OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

Report on the Activities of the AMS Committee on Science Policy, 1990 page 111

FEBRUARY 1991 , VOLUME 38, NUMBER 2

Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences

This calendar lists all meetings which have been approved prior to the date this in the issue corresponding to that of the Notices which contains the program of the issue of Notices was sent to the press. The summer and annual meetings are joint meeting, insofar as is possible. Abstracts should be submitted on special forms meetings of the Mathematical Association of America and the American Mathe­ which are available in many departments of mathematics and from the headquar­ matical Society. The meeting dates which fall rather far in the future are subject to ters office of the Society. Abstracts of papers to be presented at the meeting must change; this is particularly true of meetings to which no numbers have been as­ be received at the headquarters of the Society in Providence, Rhode Island, on signed. Programs of the meetings will appear in the issues indicated below. First or before the deadline given below for the meeting. Note that the deadline for ab­ and supplementary announcements of the meetings will have appeared in earlier. stracts for consideration for presentation at special sessions is usually three weeks issues. earlier than that specified below. For additional information, consult the meeting an­ Abstracts of papers presented at a meeting of the Society are published in the nouncements and the list of organizers of special sessions. journal Abstracts of papers presented to the American Mathematical Society Meetings

Abstract Program Meeting# Date Place Deadline Issue 864 t! March 15-16, 1991 South Bend, Indiana Expired March 865 March 22-23,1991 Tampa, Florida Expired March 866 • June 13-15, 1991 Portland, Oregon March 26 May/June 867 • August 8-11, 1991 Orono, Maine May 22t July/August (94th Summer Meeting) 868 • October 12-13, 1991 Philadelphia, Pennsylvania August 1 October 869 • October 25-26, 1991 Fargo, North Dakota August 1 October 870 • November 9-11, 1991 Santa Barbara, California August 1 October 871 • January 8-11 , 1992 Baltimore, Maryland October 2 December (98th Annual Meeting) March 13-14,1992 Tuscaloosa, Alabama tt March 20-21, 1992 Springfield, Missouri June 29-July 1, 1992 Cambridge, England (Joint Meeting with the London Mathematical Society) January 13-16, 1993 San Antonio, Texas (99th Annual Meeting) August15-19, 1993 Vancouver, British Columbia (96th Summer Meeting) (Joint Meeting with the Canadian Mathematical Society) January 12-15, 1994 Cincinnati, Ohio (100th Annual Meeting) January 10-13, 1996 Orlando, Florida (1 02nd Annual Meeting) • Please refer to page 128 for listing of Special Sessions. t Please note this deadline is earlier than previously published. tt These dates are earlier than previously published. Conferences

June 22-August 2, 1991 : Joint Summer Research Conferences in the August, 1991 : AMS-SIAM-SMB Symposium on Some Mathematical Mathematical Sciences, University of Washington, Seattle, Questions in Biology, Theoretical approaches for predicting spatial Washington. effects in ecological systems, San Antonio Texas. July 7-26, 1991 : AMS Summer Research Institute on Algebraic Groups and their Generalizations, University of Pennsylvania, University Park, Pennsylvania. Events Cosponsored by the Society

February 14-20, 1991: Section A (Mathematics) Sessions at the AAAS Annual Meeting, Washington, D.C. Deadlines

April Issue May/June Issue July/August Issue Classified Ads* February 28, 1991 April 25, 1991 June 17, 1991 News Items February 21, 1991 April 15, 1991 June 10, 1991 Meeting Announcements** February 25, 1991 April 15, 1991 June 13,1991 • Please contact AMS Advertising Department for an Advertising Rate Card for display advertising deadlines. •• For material to appear in the Mathematical Sciences Meetings and Conferences section. OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

DEPARTMENTS FEATURE COLUMNS 99 Letters to the Editor 101 Forum 104 Computers and Mathematics Jon Barwise 113 News and Announcements This month's column consists of two reviews, one on VTEX by John L. Casti 119 Funding Information for the and one on GyroGraphics by Gustaf Gripenberg. Also, Donald E. G. Maim Mathematical Sciences discusses a number theory package for microcomputers available as mathematical freeware and shareware. 120 For Your Information 122 1991 AMS Elections 111 Inside the AMS 124 Meetings and Conferences of Michael C. Reed reports on the activities of the AMS Committee on Science the AMS Policy during the past year. South Bend, IN March 15-16, 124 Tampa, FL March 22-23, 126 Invited Speakers, 128 AAAS Annual Meeting, 132 Joint Summer Research Conferences in the Mathematical Sciences, 134 1991 Summer Research Institute, 136 138 Mathematical Sciences Meetings and Conferences 149 New AMS Publications 153 AMS Reports and Communications Recent Appointments, 153 Reports of Past Meetings, 154 156 Classified Advertising 171 Forms

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From the Executive Director ... DOCTORAL PROGRAMS in mathematical sciences departments are key to AMERICAN MATHEMATICAL SOCIETY Doctoral programs the successful renewal of the profession and reform in mathematics education. They can attract individuals to careers in mathematics research, the applications of mathematics, mathematics education, and teaching. Successful graduate programs address the career path problems of EDITORIAL COMMITTEE the profession by attracting and retaining students (especially women Robert J_ Blattner (Forum Editor) students) and by preparing students for long and varied professional Michael G. Crandall careers. Robert M. Fossum (Chairman) Lucy J. Garnett, D. J. Lewis The AMS Committee on Science Policy has been discussing issues Nancy K. Stanton associated with ineffective doctoral and postdoctoral training. The Board Robert E. L. Turner (Letters Editor) on Mathematical Sciences (BMS), as a result of the serious problems in in its report "Renewing U.S. Mathematics: MANAGING EDITOR graduate education identified Donovan H. VanOsdol A Plan for the 1990s" (David II), has also been concerned with these issues. Individuals involved in these considerations have led BMS to ASSOCIATE EDITORS undertake an eighteen-month study, with financial support from the Ronald L. Graham, Special Articles Alfred P. Sloan Foundation, to identify features of successful graduate Jeffrey C. Lagarias, Special Articles and postdoctoral programs. SUBSCRIPTION INFORMATION The initial step in the study is to attempt to identify elements of a Subscription prices for Volume 38 (1991) are successful doctoral program in the mathematical sciences. It is expected $121 list; $97 institutional member; $73 individual that this process will be ongoing as the study progresses. Information member. (The subscription price for members is in­ cluded in the annual dues.) A late charge of 10% that will be considered includes: breadth of course work, programs for of the subscription price will be imposed upon or­ the retention of women and other underrepresented groups, methods used ders received from nonmembers after January 1 to qualify students for candidacy, characteristics of graduate mentorship, of the subscription year. Add for postage: Surface recruitment, role of delivery outside the United States and lndia-$15;. goals of the doctoral dissertation, graduate student to lndia-$27; expedited delivery to destinations in teaching assistants, criteria for determining graduate student financial North America-$28; elsewhere-$67. Subscrip­ support, and issues associated with postdoctoral programs. tions and orders for AMS publications should be addressed to the American Mathematical Society, Ten doctorate-granting institutions whose programs contain essential P.O. Box 1571, Annex Station, Providence, Rl elements of these criteria of a successful program will be selected. 02901-1571. All orders must be prepaid. Site visits will be conducted by teams from the study committee. The purpose of these vists will be to gather information, not to evaluate the ADVERTISING Notices publishes situations wanted and classified departments. After the site visits have been completed, the information advertising, and display advertising for publishers gathered will be analyzed and combined into composite descriptions of and academic or scientific organizations. the features of successful programs and those that are detrimental to Copyright @ 1991 by the American Mathematical successful programs. Society. All rights reserved. Printed in the United States of America. Individual doctoral degree granting departments in the mathematical The paper used in this journal is acid-free and falls sciences could undertake a self-evaluation using the criteria listed above within the guidelines established to ensure perma­ or determine their own set of criteria. There is another study being nence and durability. § Most of this publication undertaken by the Joint Policy Board for Mathematics Committee on was typeset using the TEX typesetting system. Preparation for College Teaching. This study is particularly concerned [Notices of the American Mathematical Society is published monthly except bimonthly in May, June, with the effectiveness of graduate programs in preparing students for July, and August by the American Mathematical So­ what possibly will be the career path for most of them - a career as a ciety at 201 Charles Street, Providence, Rl 02904- college teacher. A department's self-evaluation should review the features 2213. Second class postage paid at Providence, that address these needs. Rl and additional mailing offices. POSTMASTER: of its graduate program Send address change notices to Notices of the The Society will be following the BMS study, as it is anticipated American Mathematical Society, Customer Service that recommendations will be made to the professional mathematics Department, American Mathematical Society, P. 0. Box 6248, Providence, Rl 02940-6248.] Publication organizations. It is expected that the full report will be available by late here of the Society's street address, and the other fall of this year. information in brackets above, is a technical require­ William Jaco ment of the U. S. Postal Service. All correspon­ dence should be mailed to the Post Office Box, NOT the street address.

