EMISSARY M a T H Ema T I Cal Sc Ien C Es R E Sea R C H I Nsti Tute
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Bibliography
Bibliography [1] Emil Artin. Galois Theory. Dover, second edition, 1964. [2] Michael Artin. Algebra. Prentice Hall, first edition, 1991. [3] M. F. Atiyah and I. G. Macdonald. Introduction to Commutative Algebra. Addison Wesley, third edition, 1969. [4] Nicolas Bourbaki. Alg`ebre, Chapitres 1-3.El´ements de Math´ematiques. Hermann, 1970. [5] Nicolas Bourbaki. Alg`ebre, Chapitre 10.El´ements de Math´ematiques. Masson, 1980. [6] Nicolas Bourbaki. Alg`ebre, Chapitres 4-7.El´ements de Math´ematiques. Masson, 1981. [7] Nicolas Bourbaki. Alg`ebre Commutative, Chapitres 8-9.El´ements de Math´ematiques. Masson, 1983. [8] Nicolas Bourbaki. Elements of Mathematics. Commutative Algebra, Chapters 1-7. Springer–Verlag, 1989. [9] Henri Cartan and Samuel Eilenberg. Homological Algebra. Princeton Math. Series, No. 19. Princeton University Press, 1956. [10] Jean Dieudonn´e. Panorama des mat´ematiques pures. Le choix bourbachique. Gauthiers-Villars, second edition, 1979. [11] David S. Dummit and Richard M. Foote. Abstract Algebra. Wiley, second edition, 1999. [12] Albert Einstein. Zur Elektrodynamik bewegter K¨orper. Annalen der Physik, 17:891–921, 1905. [13] David Eisenbud. Commutative Algebra With A View Toward Algebraic Geometry. GTM No. 150. Springer–Verlag, first edition, 1995. [14] Jean-Pierre Escofier. Galois Theory. GTM No. 204. Springer Verlag, first edition, 2001. [15] Peter Freyd. Abelian Categories. An Introduction to the theory of functors. Harper and Row, first edition, 1964. [16] Sergei I. Gelfand and Yuri I. Manin. Homological Algebra. Springer, first edition, 1999. [17] Sergei I. Gelfand and Yuri I. Manin. Methods of Homological Algebra. Springer, second edition, 2003. [18] Roger Godement. Topologie Alg´ebrique et Th´eorie des Faisceaux. -
Tōhoku Rick Jardine
INFERENCE / Vol. 1, No. 3 Tōhoku Rick Jardine he publication of Alexander Grothendieck’s learning led to great advances: the axiomatic description paper, “Sur quelques points d’algèbre homo- of homology theory, the theory of adjoint functors, and, of logique” (Some Aspects of Homological Algebra), course, the concepts introduced in Tōhoku.5 Tin the 1957 number of the Tōhoku Mathematical Journal, This great paper has elicited much by way of commen- was a turning point in homological algebra, algebraic tary, but Grothendieck’s motivations in writing it remain topology and algebraic geometry.1 The paper introduced obscure. In a letter to Serre, he wrote that he was making a ideas that are now fundamental; its language has with- systematic review of his thoughts on homological algebra.6 stood the test of time. It is still widely read today for the He did not say why, but the context suggests that he was clarity of its ideas and proofs. Mathematicians refer to it thinking about sheaf cohomology. He may have been think- simply as the Tōhoku paper. ing as he did, because he could. This is how many research One word is almost always enough—Tōhoku. projects in mathematics begin. The radical change in Gro- Grothendieck’s doctoral thesis was, by way of contrast, thendieck’s interests was best explained by Colin McLarty, on functional analysis.2 The thesis contained important who suggested that in 1953 or so, Serre inveigled Gro- results on the tensor products of topological vector spaces, thendieck into working on the Weil conjectures.7 The Weil and introduced mathematicians to the theory of nuclear conjectures were certainly well known within the Paris spaces. -
License Or Copyright Restrictions May Apply to Redistribution; See Https
