known faculty member they feel needs to be immortalized in bronze. They come in various shapes and sizes as we shall see, but the most dramatic are often heavy, with the portrayal quite three dimensional. And bronze medal sculptors appear to like showing off their dramatic skills as well as their technical ones. The large medals often compete with those of world’s fairs or international congresses, as well as centennials, bicentennials, and such. It should be noted that the size of a medal is not necessarily proportional to the influence of the subject’s work. The medals shown here are a selection of those in the authors’ collections [1].","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44494722","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
About the cover: Early American arithmetics 关于封面:早期美国算术
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-02-11 DOI: 10.1090/bull/1666
G. Alexanderson, L. F. Klosinski
{"title":"About the cover: Early American arithmetics","authors":"G. Alexanderson, L. F. Klosinski","doi":"10.1090/bull/1666","DOIUrl":"https://doi.org/10.1090/bull/1666","url":null,"abstract":"These are the words of George Washington after examining a copy of A New and Complete System of Arithmetic Composed for the Use of the Citizens of the United States by Nicholas Pike, 1788 [3]. The Pike arithmetic was not the first arithmetic printed in the new world. The first was Hodder’s Arithmetick: Or That Necessary Art Made Most Easy published in Boston in 1719 [2], and it was based on a 1661 English arithmetic by James Hodder. Isaac Greenwood, a Hollis Professor of Mathematics at Harvard, was the first North American author to write and have published an arithmetic in the colonies. His 1729 Arithmetick Vulgar and Decimal: With the Application Thereof, to a Variety of Cases in Trade, and Commerce may have been written for his own classroom at Harvard [1]. His arithmetic never had a wide audience, and Greenwood himself was censured for drunkenness and dismissed from Harvard in 1738. The second arithmetic by a colonist was published in 1730, and it was in Dutch. Pieter Venema’s Arithmetica of Cyfer Konst [4] also had limited success. It consisted of only 63 leaves and was printed in New York by John Peter Zenger. The first popular English language arithmetic by a person born in the colonies was this 1788 arithmetic by Nicholas Pike, the arithmetic of which George Washington spoke. It also received the following recommendations:","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/bull/1666","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47679997","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
Constants of de Bruijn–Newman type in analytic number theory and statistical physics 解析数论和统计物理中的德·布吕金-纽曼型常数
IF 1.3 3区 数学
Bulletin of the American Mathematical Society Pub Date : 2019-01-19 DOI: 10.1090/BULL/1668
C. Newman, Wei Wu
{"title":"Constants of de Bruijn–Newman type in analytic number theory and statistical physics","authors":"C. Newman, Wei Wu","doi":"10.1090/BULL/1668","DOIUrl":"https://doi.org/10.1090/BULL/1668","url":null,"abstract":"One formulation in 1859 of the Riemann Hypothesis (RH) was that the Fourier transform $H_f(z)$ of $f$ for $ z in mathbb{C}$ has only real zeros when $f(t)$ is a specific function $Phi (t)$. P'{o}lya's 1920s approach to RH extended $H_f$ to $H_{f,lambda}$, the Fourier transform of $e^{lambda t^2} f(t)$. We review developments of this approach to RH and related ones in statistical physics where $f(t)$ is replaced by a measure $d rho (t)$. P'{o}lya's work together with 1950 and 1976 results of de Bruijn and Newman, respectively, imply the existence of a finite constant $Lambda_{DN} = Lambda_{DN} (Phi)$ in $(-infty, 1/2]$ such that $H_{Phi,lambda}$ has only real zeros if and only if $lambda geq Lambda_{DN}$; RH is then equivalent to $Lambda_{DN} leq 0$. Recent developments include the Rodgers and Tao proof of the 1976 conjecture that $Lambda_{DN} geq 0$ (that RH, if true, is only barely so) and the Polymath 15 project improving the $1/2$ upper bound to about $0.22$. We also present examples of $rho$'s with differing $H_{rho,lambda}$ and $Lambda_{DN} (rho)$ behaviors; some of these are new and based on a recent weak convergence theorem of the authors.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2019-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43048242","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
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