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ery college and university. No matter 4. Professors in research institu­ Letters how comprehensive and objective an tions while writing letters for non-Ph.D. internal evaluation is, the outside let­ colleges are oblivious to the higher to the Editor ters of recommendation solicited by the teaching load which the faculty carry candidates or/and by their departments every semester, unmotivated students carry away a disproportionate weight they handle, office hours they actually in deliberations at every stage (10 at maintain besides various service obli­ Tenure and Promotion UNLV!). gations. And no less is the lack of insti­ Letters of Recommendation For the last several years I have tutional support for scholarly activities On November 6 I received the follow­ been a part of this process at both ends. (e.g. UNLV budgeted travel support of ing letter. The name of the university I want to focus on letters sought by $30/faculty/year). While writing such and the person in question are deleted essentially undergraduate (non-Ph.D.) letters they often ignore that they have· for obvious reasons. institutions like UNLV from research to evaluate the entire c.v. package with October 30, 1990 respect to teaching, research and ser­ Dear Professor Askey, universities like Berkeley, Brown, and The personnel department of the ___ Northwestern, etc. Here are some ob­ vice. Invariably, they focus only upon University mathematics department is current­ servations on this matter for a possible the research component, and pass a ly considering for tenure at the rank 'debate' in this column: judgement which can adversely affect of Full Professor starting in the fall of 1991. 1. In all fairness non-Ph.D. insti­ the candidates for the rest of their lives. I would very much appreciate your evalua­ tutions should seek letters only from S.C. Bhatnager tion of 's mathematical research­ University of Nevada, Las Vegas completed works as well as the overall re­ non-Ph.D. institutions in the same ge­ (Received December 19, 1990) search program. ographic region which also have com­ If at all possible, could we have the eval­ parable programs in mathematics. uation by November 15, 1990, since we are 2. Over the years the former Mathe­ Certification Forms working under some rather strict and unavoid­ matical Association of America (MAA) for NSF Grants able time constraints? President Lynn A. Steen has exten­ If this were the first letter like this, I would like to voice some con­ sively written on broadening the def­ it could be attributed to someone who is cerns about a certification form that inition of traditional research at the very inexperienced. However it is not, is required of applicants for National collegiate level. He effectively wrote in so it is probably necessary to remind the leading article, "Renewing Under­ people about. the errors in this letter. graduate Mathematics" in the July/Aug. Policy on Letters to the Editor First, it is a very poor idea to have such Letters submitted for publication in Notices are a small time interval. Tenure decisions 1985 issue of Notices. "For too long reviewed by the Editorial Committee, whose task is to determine which ones are suitable for pub­ are very important, and universities mathematics and mathematics teach­ ers have suffered from a rigid, narrow lication. The publication schedule normally re­ need the best advice possible. There quires from two to four months between receipt are times when I read ten papers or definition of professional activity. To of the letter in Providence and publication of the more before writing a letter on a tenure save face with our peers in the sci­ earliest issue of Notices in which it could appear. ences and humanities, we expect of Publication decisions are ultimately made by decision. This can not be done in a majority vote of the Editorial Committee, with week. Along with adequate time, it ourselves a productive research pro­ ample provision for prior discussion by commit­ is more than a courtesy to include a gram; to save face with our peers in tee members, by mail or at meetings. Because of publication list and other material that mathematics, we adopt the mathemati­ this discussion period, some letters may require cian's elite definition of research. The as much as seven months before a final decision might be useful in helping to form an is made. Letters which have been, or may be, opinion of a person. The publication result too often is confusion, frustra­ published elsewhere will be considered, but the list should have the papers numbered, tion, and well-intentioned hypocrisy in Managing Editor of Notices should be informed faculty tenure and promotion proceed­ of this fact when the letter is submitted. so that a specific paper can be referred The committee reserves the right to edit let­ to by number. ings." In my opinion, letters sought ters. Please, when asking for advice, pro­ by non-Ph.D. institutions from Ph.D. Notices does not ordinarily publish com­ institutions further elevate the level of plaints about reviews of books or articles, al­ vide as much help as possible, and though rebuttals and correspondence concerning allow sufficient time so that a serious hypocrisy. reviews in Bulletin of the American Mathemat­ letter can be written. 3. Apart from this 'validation', let­ ical Society will be considered for publication. Richard Askey ters which are particularly requested All published letters must include the name of without the knowledge of the candi­ the author. University of Wisconsin Letters should be typed and in legible form (Received November 19, 1990) dates, are often meant to 'settle scores' or they will be returned to the sender, possibly with the candidates. The point here is resulting in a delay of publication. that generally in every deliberation a Letters should be mailed to the Editor of No­ tices, American Mathematical Society, P.O. Box This is the time of the year when negative comment, or a comment hav­ 6248, Providence, RI 02940, or sent by email to the process of tenure and promotion ing even a semblance of negativity is [email protected], and will be acknowl­ gets in full swing in just about ev- brought out and stretched. edged on receipt.

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Science Foundation (NSF) grants ex­ Sheet does contain an advisory about using weaponry, dangerous machinery, ceeding $100,000. The two statements these two certification statements, but etc.), I can see no justification for that applicants must sign are enti­ it is in small print and appears after the the invasion of privacy ensuing from tled "CERTIFICATION REGARDING signature line. Since it is not required the requirement of a special anti-drug LOBBYING" and "CERTIFICATION that the applicant initial the separate certification-going beyond the already REGARDING DRUG-FREE WORK­ certification page, it is quite possible to existing legal proscriptions-from ev­ PLACE REQUIREMENTS," only the unwittingly sign the certification. In my ery federal grant applicant. latter of which I find inherently objec­ case, a secretary gathered signatures for Secondly, clause (a) in Alternate II, tionable. I address these concerns to the the Cover Sheet after all applicants in restricting possible unlawful activities AMS membership at large, as well as our group had looked over the rest of "in conducting any activity with the to the NSF and the federal government, the proposal. It was only by chance grant," is unreasonably vague because because a significant fraction of AMS that I happened to notice the second, the recipients of this kind of grant are members apply at one time or another unattached page. often engaged in research-related activ­ for multi-person multi-year grants to­ Secondly, while the content of the ities for most of their waking hours. taling at least $100,000. If many AMS Certification Regarding Lobbying seems The boundaries between time spent members wish to take actions in re­ reasonable, the content of the Certifi­ conducting grant-related activities and sponse to this certification requirement, cation Regarding Drug-Free Workplace personal time is shadowy, to say the our response will be more credible in Requirements is objectionable. The rea­ least, and the clause as it stands re­ concert. sons I find it objectionable are given stricts such possible actions as making The first concern I have is about in the following statement which I felt a political statement on the drug issue the format. The words "THIS PAGE compelled to attach to the certification via non-violent civil disobedience any MUST BE SUBMITTED AS PART statement. time during normal working hours. OF THE PROPOSAL'' appear at the Regarding the Drug-Free Work­ In short, I feel that in order to top of a page detailing a statement place loyalty oath, I feel compelled uphold the constitution of the United regarding the use of federal money to raise the following objections. States, I must insist on attaching this for lobbying. A footnote at the bottom Firstly, the issue of use and abuse statement to the Certification Regarding of this page states that "By signing of controlled substances is completely Drug-Free Workplace Requirements. the Cover Sheet and submitting this irrelevant to the nature of my work, and I thank the editors of Notices of the page as part of the proposal, the ap­ indeed to any work contracted under an AMS for allowing me to voice these plicant is providing Certification Re­ NSF grant in this subfield of mathemat­ concerns and hope to hear from any garding Lobbying". The reverse of this ics. While I can see the motivation for members of the AMS who share them. page contains a similar statement on taking extra measures against the use Robin Pemantle the Certification Regarding Drug-Free of illegal drugs in situations involv­ Oregon State University Workplace Requirements; none of the ing public safety (e.g. by employees (Received November 29, 1990) other forms is two-sided. The Cover