License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use EMIL ARTIN BY RICHARD BRAUER Emil Artin died of a heart attack on December 20, 1962 at the age of 64. His unexpected death came as a tremendous shock to all who knew him. There had not been any danger signals. It was hard to realize that a person of such strong vitality was gone, that such a great mind had been extinguished by a physical failure of the body. Artin was born in Vienna on March 3,1898. He grew up in Reichen- berg, now Tschechoslovakia, then still part of the Austrian empire. His childhood seems to have been lonely. Among the happiest periods was a school year which he spent in France. What he liked best to remember was his enveloping interest in chemistry during his high school days. In his own view, his inclination towards mathematics did not show before his sixteenth year, while earlier no trace of mathe matical aptitude had been apparent.1 I have often wondered what kind of experience it must have been for a high school teacher to have a student such as Artin in his class. During the first world war, he was drafted into the Austrian Army. After the war, he studied at the University of Leipzig from which he received his Ph.D. in 1921. He became "Privatdozent" at the Univer sity of Hamburg in 1923. -
Right Ideals of a Ring and Sublanguages of Science
RIGHT IDEALS OF A RING AND SUBLANGUAGES OF SCIENCE Javier Arias Navarro Ph.D. In General Linguistics and Spanish Language http://www.javierarias.info/ Abstract Among Zellig Harris’s numerous contributions to linguistics his theory of the sublanguages of science probably ranks among the most underrated. However, not only has this theory led to some exhaustive and meaningful applications in the study of the grammar of immunology language and its changes over time, but it also illustrates the nature of mathematical relations between chunks or subsets of a grammar and the language as a whole. This becomes most clear when dealing with the connection between metalanguage and language, as well as when reflecting on operators. This paper tries to justify the claim that the sublanguages of science stand in a particular algebraic relation to the rest of the language they are embedded in, namely, that of right ideals in a ring. Keywords: Zellig Sabbetai Harris, Information Structure of Language, Sublanguages of Science, Ideal Numbers, Ernst Kummer, Ideals, Richard Dedekind, Ring Theory, Right Ideals, Emmy Noether, Order Theory, Marshall Harvey Stone. §1. Preliminary Word In recent work (Arias 2015)1 a line of research has been outlined in which the basic tenets underpinning the algebraic treatment of language are explored. The claim was there made that the concept of ideal in a ring could account for the structure of so- called sublanguages of science in a very precise way. The present text is based on that work, by exploring in some detail the consequences of such statement. §2. Introduction Zellig Harris (1909-1992) contributions to the field of linguistics were manifold and in many respects of utmost significance. -
Brauer Groups and Galois Cohomology of Function Fields Of
Brauer groups and Galois cohomology of function fields of varieties Jason Michael Starr Department of Mathematics, Stony Brook University, Stony Brook, NY 11794 E-mail address: [email protected] Contents 1. Acknowledgments 5 2. Introduction 7 Chapter 1. Brauer groups and Galois cohomology 9 1. Abelian Galois cohomology 9 2. Non-Abelian Galois cohomology and the long exact sequence 13 3. Galois cohomology of smooth group schemes 22 4. The Brauer group 29 5. The universal cover sequence 34 Chapter 2. The Chevalley-Warning and Tsen-Lang theorems 37 1. The Chevalley-Warning Theorem 37 2. The Tsen-Lang Theorem 39 3. Applications to Brauer groups 43 Chapter 3. Rationally connected fibrations over curves 47 1. Rationally connected varieties 47 2. Outline of the proof 51 3. Hilbert schemes and smoothing combs 54 4. Ramification issues 63 5. Existence of log deformations 68 6. Completion of the proof 70 7. Corollaries 72 Chapter 4. The Period-Index theorem of de Jong 75 1. Statement of the theorem 75 2. Abel maps over curves and sections over surfaces 78 3. Rational simple connectedness hypotheses 79 4. Rational connectedness of the Abel map 81 5. Rational simply connected fibrations over a surface 82 6. Discriminant avoidance 84 7. Proof of the main theorem for Grassmann bundles 86 Chapter 5. Rational simple connectedness and Serre’s “Conjecture II” 89 1. Generalized Grassmannians are rationally simply connected 89 2. Statement of the theorem 90 3. Reductions of structure group 90 Bibliography 93 3 4 1. Acknowledgments Chapters 2 and 3 notes are largely adapted from notes for a similar lecture series presented at the Clay Mathematics Institute Summer School in G¨ottingen, Germany in Summer 2006. -
