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Mathematical Sciences, University of California, Santa Cruz, California Notices of the American Mathematical Society june 1986, Issue 248 Volume 33, Number 3, Pages 441-592 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to the press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change: this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and supplementary announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the headquarters office of the Society. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence. Rhode Island. on or before the deadline given below for the meeting. Note that the deadline for abstracts for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcements and the list of organizers of special sessions. ABSTRACT MEETING# DATE PLACE DEADLINE ISSUE August 3-11. 1986 Berkeley, California EXPIRED (International Congress of Mathematicians) 828 October 10-11, 1986 Logan, Utah tAugust 18 October 829 October 17-18, 1986 Charlotte, North Carolina tAugust 20 October 830 October 31-November 1, Denton, Texas tAugust 25 October 1986 831 January 21-24, 1987 San Antonio, Texas October 15 January (93rd Annual Meeting) April 3-4, 1987 Kent, Ohio April 25-26, 1987 Newark, New Jersey January 6-9, 1988 Atlanta, Georgia (94th Annual Meeting) August 8-12. 1988 Providence, Rhode Island (AMS Centennial Celebration) January 11-14, 1989 Phoenix, Arizona (95th Annual Meeting) t Please note change from March 1986 calendar. DEADLINES Advertising (Aug. 1986 Issue) June 17, 1986 (Oct. 1986 Issue) Sept. 3. 1986 (Nov. 1986 Issue) Oct. 1. 1986 News/SMIC (Aug. 1986 Issue) May 29. 1986 (Oct. 1986 Issue) Aug. 18. 1986 (Nov. 1986 Issue) Sept. 15. 1986 Other Events Sponsored by the Society May 28, 1986. Symposium on Some Mathematical Questions in Biology, Modeling Circadian Rhythms, Philadelphia, Pennsylvania. Details: March issue. June 22-August 2. 1986, Joint Summer Research Conferences in the Mathematical Sciences, University of California, Santa Cruz, California. Details: January issue. July 7-25, 1986, AMS Summer Research Institute on Representations of Finite Groups and Related Topics, Humboldt State University, Arcata, California. Details: March issue. Subscribers' changes of address should be reported well in advance to avoid disruption of service: address labels are prepared four to six weeks in advance of the date of mailing. Requests for a change of address should a/ways include the member or subscriber code and preferably a copy of the entire mailing label. Members are reminded that U. S. Postal Service change-of-address forms are not adequate for this purpose. since they make no provision for several important items of information which are essential for the AMS records. Suitable forms are published from time to time in the Notices of the American Mathematical Society (e.g. March 1985. page 325). Send change of address notices to the Society at Post Office Box 6248. Providence. Rl 02940 [Notices of the American Mathematical Society is published seven times a year (January. March. June. August. October. November. December) by the American Mathematical Society at 201 Charles Street. Providence. Rl 02904. Second class postage paid at Providence. Rl and additional mailing offices. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, Membership and Sales Department, American Mathematical Society. P. 0. Box 6248. Providence. Rl 02940.) Publication here of the Society's street address. and the other information in brackets above. is a technical requirement of the U. S. Postal Service. All correspondence should be mailed to the Post Office Box. NOT the street address. Members are strongly urged to notify the Society themselves of address changes. since reliance on the postal service chance-of-address forms is liable to cause delays in processing such requests in the AMS office. Notices of the American Mathematical Society Volume 33, Number 3, June 1986 EDITORIAL COMMITTEE Paul F. Baum. Ralph P. Boas Raymond L. Johnson. Mary Ellen Rudin Steven H. Weintraub. Daniel Zelinsky 443 The Mordell Conjecture Everett Pitcher (Chairman) David Harris MANAGING EDITOR 450 NSF Budget Request for Fiscal 1987 James A. Voytuk 462 Mathematical Sciences: A Unifying and ASSOCIATE EDITORS Dynamical Resource Stuart Antman. Queries Hans Samelson. Queries 480 Reports to the Members of the Society Ronald L. Graham. Special Articles 482 Mathematical Software SUBSCRIPTION INFORMATION 486 Washington Outlook Subscription prices for Volume 33 (1986) are $85 list: $68 institutional member: 488 International Congress of Mathematicians $51 individual member. (The subscription 497 News and Announcements price for members is included in the annual