This is the second edition of The Joy of TEX. the user-friendly 1980 Mathematics Subject Classifications: 00, 68 guide to A_MS-TE)(, which is a software package based on the ISBN 0-8218-2997-1, LC 90-1082 revolutionary computer typesetting language TE)(. A_MS-TEX 320 pages (softcover), September 1990 was designed to simplify the typesetting of mathematical IndiVIdual member $30, List price $38, quantities, equations, and displays, and to format the output Institutional member $34 according to any of various preset style specifications. This To order, please specify JOYT/NA second edition of Joy has been updated to reflect the changes t ~4i introduced in Version 2.0 of the A_MS-TEX macro package. .., ~ , ... I .,.; The first two parts of the manual, "Starters" and "Main Courses," teach the reader how to typeset the kind of text and ~ mathematics one ordinarily encounters. "Sauces and Pickles," the third section, treats more exotic problems and includes A a 60-page dictionary on special techniques. The manual Gourmet Guide also includes descriptions of conventions of mathematical typography to help the novice technical typist. Appendices to Typesetting list handy summaries of frequently used and more esoteric Ail prices subject to change. Free shipment by symbols. surface; for air delivery, please add $6.50 per title. withtheAMS- TEX This manual will· prove useful for technical typists as well as Prepayment required. Order from American macro package scientists who prepare their own manuscripts. For the novice, Mathematical Society, P.O. Box 1571, Annex exercises sprinkled generously throughout each chapter Station, Providence, Rl 02901-1571, or call toll free encourage the reader to sit down at a terminal and learn 800-321-4AMS (321-4267) in the continental U.S. M. D. SPIVAK, Ph.D. through experimentation. and Canada to charge with VISA or MasterCard.

100 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Forum

The Ohio State University The Forum section publishes short articles on issues that are of Young Scholars Program interest to the mathematical community. Articles should be between During the spring of 1988, Ohio State University selected 1000 and 2500 words long. Readers are invited to submit articles 200 minority pre-seventh graders from low-income families for possible inclusion in Forum to: in eight Ohio school districts (Akron, Canton, Cincinnati, Notices Forum Editor Cleveland, Columbus, Dayton, Toledo, and Youngstown) to American Mathematical Society participate in a two-week Summer 1988 Institute on the Ohio P.O. Box 6248 State Campus. These 200 students, or their alternates, will Providence, RI 02940 return to the OSU campus each summer and receive year­ or electronically to [email protected] round academic enrichment, career exploration, mentoring, and personal development programs until they graduate Filling the Math and Science Pipeline from high school. Each year, 400 new pre-seventh graders will be selected so that in six years the program will with Young Scholars accommodate 2,400 youngsters. Besides attending the six Carolyn Mahoney summer institutes, the students and their parents or guardians California State University, San Marcos must agree that the student will follow a college preparatory Franklin Demana program in high school. The Ohio State University The YSP participants were nominated by teachers, guid­ ance counselors, or principals and were selected based on Introduction academic performance, test scores, leadership, community Underachievement and lack of confidence in mathematics, involvement, and family circumstances. The pre-seventh and consequently in the sciences, is pervasive in this country. grade summer institute has three academic components: The mathematical innumeracy of our citizenry portends not Biological Sciences, English and Ethnic Studies, and Cal­ only a dire social, but a potentially dire educational and culator Enhanced Pre-Algebra. The mathematics curricular economic situation for this country. The proportion of the plan for the remaining five years consists of Geometry and population made up of non-white males is growing rapidly, Spatial Visualization, Statistics and Probability, Graph The­ yet minorities and women are notably absent in mathematics ory, Number Theory, and an integrated mathematics-science science programs at both the undergraduate and graduate capstone experience. The mathematics component of the levels. The Mathematical Sciences Education Board in a OSU-YSP seeks to address the important pipeline issues recent report entitled Everybody Counts (1989) states that: identified above. It seeks to provide bright and talented minority students "White males, thought of only a generation ago as with: the mainstays of the economy, will comprise only 15 1. Increased self-confidence and a "can-do" attitude when percent of the net additions to the labor force between approaching mathematics. 1985 and 2000." 2. Improved ability to engage in critical thinking and to Our country's future economic prosperity and politi­ formulate complex problems mathematically. cal strength will be determined to a great extent by the 3. Improved awareness of the importance of group contributions of members of minority groups and women. cooperation in study and problem-solving. To address this problem, Ohio State University (OSU) 4. Increased ability to use calculators and computers, has instituted the Ohio State University Young Scholars and understanding about the importance of technology in Program (YSP) which is designed to increase the pool of education and careers. college-bound students from traditionally underrepresented The YSP seeks to provide the parents and guardians of groups. participating students with other benefits such as:

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1. Better understanding about the educational system were used to provide a numerical foundation from which and deeper appreciation about the value of mathematics to algebraic ideas can grow and flourish. Concepts and rela­ students and their careers. tionships were encountered in problem settings before they 2. Insight into how technology and group study enhances were formalized. conceptual understanding of mathematics. Each student was provided with a scientific calculator 3. Opportunity to interact with teachers and administra­ and other supplies. They learned quickly how to use a tors in the school systems of the participants. calculator when doing mathematics. A typical mathematics The YSP seeks to provide the teachers involved in the class began with the teacher presenting an idea while in­ program with the following: volving the entire class in the discussion, then presenting 1. Professional development through training about al­ model problems using the idea, followed by students doing ternative teaching techniques. similar problems at the chalkboard, further teacher-student 2. Opportunity for hands-on experiences with calculators and student-student interaction, and ending with seat work and computers. with the teacher and assistant roaming the room providing 3. Exposure to innovative curricular materials that can individual help and checking individual work. The class­ be taken back to their classrooms. room atmosphere supported differences in learning styles, 4. Increased confidence in teaching mathematics. especially as related to gender. Doing mathematics with cal­ The program seeks to enhance teacher technique in culators facilitates investigating, exploring, and mathematical building peer support groups for students, especially mi­ talk about concepts. norities and females, and strives to heighten sensitivity to Whenever possible, concepts were explored with hands­ gender and culture differences in perception and perfor­ on activities. For example tennis balls were "shot" into mance in mathematics. The program provides involvement wastebaskets and the percent made calculated. Daily home­ with a professional network that links middle and high work assignments were completed in study sessions, graded school teachers with college and university mathematicians by the teachers, and discussed the next day in class. Students throughout the state. It also creates a support system for understood the notion of percent in fraction form, decimal minority and women mathematics teachers-teachers who form, and percent form by the end of the first week. often have few role models and little contact with other The goal for the second week was to build as much mathematics educators. student understanding as possible about markups, discounts, The YSP also benefits college and university mathe­ and population changes over time. Calculators allowed the maticians involved by providing interaction with pre-college teachers to ask interesting real-world questions which could students and expanding linkages with pre-college teachers. be solved numerically using a ·guess-and-check approach, as Colleges and universities will benefit by the expanded pool illustrated by the following problem: well prepared for collegiate of highly qualified students "Mattie is making $8.56 per hour after a 7% salary study. increase. What was her old salary?" Students were encouraged to guess the answer and then Instructional Format check. Repeated guess-and-check helps students understand and Mathematical Content the concept of markup. Students were also required to In the summer of 1988, the mathematics classes met for write "problems" that could be solved using a mathematical 75 minutes each of ten mornings in groups of 25 with expression such as x - 0.08x. Most students wrote about a a teacher and a teaching assistant. The teaching assistant sale at a clothing store--others wrote about cars and jewelry. also sei'Ved as a tutor for the half-hour study session that In addition to confirming student understanding about the all participants attended in the evening. Based on this meaning of an 8% discount, this type of exercise provides experience, the length of the mathematics classes have a gentle but subtle opportunity for building understanding been reduced to one hour and the class size to 17-all about a variable. other features remain the same. The teaching assistants The young scholars came to understand percent increase were OSU undergraduate, graduate, or professional students. and percent decrease reasonably well. The mathematics teachers were regular teachers of middle school, high school, junior college, or university, with ethnic Preliminary Evaluation backgrounds including Black, Hispanic, and Caucasian. A Although it is difficult to generalize about student perfor­ one-week training session for teachers and assistants was mance based on two weeks of instructional activity, the YSP held the week before the Institute. program evaluation gave strong support for two major points. Percent was chosen as a primary topic for the first First, all students are capable of doing quality mathemat­ summer because it is traditionally thought to be hard for ics. Second, technology helps students achieve considerably minorities and women and because it is rich in realistic more in mathematics. and interesting applications. The textual materials placed The same test was given as a pre-test and a post­ heavy emphasis on problem solving and were significantly test to the 200 summer 1988 YSP participants. The YSP dependent on the use of hand-held calculators. Calculators students scored 23% on the pre-test and 59% on the