Council Congratulates Exxon Education Foundation
from.qxp 4/27/98 3:17 PM Page 1315 From the AMS ics. The Exxon Education Foundation funds programs in mathematics education, elementary and secondary school improvement, undergraduate general education, and un- dergraduate developmental education. —Timothy Goggins, AMS Development Officer AMS Task Force Receives Two Grants The AMS recently received two new grants in support of its Task Force on Excellence in Mathematical Scholarship. The Task Force is carrying out a program of focus groups, site visits, and information gathering aimed at developing (left to right) Edward Ahnert, president of the Exxon ways for mathematical sciences departments in doctoral Education Foundation, AMS President Cathleen institutions to work more effectively. With an initial grant Morawetz, and Robert Witte, senior program officer for of $50,000 from the Exxon Education Foundation, the Task Exxon. Force began its work by organizing a number of focus groups. The AMS has now received a second grant of Council Congratulates Exxon $50,000 from the Exxon Education Foundation, as well as a grant of $165,000 from the National Science Foundation. Education Foundation For further information about the work of the Task Force, see “Building Excellence in Doctoral Mathematics De- At the Summer Mathfest in Burlington in August, the AMS partments”, Notices, November/December 1995, pages Council passed a resolution congratulating the Exxon Ed- 1170–1171. ucation Foundation on its fortieth anniversary. AMS Pres- ident Cathleen Morawetz presented the resolution during —Timothy Goggins, AMS Development Officer the awards banquet to Edward Ahnert, president of the Exxon Education Foundation, and to Robert Witte, senior program officer with Exxon. -
Mathematical Sciences Meetings and Conferences Section
OTICES OF THE AMERICAN MATHEMATICAL SOCIETY Richard M. Schoen Awarded 1989 Bacher Prize page 225 Everybody Counts Summary page 227 MARCH 1989, VOLUME 36, NUMBER 3 Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences This calendar lists all meetings which have been approved prior to Mathematical Society in the issue corresponding to that of the Notices the date this issue of Notices was sent to the press. The summer which contains the program of the meeting. Abstracts should be sub and annual meetings are joint meetings of the Mathematical Associ mitted on special forms which are available in many departments of ation of America and the American Mathematical Society. The meet mathematics and from the headquarters office of the Society. Ab ing dates which fall rather far in the future are subject to change; this stracts of papers to be presented at the meeting must be received is particularly true of meetings to which no numbers have been as at the headquarters of the Society in Providence, Rhode Island, on signed. Programs of the meetings will appear in the issues indicated or before the deadline given below for the meeting. Note that the below. First and supplementary announcements of the meetings will deadline for abstracts for consideration for presentation at special have appeared in earlier issues. sessions is usually three weeks earlier than that specified below. For Abstracts of papers presented at a meeting of the Society are pub additional information, consult the meeting announcements and the lished in the journal Abstracts of papers presented to the American list of organizers of special sessions. -
Major Awards Winners in Mathematics: A
International Journal of Advanced Information Science and Technology (IJAIST) ISSN: 2319:2682 Vol.3, No.10, October 2014 DOI:10.15693/ijaist/2014.v3i10.81-92 Major Awards Winners in Mathematics: A Bibliometric Study Rajani. S Dr. Ravi. B Research Scholar, Rani Channamma University, Deputy Librarian Belagavi & Professional Assistant, Bangalore University of Hyderabad, Hyderabad University Library, Bangalore II. MATHEMATICS AS A DISCIPLINE Abstract— The purpose of this paper is to study the bibliometric analysis of major awards like Fields Medal, Wolf Prize and Abel Mathematics is the discipline; it deals with concepts such Prize in Mathematics, as a discipline since 1936 to 2014. Totally as quantity, structure, space and change. It is use