dues.) A late charge of 10% of 505 NSF News & Reports the subscription price will be imposed 509 For Your Information upon orders received from nonmembers after January 1 of the subscription 515 Mathematical Text Processing year. Add for postage: Surface delivery 516 Letters to the Editor outside the United States and lndia-$8: 519 Queries to lndia-$18: expedited delivery to destinations in North America-$12: 521 Acknowledgment of Contributions elsewhere-$15. Subscriptions and 545 Election Information orders for AMS publications should be addressed to the American Mathematical 546 Future Meetings of the Society Society, P.O. Box 1571. Annex Station. Logan, October 1D-11, 546 Providence. Rl 02901. All orders must be Charlotte, October 17-18, 548 prepaid. Denton, October 31-November 1, 549 ADVERTISING &. INQUIRIES Notices publishes situations wanted Invited Speakers and Special Sessions, 550 and classified advertising. and display 552 Call for Topics for 1988 Conferences advertising for publishers and academic or scientific organizations. Requests for 554 Special Meetings information: 561 New AMS Publications Advertising: Wahlene Siconio 568 Miscellaneous Change of address or subscriptions: Cheryl Rotella Personal Items, 568 Book order number 800-556-7774. Deaths, 568 Visiting Mathematicians, 569 CORRESPONDENCE. including 572 AMS Reports and Communications changes of address should be sent to Recent Appointments, 572 American Mathematical Society, P.O. Box 6248. Providence, Rl 02940. Statistics on Women Mathematicians, 572 Second class postage paid at Providence. 573 Advertisements Rl. and additional mailing offices. 590 AWM Questionnaire Copyright © 1986 by the American Mathematical Society. All rights reserved. 591 New AMS Publications Order Form and Printed in the United States of America. Mailer Notices: highlights David Harris, in his feature article on "The Mordell Conjecture," explains the significance of Faltings' proof of the conjecture in relation to other important conjectures in the theory of abelian varieties. Page 443. The proposed NSF budget for FY 1987 is examined for the areas related to the mathematical sciences and is compared with the actual funding levels over the past ten years. Page 450. The Board on Mathematical Sciences, in a recent report entitled "Math­ ematical Sciences: A Unifying and Dynamic Resource," assesses and monitors some trends in pure and applied mathematics. Page 462. The Treasurer of the AMS reports on the financial status of the Society for 1985. Page 480. Joseph Buhler's column contains an article by Avner Ash which reviews the software package "Matlab," a high-level language used to manipulate two­ dimensional matrices. Page 482. Kenneth Hoffman, in his Washington Outlook column, recaps the accomplish­ ments of the mathematical community since the issuance of the David Report in 1981. Page 486. The ICM-86 current schedule of plenary and 45-minute lectures is posted for the August meeting in Berkeley. Page 488. Peter Lax, Herbert Simon, and Antoni Zygmund are awarded the National Medal of Science for 1986. Page 497. National Mathematics Awareness Week put mathematics into public view and demonstrated the influence of the mathematical community. Page 509. The NSF report on graduate science/engineering enrollments alerts the scientific community to the pending shortage of Ph.D.'s. Page 511. The Mordell Conjecture David Harris 1. The basic results. On 19 July 1983, the New solutions of an equation transforms the algebraic York Times printed an article [NYT] on the problem of solving a Diophantine equation into solution by a West German mathematician named the geometric problem of finding points on its Faltings of "one of the outstanding mathematical locus of solutions. The rest of this article deals problems of the century" (in the opinion of Serge with the problem of integer and rational points Lang). Spencer Bloch of the University of Chicago on curves. §3 describes the pioneering work of said that the German's achievement "answers Mordell, Weil, and Siegel in launching the subject. questions that seemed absolutely unanswerable In §4, we describe the early attempts to deal with before." The most eye-catching part of Faltings' Mordell's Conjecture, climaxing in the work of paper [Fal] is a proof of the so-called Mordell the Soviet school. In §5, the work of Faltings is Conjecture, a fundamental question in the theory sketched. Finally, in §6, we discuss the problem of of Diophantine equations. effectively using Faltings' work to solve real-world Until recently, most experts had believed Diophantine equations. that the Mordell Conjecture would not soon be SIEGEL'S THEOREM.
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