102 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Forum post-test. Considering that it followed only two weeks of Summary instruction and that the test was quite ambitious, the post­ Exit interviews were conducted with many of the students. test performance of the YSP students was most impressive. This anecdotal information indicates that the students thought Interested readers can obtain a copy by writing one of the mathematics was fun and that their teacher was supportive authors. and truly interested in helping them understand mathematics. Because the students genuinely seemed to enjoy themselves and because the test results mentioned above provide strong Academic Year Enrichment evidence that the students improved themselves in the short While funding for academic year activities was not part of run, the mathematics staff is optimistic about retaining the original YSP budget or plan, it quickly became clear that many of these scholars through high school. Indeed, 90% such activity was desirable and necessary. The YSP staff of the students who completed the first year returned for applied for and obtained a grant from the Ohio Board of the second year-100% of the Akron participants returned Regents to partially fund 1989-1990 academic year activities for the Summer 1989 Institute. We are convinced that all for the Cleveland, Columbus, and Dayton school_ systems. students can succeed in mathematics if the mathematics These three cities have 36% of all the minority children is exciting, realistic, and higher expectations are set for in the state of Ohio. The sessions are approximately three students. hours long and generally held on Saturdays at local school, college, university, government, or business sites. References Students, parents, and teachers were invited to the first Margaret Comstock and Franklin Demana. "The Calculator is a enrichment session. A local school mathematics supervisor Problem Solving Concept Developer," The Arithmetic Teacher, Febru­ talked to parents about what the students were doing in ary, 1987: 48-51. school mathematics, how the parents can help, and the role Franklin Demana and Joan R. Leitzel. Levell - Getting Ready for of mathematics in future studies and careers. A member of Algebra. D.C. Heath and Company, Lexington, MA, 1988. the YSP staff described YSP to local teachers and discussed Franklin Demana and Joan R. Leitzel. "Establishing Fundamental Concepts through Numerical Problem Solving." The Ideas ofAlgebra, ways they could become involved in the program. Parents K-12. 1988 Yearbook, National Council of Teachers of Mathematics: and teachers were provided time to interact with each other 61-68. and to observe the students in the mathematics portion of the Mathematical Sciences Education Board. "Everybody Counts - A session. Local teachers and mathematicians, in consultation Report to the Nation on the Future of Mathematics Education." Na­ with the YSP staff, were responsible for the mathematics tional Academy Press, Washington, D.C., 1989. portion of the programs. The summer material was not Kenneth J. Travers, Director. "Second International Mathematics repeated, but the exploring, problem-solving strategy and Study, Detailed National Report United States," Stripes Publishing Company, Champaign, IL, 1985. approach to mathematics started in the summer sessions was continued. Career exploration was incorporated into some of the sessions and was led by professionals in business or industry who use mathematics and science in their careers. Errata The final session brought everyone back together to help In the article "The Academic Elite in Mathematics: Linkages evaluate the effectiveness of the enrichment activities. Among Top-Ranked Graduate Programs" (December 1990 A grant has recently been received from the National Notices, p. 1355) the final two references were incorrectly Science Foundation to add three more school districts to run as one. The two should be: the 1990-1991 enrichment activities and to have all eight 6. Gross, G.R. Am. Sociologist, 1970, 5, 25-29. districts participate in the 1991-1992 activities. 7. Schichor, D., Am. Sociologist, 1970, 5, 157-160.

FEBRUARY 1991, VOLUME 38, NUMBER 2 103 Computers and Mathematics

Edited by Jon Barwise

This month's column Most of the submissions to the column have been electronic. I would estimate that those typically take about one-fifth the time for me and my secretary as those where we have to rely exclusively on hard copy The Changing Face of Mathematics mail. This does not include the savings of typesetting time in Prov­ Whether we like it or not, computers are changing the face of idence. Email has meant that mak~ng suggestions, getting revisions, mathematics in radical ways, from research, to teaching, to writing, and answering questions about format and so on is just far simpler and personal communication. and publication. Over the past couple of years quicker. This seems worth keeping in mind as we move forward with we have seen numerous articles about these developments. new vehicles of mathematical publication. Electronic mail has not got­ Computers are even forcing us to expand our ideas about what ten the play in this column it deserves given its developing importance constitutes doing mathematics, by making us take much more seriously to the mathematical community. . the role of experimentation in mathematics. (I draw attention to a new The editing of this column is being taken over by Keith Devlin, an journal devoted to experimental mathematics below.) occassional contributor to it in the past. Devlin is well known for his One view of the future is that mathematics will come to have (or work in set theory, for a regular column on computer and mathematics already has) two distinct sides: experimentation, which can exploit the in The Guardian, and for his recent book Mathematics: The New Golden speed and graphic abilities of programs like Maple and Mathematica, Age. He can be contacted at: to allow us to spot regularities and make conjectures, and proof, very Professor Keith Devlin much in the style of today's mathematics. Department of Mathematics A more extreme view of the future is that computers will become Colby College an important partner in giving proofs as well. We have seen a few Waterville, Maine 0490 I examples of this, as with the Four Color Theorem. Logic framework email: [email protected] systems (discussed by de Bruijn last month) are working toward the creation of environments where mathematics is done in partnership The Journal of Experimental Mathematics with the computer, the latter acting as a kind of omnipresent referee One of the topics that has come up several times over the past looking over your shoulder. couple of years in this column is the development of experimental There are even more radical futures imaginable. The logical frame­ techniques in mathematics, both for the discovery of new insights and work systems by and large tend to assume that definitions and theorems conjectures. A new journal in this area has now been formed devoted will still be expressed in something like the way they are today, only to the publication of experimental mathematics. Part of the draft an­ more formal. But I can imagine a time when the very statement of a nouncement I have seen reads "It is hoped that the journal will help result, as well as its proof, may depend on the technology available to generate a climate in which accounts of interesting experiments are us. For example, imagine representing some continuous varying activ­ not confined to private notebooks and suppressed from accounts of the ity A(t), with the change over time dynamically represented by time mathematics they inspire, but see the light of day, to the benefit of itself. Or imagine theorems of geometric topology whose very state­ researchers, students, and the mathematical community in general." ment required the drawing of a picture too intricate to be drawn by Is this to be taken seriously? If you have any doubts, the list of hand. Mathematical science fiction? I think not. editors and advisors to the journal should be interesting: F. Almgren, Whether we applaud or abhor all these changes in mathematics, H. Cohen, R. Devaney, D. Epstein (Editor-in-chief), R. Graham, D. there is no denying them by turning back the clock, anymore than there Hoffman, H.W. Lenstra, S. Levy, R. Llave, B. Mandelbrot, A. Marden, is in the rest of life. Computers are here to stay, just as writing is, and D. Mumford, U. Pinkall, P. Sarnak, J.P. Serre, and W. Thurston. they are changing our subject. At least this is my firm conviction, and As the above quote and this list make clear, what we are talking it is the reason I have been willing to serve as editor of this column about is nothing less than a possible revolution in the way mathe­ for something over two years. maticians think about and report their work. Anyone familiar with the This is my last month as editor. I would like to mark it by express­ standards of experimentation in other branches of science can only ing my appreciation to all who have helped: those who have written wonder what standards will evolve for judging experimental work in articles, reviewers. letters, etc., and the very obliging Notices staff in mathematics. It is an exciting event. Providence, especially Carol McConway. I also appreciate the encour­ Anyone interested in more details about the journal, or wanting to agement of the many mathematicians who have written or otherwise submit an article for consideration, can contact: expressed their interest in the column. It has not been just what I had Klaus Peters envisioned, but I like to think it has played a small role in helping us Jones & Bartlett get up to speed as a community. 20 Park Plaza It is perhaps worth mentioning another factor that has made editing Boston, MA 02166 the column less of a burden than one might expect: electronic mail. email: cdp !kpeters@ labrea.stanford.edu