of abstraction there are 120 nominees of major awards are received in these and logical reasoning, from counting, calculation, honors. The data allow us to observe the evolution of the profiles of measurement and the study of the shapes and motions of winners and nominations during every year. The analysis shows physical objects. According to the Aristotle defined that top ranking of the author’s productivity in mathematics mathematics as "the science of quantity", and this definition discipline and also that would be the highest nominees received the prevailed until the 18th century. Benjamin Peirce called it "the award at Institutional wise and Country wise. competitors. The science that draws necessary conclusions". United States of America awardees got the highest percentage of about 50% in mathematics prize. According to David Hilbert said that "We are not speaking Index terms –Bibliometric, Mathematics, Awards and Nobel here of arbitrariness in any sense. -
January 2002 Prizes and Awards
January 2002 Prizes and Awards 4:25 p.m., Monday, January 7, 2002 PROGRAM OPENING REMARKS Ann E. Watkins, President Mathematical Association of America BECKENBACH BOOK PRIZE Mathematical Association of America BÔCHER MEMORIAL PRIZE American Mathematical Society LEVI L. CONANT PRIZE American Mathematical Society LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION Association for Women in Mathematics ALICE T. S CHAFER PRIZE FOR EXCELLENCE IN MATHEMATICS BY AN UNDERGRADUATE WOMAN Association for Women in Mathematics CHAUVENET PRIZE Mathematical Association of America FRANK NELSON COLE PRIZE IN NUMBER THEORY American Mathematical Society AWARD FOR DISTINGUISHED PUBLIC SERVICE American Mathematical Society CERTIFICATES OF MERITORIOUS SERVICE Mathematical Association of America LEROY P. S TEELE PRIZE FOR MATHEMATICAL EXPOSITION American Mathematical Society LEROY P. S TEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH American Mathematical Society LEROY P. S TEELE PRIZE FOR LIFETIME ACHIEVEMENT American Mathematical Society DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS Mathematical Association of America CLOSING REMARKS Hyman Bass, President American Mathematical Society MATHEMATICAL ASSOCIATION OF AMERICA BECKENBACH BOOK PRIZE The Beckenbach Book Prize, established in 1986, is the successor to the MAA Book Prize. It is named for the late Edwin Beckenbach, a long-time leader in the publica- tions program of the Association and a well-known professor of mathematics at the University of California at Los Angeles. The prize is awarded for distinguished, innov- ative books published by the Association. Citation Joseph Kirtland Identification Numbers and Check Digit Schemes MAA Classroom Resource Materials Series This book exploits a ubiquitous feature of daily life, identification numbers, to develop a variety of mathematical ideas, such as modular arithmetic, functions, permutations, groups, and symmetries. -
Mathematics People
NEWS Mathematics People Assaf Naor was born in 1975 in Rehovot, Israel. He Naor Awarded received his PhD in mathematics from the Hebrew Univer- sity of Jerusalem in 2002 under the supervision of Joram Ostrowski Prize Lindenstrauss. He held positions at Microsoft Research, Assaf Naor of Princeton University the University of Washington, and the Courant Institute of has been awarded the 2019 Ostrowski Mathematical Sciences before joining the faculty of Prince- Prize “for his groundbreaking work in ton University in 2014. His honors include the European areas in the meeting point of the ge- Mathematical Society Prize (2008), the Salem Prize (2008), ometry of Banach spaces, the structure the Bôcher Memorial Prize (2011), and the Nemmers Prize of metric spaces, and algorithms.” The (2018). He is a Fellow of the AMS. He gave an invited ad- prize citation reads in part: “The na- dress at the 2010 International Congress of Mathematicians. ture of his contribution is threefold: The Ostrowski Prize is awarded in odd-numbered years Solutions of hard problems, setting for outstanding achievement in pure mathematics and the foundations of numerical mathematics. It carries a cash Assaf Naor a significant research direction for himself and others to follow, and award of 100,000 Swiss francs (approximately US$100,300). finding deep connections between pure mathematics and —Helmut Harbrecht, Universität Basel computer science. “Since the mid-nineties, geometric methods have played an influential role toward designing algorithms for com- Pham Awarded 2019 putational problems that a priori have little connection . to geometry. Assaf Naor is the world leader on this topic, ICTP-IMU Ramanujan Prize building a long-term, cohesive research program. -