104 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY It ··-~ " - m•m mmmO••m Computers and Mathematics

A Universal Metarule and postmarked no later than March 15. 1991. Faculty who are selected Verena Huber-Dyson writes to share the following rule with ev­ to participate will be notified by April 15. Direct inquiries to the above eryone interested in computers or logic. "On page 4 of 'Government address. Tel: (603)862-2320. Email: [email protected] Regulations' of the Boating Course of the Canadian Power and Sail Squadrons. we find the following ______lllllllllllf ...... - .. "RULE: In spite of very definite rules governing cases where danger of collision is present, there is one last rule that may nullify all other rules. Everything possible must be done to avoid collision.'' Reviews of Mathematical Software Three cheers for the Canadian Squadrons! It is my favorite rule and I had adopted it for life long before meeting them. I would call it the Universal Meta Rule. It predates Rosser, but it makes the perfect explication for Rosser's Proof Predicate." V'JEX Typesetting Package Faculty Workshop on Computer-Aided Reviewed by John L. Casti* Instruction in Linear Algebra and Differential Equations Lee L. Zia A 1EX for Tomorrow Department of Mathematics Someone once described mathematical research as a lot of University of New Hampshire hard work in looking for the easy way. And so it is too Durham, NH 03824 for most mathematicians when it comes time to getting A three week workshop on computer-aided instruction in linear those "easy ways" down on the printed page: a lot of algebra and differential equations will be held June 9-28, 1991 at the hard work fighting with various scientific word processors University of New Hampshire. The project directors are Lee Zia and or typesetting programs looking for the easy way to a Homer Bechtell of the UNH Department of Mathematics. This three­ paper or book printed in the format that's de riguer in the week National Science Foundation supported summer workshop targets undergraduate mathematics faculty who teach linear algebra or differ­ world of mathematical publishing. So, given the peculiarities ential equations, but have minimal experience with computer-aided of mathematical orthography and the rather arbitrary, yet instruction (CAl) in their courses. Faculty will seek to enhance their rigidly prescribed, style to which mathematical documents teaching by creating CAI materials, e.g. in-class demonstrations, prob­ must adhere, it's no wonder that the mathematical world, lem sets, syllabi, and operational procedures, that effectively integrate led by the American Mathematical Society, welcomed the computer technology into their instructional plans. Morning sessions appearance of the 1FX typesetting program a decade or so will survey and reinforce specific mathematical concepts, address the development of pedagogical strategies. and examine the design of cur­ ago. Yet despite the intensive development and support of riculum materials. Each afternoon, participants will work in teams to 1FX by the AMS and a host of professional and amateur formulate, produce, and evaluate CAl materials appropriate to their software developers, those who are regular 1FX users (like individual courses. Every Wednesday, guest visitors will supplement this reviewer) are painfully aware that all is not well in even these regular activities with talks and discussions on applications and this typesetter's paradise. broad pedagogical issues raised by CAL Speakers who have tentatively During the course of preparing a document for publica­ agreed to participate are Gil Strang, MIT; Deborah Hughes Hallett. Har­ tion, did you ever wish you could: vard; Lester Senechal, Mount Holyoke College and the IBM Institute for Academic Technology; Kathy Heid, Penn State; Jere Confrey, Cor­ • Scale fonts to an arbitrary point size? Or rotate them nell; and Gareth Williams, Stetson. In addition, Hiiseyin Kol{ak from through any angle? Or use just the font outline? Or the University of Miami and author of the award-winning software fill-in that outline with some gray, cross-hatched, zebra­ package PHASER will be in residence all three weeks of the work­ striped or other fill pattern? Or maybe put something shop. slightly outrageous like this into a document or onto a Room and board will be provided for thirty participants. Interested transparency? (See next page.) faculty should prepare an application that includes the following items: • Insert a graphics file written in a format other than • Statement of interest in and experience with computer-aided in­ struction, Postscript into your 1FX output via the \special com­ • Preliminary description of types of courseware to be produced and mand? how they might be used, • Save the 5-10 megabytes of hard disk space needed to • Statement of the expected impact that participation in the workshop store the many pixel font files for the printer (and maybe will have on teaching and curriculum. the previewer) you're using? • Indication of preference to work on either linear algebra or differ­ ential equations for courseware projects (each of which is limited to fifteen participants), • Curriculum vita, and *John L. Casti is a Professor of Operations Research and System Theory • Letter of support from chair or dean regarding computational facil­ at the Technical University of Vienna. Austria. His research interests are in ities and potential to carry out CAl projects at the home institution. mathematical modeling of living systems. His recent works include the text Application materials should be sent to: Alternate Realities: Mathematical Mode/in!? l!t' Nature and Man (Wiley. 1989) and the general-science volumes Paracliwns Lost: ImaJ?eS of Man in the Mirror CAl Workshop of Science and Searching j(w Certaillfy: What Scientists Can Know ah1mt the c/o Department of Mathematics Future (Morrow. 1989. 1991)-all typeset in 1fX. His address is: Institute for University of New Hampshire Econometrics. Operations Research and System Theory. Technical University Durham, NH 03824 of Vienna. Argentinierstrasse 8, A-1 040 Vienna. Austria.

FEBRUARY 1991, VOLUME 38, NUMBER 2 105 ...... ______Computers and Mathematics

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• Make use of a simple, user-friendly shell program that clear, I think, that if you want to have a lot of different would painlessly take you through the eternal 1}3X cycle: typefaces available at a number of point sizes, then it's going ASCII source file --+ DVI file --+ previewed document to require a lot of memory to store the grid pattern for each --+ (printed document) --+ revised 1}3X source file --+ · · ·? character from each typeface at each point size you might • Have just one driver for all dot-matrix printers? And one want to use. And, in fact, most versions of 1}3X require hard driver for all laser printers? And a single driver for all disk space of 5-10 megabytes to store a reasonable selection Postscript printers? of such raster-based fonts. If these are the kinds of things that you put on your Vector fonts are created using an entirely different wish list for Santa, hoping against hope that he'd leave them philosophy. Instead of generating the grid pattern for 10- under your computer last Christmas, then forget about Santa. point Computer Modem Roman "Jll' in advance and storing All of the above and much, much more is now available it up for use as needed, a vector-based Computer Modem from MicroPress, Inc. at 68-30 Harrow Street, Forest Hills, Roman "Jll' consists of just a simple mathematical formula NY 11375 (phone: (718)575-1816) in a complete-with­ specifying the outline of the symbol "Jll' according to everything $299 package called V1}3X. This package is the stylistic conventions of the Computer Modem Roman available for IBM PCs or compatibles running DOS 3.xx typeface. Since the vector description of the character "Jll' is with 640K RAM memory and a hard disk. In addition to the just a mathematical formula, it then becomes a rather simple typesetting program itself, the package includes a previewer task to employ elementary mathematical transformations of that works with all major graphics adapters (CGA, EGA, this formula to do things like rotate, shrink, expand, invert, Hercules, and VGA), as well as drivers for portrait and or fill-in the outline of this character. So instead of having landscape printing on virtually all 9- and 24-pin dot matrix, to store up a very large number of fixed grid patterns, inkjet, normal laser, and Postscript printers. vector font users need only store a simple formula for each character. Vectors and Rasters From a theoretical point of view, the shift from raster to Since the fundamentals of the V1}3X philosophy and structure vector fonts amounts to little more than just the traditional have been admirably described in a recent article [1] by its tradeoff between computer storage and processing time. developer Michael Vulis, I'll confine most of my remarks in However, the practical payoffs are considerable, since it's this review to a consideration of the package from the user's impossible, in essence, to generate a raster pattern for every point of view. But since the principle feature distinguishing possible rotation, point size, fill pattern, and so forth for V1}3X from other versions of 1}3X is the use of vector every possible character in every typeface you might want to rather than raster fonts, it's useful first to review briefly the use. Thus, while the storage advantages of vector fonts are difference between the two. not entirely trivial, the real advantage lies in the flexibility The simplest way to see how raster fonts differ from such fonts confer. You can just do things with the characters their vector counterparts is to consider a single character, say that are for all practical purposes impossible, or at least the letter "Jll' in Computer Modem Roman at 10 points. In exceedingly difficult and time-consuming, to do with their conventional implementations of 1}3X, this character is stored raster-based cousins. Now back to V1}3X. as a grid or raster pattern in which certain gridpoints are Having had hands-on experience with the use of 1}3X to "ON" while the others are "OFF." The particular ON-OFF typeset four books and innumerable articles, correspondence pattern is then a bitmapped representation of the character items, and other miscellany over the past five years or so, "Jll' in the style specified by the typeface Computer Modem I've wished all of the wishes on the above wish list at one Roman at a size of 10 points. From this description it's time or another-and then some. So what's V1}3X's secret

106 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ···········-··········---····-··-····--············-················ ··------Computers and Mathematics formula for granting them? Like all good recipes, there is V'IFX to preview some DVI files generated using normal no single answer. But also like all good recipes, there is a 1fX. But this is not really much of a problem from a critical ingredient without which the formula doesn't work practical standpoint, since most users will have retained at all. In V1E;X's case, the not-so-secret critical ingredient their earlier 1FX source files and, hence, can easily generate is simply to jettison entirely raster-based fonts and replace a V'IFX DVI file as needed. And I've been assured by the them with vector fonts. vendor that the next release of V'IFX will solve completely By this simple step, instead of maintaining a library of the backward compatibility problem in any case-without bit maps for each font supported at a collection of discrete the need to reprocess the source file. point sizes, V1E;X keeps only one version of each font. The Next the question of speed. Here there are several factors: single version of each font is basically a set of mathematical compilation time for the 1FX source file, previewer speed, formulas describing how to create every character in the font. and printer speed. To take a concrete example of the first, I This algorithmic encoding of characters is then expanded used as a test file the Solutions Manual I recently prepared into raster images at run time. By this procedure, not only for my mathematical modeling textbook Alternate Realities: are the number of available fonts dramatically increased­ Mathematical Models ofNature and Man (Wiley, 1989). This since the algorithm can easily do things like rotate, slant, Solutions Manual is a 71-page document, containing a lot of compress, magnify, and create and fill font outlines-but mathematical expressions as well as 19 Postscript graphics also the amount of hard disk space needed to store the insertions. The compilation time (on a 16MHz 386 machine font files shrinks by many megabytes. Even further storage with a 35ms hard disk) using V1fX's version of AvP'-'IFX reduction is made possible by recognizing that many of the was 5 minutes and 37 seconds, while normal AvP'-'IFX standard 1BX fonts are just slanted or stretched versions of took 2 minutes and 10 seconds-less than half as long. some other font, thereby obviating the need to store the Very likely, a large part of this difference can be accounted information for several variations on the same theme, e.g., for by the fact that V1E;X does not use 386 memory in cmti10 is just a slanted version of cmu10. protected mode, unlike normal 1fX. However, I understand that MicroPress has corrected this oversight in the most Matching Up with "Normal" 'lEX recent release of their product. For those (like myself) who have been using "normal" 1BX As for previewing, the V'IFX previewer also took slightly for several years, the overriding question that immediately longer to get the pages onto the screen as compared with comes to mind is: Why should I spend the time, energy, and the normal 1FX preview program I used, a package called money inevitably involved in shifting over to a new version TF}( Preview that is marketed by Arbortext, Inc. (some of of 1fX, be it V'IFX or otherwise? While the advantages of this difference is probably due to the fact that the Arbortext V'IFX cited above are readily apparent, what's not so evident package has its own set of screen fonts and doesn't need to is the price that has to be paid to get them (other than the make use of the printer fonts or generate screen fonts on the obvious initial ante of $299). While each potential user will fly). ultimately have to come to grips with this question within On the other hand, the V'IFX Postscript driver for my the context of his or her own particular computing needs printer (a QMS-PS810) was far and away faster than either and environment, let me briefly outline my own experience the driver from PC'IFX or that from Arbortext. I don't know in making the decision to switch over to a new 1fX. why this should be the case, but there it is. It's perhaps worth First of all, the problem of compatibility. Will files noting that V1E;X doesn't store the Postscript file to disk, created earlier with normal 1FX (hereafter when I use that as do all the other Postscript drivers I've used. Maybe, in term for purposes of comparision, I'm referring to the "Big" some mysterious way, part of the speedup can be accounted PCTF}( 386, ver. 3.0 implementation of 1BX marketed by for by this fact. Let me note, however, that if you do want Personal 1E;X, Inc.) still run on V1E;X? Happily, for the to have the Postscript file, there is an optional switch for the most part the compatibility issue has turned out not to be driver that allows writing the file to disk rather than to the a problem. V'IFX has provided a new 1FX primitive called printer. In summary, taking compilation time, previewing, \aliasfont by which all the standard CM font names are and printing together, my impression is that there's not much translated into their V'IFX counterparts. These translations to choose between these packages when it comes to overall are all gatliered together into a single input file that can be throughput time. made part of the V'IFX format file and thereafter forgotten Hard disk space is a topic that I've already taken up in about. Thus, with some very minor (and very obvious) the foregoing paragraphs. The total space required to store fiddling here and there, all of my earlier 1BX files work just the V'IFX program, TFM library, special macro packages fine with V1E;X. Moreover, if you want to use V1E;X fonts like AvP'-'IFX, font algorithms, device drivers, and other in a normal 1FX environment, MicroPress offers a program miscellaneous bits and pieces comes to about 1MB. By way called PXLGEN that enables you to painlessly generate a of comparison, the same items for my implementation of raster version of any V'IFX font at whatever point size and normal 1BX checks in at just under 1OMB! So if it's disk orientation you want to use it. So the compatibility direction space you're after, there is really no contest. Of course, as V'IFX -+ normal 1BX poses no problem whatsoever. In the hard disks continue to get bigger, faster and cheaper, this other direction, I experienced a bit of difficulty in using bulk memory factor will soon fade away into irrelevance.