Artin and Levin Awarded National Medal of Science Elaine Kehoe
COMMUNICATION Artin and Levin Awarded National Medal of Science Elaine Kehoe Michael Artin of particularly the no- the Massachusetts tion of rational singu- Institute of Technol- larity. He also found a ogy and Simon Levin striking example, with of Princeton Univer- Mumford, of a unira- sity have been hon- tional variety that is ored with the 2015 not rational, and in National Medal of joint work with Swin- Science, the United nerton-Dyer proved States’ highest honor the Shafarevich-Tate for achievement in conjecture for elliptic science. curves over rational The Work of Michael function fields whose Artin minimal models are The Notices asked K3 surfaces. Other David Harbater of the work of his related Photo by Donna Coveney. algebraic geometry to Photo by Brian Wilson, Princeton Office of Communications. Michael Artin University of Pennsyl- Simon Levin vania to comment on topology, including the work of Artin. Harbater responded: “Michael Artin his work with Mazur is one of the founders of modern algebraic geometry, on étale homotopy and the study of diffeomorphisms of developing, together with Grothendieck, the notions of compact manifolds. Grothendieck topology and étale cohomology, which “In a quite different direction, he brought ideas of were later key to the proofs of the Weil conjectures and algebraic geometry to bear on noncommutative algebra, many other developments. By introducing the notions of dramatically changing the landscape in that area. This algebraic spaces and algebraic stacks, he created a con- work included both the study of noncommutative alge- text that permitted algebraic geometers to go beyond the bras associated to schemes and also the introduction of limitations of schemes. -
Vii. Communication of the Mathematical Sciences 135 Viii
¡ ¢£¡ ¡ ¤ ¤ ¥ ¦ ¡ The Pacific Institute for the Mathematical Sciences Our Mission Our Community The Pacific Institute for the Mathematical Sciences PIMS is a partnership between the following organi- (PIMS) was created in 1996 by the community zations and people: of mathematical scientists in Alberta and British Columbia and in 2000, they were joined in their en- The six participating universities (Simon Fraser deavour by their colleagues in the State of Washing- University, University of Alberta, University of ton. PIMS is dedicated to: British Columbia, University of Calgary, Univer- sity of Victoria, University of Washington) and af- Promoting innovation and excellence in research filiated Institutions (University of Lethbridge and in all areas encompassed by the mathematical sci- University of Northern British Columbia). ences; The Government of British Columbia through the Initiating collaborations and strengthening ties be- Ministry of Competition, Science and Enterprise, tween the mathematical scientists in the academic The Government of Alberta through the Alberta community and those in the industrial, business and government sectors; Ministry of Innovation and Science, and The Gov- ernment of Canada through the Natural Sciences Training highly qualified personnel for academic and Engineering Research Council of Canada. and industrial employment and creating new op- portunities for developing scientists; Over 350 scientists in its member universities who are actively working towards the Institute’s Developing new technologies to support research, mandate. Their disciplines include pure and ap- communication and training in the mathematical plied mathematics, statistics, computer science, sciences. physical, chemical and life sciences, medical sci- Building on the strength and vitality of its pro- ence, finance, management, and several engineer- grammes, PIMS is able to serve the mathematical ing fields.