FEBRUARY 1991, VOLUME 38, NUMBER 2 107 Computers and Mathematics

But for the moment it may still be a consideration for many mix printing of both landscape and portrait mode pages potential users. would also be useful. As a final point of comparison, let me note that adding • Parts of the V'IFX implementation of both the plain a new raster-based font to normal 1FX (like the new AMS and ~-'IFX font tables don't agree with normal'IFX, cyrillic or Euler Fraktur fonts) can easily soak up a megabyte e.g., the cap Greek characters like r, Cl>, and '¥ should or two of storage space. To add such a font to V'IFX usually normally appear as they do here, i.e., unslanted. But in requires about 30K of disk memory. The comparison is V'IFX they appear slanted, due to a hard-to-comprehend clear: if you want a system with lots of fonts but have only modification of the cmr10 character table. An even limited space, V'IFX is the way to go. worse problem with this character table, at least from an aesthetic point of view, is a change in the left and The Downside right parentheses characters. In V'IFX they are of constant While the foregoing remarks show my enthusiasm for V'IFX, width like this ( (( )) ) instead of being fatter in the middle they should not be interpreted as an unqualified clean bill of and tapering at the top and bottom as they should like this health. The package does have some flaws and undesirable ((( ))). Hopefully, this character table, which is so peculiarities. Here are a few that I've discovered: essential to 'IFXnicians, will be repaired in the very near • A couple of the commands discussed in the documen­ future. Another minor character glitch I noted involved tation, like the one referring to the use of raster fonts primed characters in math mode. For example, V'IFX in conjunction with V'IFX's vector fonts, appear not to gives V' rather than the correct spacing V '. Interestingly, work or are mislabeled either in the manual or on the this misspacing with primes seems to occur only with screen. some characters like V. • The font metrics for the V1FX versions of the CM fonts • Strangely, the V'IFX graphics insertion possibilities are seem to be just a bit different than their normal 1FX both very sophisticated and rather crude at the same counterparts, since on odd occasions V'IFX and normal time. On the positive side, V'IFX allows the direct 1FX give slightly different line breaks or page breaks for insertion of bitmapped graphics written in formats like the same file. In this connection, a V'IFX user should be PCX or MacPaint. Unfortunately, not all graphics files aware of the fact that in the normal 1FX release of the are created equal, and when I tried to make use of Computer Modem font family, several fonts appear at a this capability with a variety of PCX files generated by design size greater than 10 points (e.g., cmr17, cmti12, different graphics programs, only one of them previewed etc.). The V'IFX solution to generating these fonts is just and printed as per the V'IFX documentation. On an even to magnify the corresponding 10-point V'IFX version by more downbeat note, the insertion of Postscript graphics the appropriate scale factor. So, for example, the V'IFX with V'IFX is a bloody nuisance. The problem is that the version of the 12-point text italic font cmti12 is obtained vendor has not provided a proper prologue file allowing by scaling up 10-point text italic by 20%. As illustrated the user to conveniently scale the figure and position it by Donald Knuth on page 16 of The TF}(book [2], this on the page. Thus, the Postscript file must be inserted procedure can sometimes produce undesirable results, via the \special command, making sure to remember since "a well designed font will be drawn differently at to leave the requisite amount of blank space via an different point sizes." With this consideration in mind, appropriate \ vskip statement. And when I used this it would be a good idea for MicroPress to consider a old-fashioned, brute-force approach, V'IFX decided first standard vector font release that includes design point to scale down every one of my pictures to postage stamp­ sizes other than 10 points-this is especially important sized proportions before inserting them into the printed for large point-size fonts like cmr17. A good way to output. Thus, to recover the properly-sized pictures, I fix this kind of problem once and for all would be for had to open up the Postscript file describing the figure MicroPress to develop a vector-font version of Metafont, and insert an appropriate magnification statement into so that users could create their own version of whatever the Postscript code in order to undo V'IFX's arbitrary fonts they want without having to do too much scaling and certainly unwanted automatic downsizing. beyond the design size of the font. But, even taken as a whole, these are relatively minor • The V'IFX previewer is pretty crude when compared with quibbles, most of which I'm promised by MicroPress will some of the others on the market, as it has no provisions be addressed in future releases of the program-maybe even for page outline, ruler sticks, "two-up" viewing, moving by the time this review appears. back-and-forth between nonadjacent pages, or "on-the­ fly" changes of magnification. In fact, from a user's standpoint I would say that the previewer is presently General Summary the least satisfactory component of the overall V'IFX 1FX has been alive and well as a text-formatting package package. for over a decade now, an enviable achievement in an era in • The printer drivers could benefit mightily by the inclusion which the useful lifetime of most software packages can be of an interactive option by which one could single out measured in a period of months to at most a year or two. sets of noncontiguous pages for printing. The ability to Nevertheless, 'IFX's age is starting to show. And nowhere

108 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -----··························· ···············-·······················-·-···········-··-··-·----·----··---······-·------·------·························-·· ... . ·····························-·· -···································· Computers and Mathematics are the wrinkles more apparent and the blemishes more Finally there is also a program ACROTRAN that trans­ disfiguring than in the use of raster fonts. V'IEX is the first lates DXF format files (used in some computer aided design package to take this bull by the horns and get into the market programs) into ACROSPIN data files. with a real alternative. No doubt there will be others. But The animation produced by ACROSPIN is very good. for now, if you want the 'lEX of tomorrow in your computer Of course, one can get better results on a workstation but the today, MicroPress is the place and V'IEX is the solution. point is that this program really works on PC's. The manuals are well written and the ACROSPIN program contains a References help screen so it is quite easy to get started. The programs [1] Vulis, M. "V'IFX Enhancements to the 1FX Language." do what they intend to do so well that it is probably unfair TUGboat, Vol 11, No. 3, September 1990, 429--434. to complain about what one cannot do, i.e., use shading, [2] Knuth, D. The Tj;}(book, Reading, MA: Addison-Wesley, 1984. remove hidden lines etc. Now for the crucial question, what does one really do with these programs? It is great fun to look at objects turning -·-·----·······--·---··-····-·------·····-··-·-······-·-········-·····--···-· around and to be able to scale and speed up the movements etc., but surely there must be some kind of less frivolous GyroGraphics Ver. 2.2 use. The programs perform their tasks with such ease that Reviewed by Gustaf Gripenberg* one is likely to forget that they, from a pedagogical point of view, are and remain tools. It may take some effort to learn This package creates and dynamically rotates, translates, and how to use them to demonstrate mathematical concepts and scales 3-dimensional wire frame objects and point clouds. It to stimuiate students to think and explore on their own. The runs on IBM-PC compatible computers and supports all the value of this package may also be dependent on to what standard graphics cards. The minimum memory requirement extent it is true that, if one wants to display 3-dimensional is about 80k and the operating system should be DOS 2.1 objects, then it is really essential that one be able to tum or later. them around and not just look at them from one point. The objects are displayed by a program called The price of the complete GyroGraphics package in­ ACROSPIN. It gives a remarkably smooth animation of cluding Acrospin and the Acrospin manual is $75 plus $3 rotating objects and in addition to rotation around three shipping and handling each. It is available from fixed axes it can translate and shrink or enlarge the object. ACROSPIN takes as input files containing the information Cipher Systems about what lines and points should be displayed. The format 717 Willow Drive for these files is quite simple and well described in the Stillwater, OK 74075 manual. However, except for the simplest possible objects, 405-377-4432 it is almost necessary to use some program to create these files from the data. I tested this by writing a short program that made it possible to view solutions of 3-dimensional differential equations and it turned out to be a relatively Mathematical Freeware simple task. If one wants to make life more difficult, one can, of course, try to utilize all possibilities of using different and Shareware colors and putting the objects into different "levels" which makes it possible to tum on and off variou~ parts of the object one is viewing. To help the user in writing programs that produce data files that can be displayed, a number A Number Theory Package of Turbo Pascal programs of this kind are included in the package. For example, there are subroutines that generate for Microcomputers ordinary text. One part of the package is a program called GYRO that This number theory package is intended to be useful for creates ACROSPIN data files for rotation surfaces, graphs of exploratory research and for teaching. The routines are functions of two variables over rectangular or polar domains, available in three implementations - Turbo Pascal for the curves, or vector fields. The curves, for example, must be Macintosh and for IBM compatibles, and UBASIC (for given in parametric form, but the program can calculate IBM compatibles). Multiprecision arithmetic routines are velocity and acceleration vectors. included for the Turbo Pascal implementations (UBASIC A program GGMENU offers a menu of the objects that contains multiprecision arithmetic built-in). There are about can be viewed (up to 20). One has the option of displaying 50 number theoretic algorithms, including routines for pri­ on the menu a short description of the object by writing a mality testing, elliptic curve factoring, Shank's square form textfile and giving it the same name as the datafile. factoring, calculating continued fractions, solving systems of linear diophantine equations, and all the common functions. *Gustaf Gripenberg is in the Department of Mathematics at the University These are available from the author via anonymous ftp over of Helsinki. He can be reached by email at [email protected]. the Internet. To obtain the package, login to your home

FEBRUARY 1991, VOLUME 38, NUMBER 2 109 ··································------Computers and Mathematics system, and issue these commands (each of which should set type ascii be completed with a return keystroke): (The files are ascii) mget * (Transfer the files. They will have the same names and be home directory) ftp vela.acs.oakland.edu in your (This establishes a file transfer connection) quit ftp program) login anonymous (Leave the (Login to Oakland's ftp node - give your name as your You are now back in your home system. If you have password) any trouble, there should be an expert in "ftp" at your cd pub institution, or you may send electronic mail to me at my (Change directory) address: [email protected], Donald E. G. Maim, cd numbdroid Department of Mathematical Sciences, Oakland University, (Change directory again) Rochester, MI 48309-4401; (313)370-3425.

Mathematical Impressions Anatoli't T. Fomenko "I think ofmy drawings as if they were photographs ofa strange but real world, and the nature of this world, one ofinfinite objects and processes, is not well known. Clearly there is a connection between the mathematical world and the real world.... This is the relationship I see between my drawings and mathematics." Anatolii Fomenko, in the Introduction

Anatoli'f Fomenko is a Soviet mathematician with a talent for expressing abstract mathematical concepts through artwork. Some of his works echo those ofM.C. Escher in their meticulous rendering of shapes and patterns, while other pieces seem to be more visceral expressions of mathematical ideas. Stimulating to the imagination and to the eye, his rich and evocative work can be interpreted and appreciated in various ways-mathematical, aesthetic, or emotional. This book contains 84 reproductions of works by Fomenko (23 of them in color). In the accompanying captions, Fomenko explains the mathematical motivations behind the illustrations as well as the emotional, historical, or mythical subtexts they evoke. The illustrations carry the viewer through a mathematical world consisting not of equations and dry logic, but of intuition and inspiration. Since the mid-1970s, Fomenko has created more than 280 illustrations. Not only have his images filled pages of his own numerous books on geometry, but they have also been chosen to illustrate books on other subjects, such as statistics, probability, and number theory. In addition, his works have found their way into the Soviet scientific and popular press and have been displayed in more than 100 exhibits in the Soviet Union, Holland, India, and much of Eastern Europe. Fomenko describes his images as "deep reflections about the essence of being and about theplace of modem man­ in particular, the learned man-in the stormy and unpredictable world surrounding him." His illustrations are the product of a sensitive, aesthetically attuned mind diving deep below the surface of modem mathematics and emerging with great stories to tell. ======1980 Mathematics Subject Classification: 00 All prices subject to change. Free shipment by surface; for air delivery, ISBN 0-8218-0162-7, LC 90-47514 please add $6.50 per title. Prepayment required. Order from Amer­ 194 pages (hardcover), December 1990; ican Mathematical Society, P.O. Box 1571. Anex Station, Providence, Individual member $36. List price $45. RI 02901-1571, or call toll free 800-321-4AMS (321-4267) in the To order, please specify MATIMP/NA continental U.S. and Canada to charge with VISA or MasterCard.

110 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS

Report on the Activities of met with the CSP in Washington on December 1 for the AMS Committee an extended discussion of policy issues in education, in particular the relationship of proposed AMS activities to on Science Policy, 1990 the ongoing activities of the MAA. The discussion was Michael C. Reed, Chair attended by representatives of the Mathematical Association The AMS Committee on Science Policy (CSP) met three of America (MAA): Lida Barrett (President), Marcia Sward times in 1990, two half-day meetings, one in Albuquerque (Executive Director), and John Thorpe (Chair, Science Policy (April 19) and the other in Columbus (August 9), and a Committee). two-day meeting November 30-December 1 in Washington, In Columbus, the CSP discussed the David II Report DC. The CSP does not make AMS policy; the Council does (Renewing U.S. Mathematics: A Plan for the 1990s, NRC, that. The CSP discusses a broad range of policy questions 1990) focusing on the questions: What are the responsibilities brought to it by the officers of the Society, the Council, of the research universities for K-12 education, for bringing or individual members, and makes recommendations to the women and minorities into the profession, for technology officers and the Council. What follows are brief descriptions transfer from mathematics to the sciences? The Report of the main issues discussed by the Committee during the says that departments should give "increased recognition" past year. to faculty members who participate in these activities. The CSP discussed the idea of small research awards What does this mean? How shall it be accomplished in and recommended to the Council that the AMS raise funds practice? These are difficult questions and agreement was from foundations, from corporations, and from individual not reached on recommendations. The CSP sponsored a members for such a program. This recommendation was panel discussion at the Columbus meeting on the same later approved by the Council. The CSP also stated that all topic. The panelists were: Phillip Griffiths, Chair, Board types of support discussed in the David I Report (Renewing on Mathematical Sciences, NRC; Arthur Jaffe, Harvard U.S. Mathematics: Critical Resource for the Future, National University; Robert O'Malley, incoming President of the Research Council (NRC), 1984) as necessary for research Society for Industrial and Applied Mathematics (SIAM); and (salary, travel, equipment, etc.) are suitable modes for AMS Judith Sunley, Director, Division of Mathematical Sciences, small award support. National Science Foundation (NSF). The CSP heard a report from the Executive Director, In Albuquerque, the CSP discussed the changing sit­ William H. Jaco, about considerations involved in relocation uation in Eastern Europe and ways in which individual of some or all AMS activities to Washington, DC. After mathematicians and the AMS could provide help to math­ extended discussion, the CSP stated that there are strong ematicians in Eastern European countries. In Washington, scientific and policy reasons for moving the AMS to this was followed up by a broader discussion of the AMS Washington and recommended continued investigation of role in helping mathematicians in all currency poor coun­ the costs, both personnel and financial. tries. This discussion was attended by representatives of In Albuquerque, the CSP discussed at length the idea the international programs at the NSF. There are difficult of an AMS Committee on Education (COB), whether such policy questions here: How does the AMS decide which a committee would be useful, and what its relationship countries to help and at what cost to the AMS? How can would be to the CSP and the Council. The CSP strongly the AMS be sure that assistance provided is accessible to all recommended to the Council the formation of such a standing mathematicians regardles of race, gender, or religious affil­ committee and wrote a proposed charge to such a committee. iation? Would programs such as these divert attention from The Council has since approved the recommendation (with pressing research and educational assistance needed in the a slightly altered charge-see Notices, October 1990, pages United States? A panel discussion on this topic was spon­ 1146-1147), and the President has appointed the COB. Its sored by the CSP at the San Francisco meeting. Panelists chair, Ramesh Gangolli of the University of Washington, were: Pavol Brunovsky, Comenius University, Czechoslo-

FEBRUARY 1991, VOLUME 38, NUMBER 2 111 Inside the AMS

vakia; Samuel Gitler, University of Rochester; William H. with this problem is to reduce the amount of salary dollars Jaco, AMS; Joseph Kohn, Princeton University (moderator); going to currently supported Pis so that the money can Harold Stolberg, Division of International Programs, NSF; be used to increase the number of Pis. This raises several James Timourian, University of Alberta; and H. H. Wu, difficult questions: What are the benefits and drawbacks of University of California at Berkeley. At the San Francisco spreading support more widely (and therefore more thinly) meeting, the CSP also sponsored Timothy O'Meara, provost in the mathematics community? What are the goals (or of the University of Notre Dame, as its government and· should be the goals) of federal research support and how public policy speaker on the topic "The Public Perception efficacious is salary support as opposed to non-salary support of Mathematics and Mathematicians." in achieving those goals? Marvin Wunderlich, Director of In Columbus and again in Washington, the CSP discussed the Mathematical Sciences Program at the National Security the job market for young mathematicians in the United Agency, described the alternate modes of funding being States. What is happening and what are the underlying developed at that agency. Jaco described the status of the reasons? What can the AMS do to help? Various schemes small awards program that the AMS is trying to develop, and were discussed to reduce the amount of "overapplying" and Sunley spoke strongly for the importance of salary support. to make the market mechanisms more efficient. The CSP The CSP discussed the issues but made no recommendations. heard a report from Jaco on the electronic bulletin board At the Washington meeting, both Jaco and Sward made created in the past summer to match late job seekers with presentations concerning cooperation and possible confedera­ departments needing assistance. The CSP strongly supported tion between the AMS and MAA. In the ensuing discussion, these AMS activities. it became clear that the CSP felt that there were many A prime topic of the Washington meeting was technology (perhaps not insurmountable) problems on both sides with transfer from mathematics to other disciplines. The CSP was confederation, but that all means to further cooperation addressed by James Glimm, the chair of SIAM's Committee should be taken. In addition, the CSP felt that it was natural on Science Policy, who is writing a long report on this and wise to bring SIAM into these cooperative activities. The subject for the Board on Mathematical Sciences of the CSP recommended to the President of the AMS four specific National Research Council (Mathematics: A Wellspring for areas in which he should initiate cooperation between the American Technology and Economic Competitiveness, to three societies immediately: (1) Student Chapters; the per­ appear in 1991 ). He emphasized the difficulty of technology sonnel in the three societies and Pi Mu Epsilon responsible transfer and its importance for the future health of the for student chapters should work together to avoid needless entire mathematics community. Statements were also made turf battles and to co-sponsor activities wherever possible. by Louis Auslander, Defense Advanced Research Projects (2) Data Collection; there is much too much data collection Agency; Jagdish Chandra, Army Research Office; and Jerrold being done by individual societies and other organizations Marsden, U.C. Berkeley (who is also a member of CSP). and agencies. The three societies should work together to All emphasized the need for cultural change within the do it right. (3) Rewards; the three presidents should appoint mathematics community so that those who engage in these an ad hoc Committee on Rewards to discuss and propose activities feel the support of the community. This topic will ways to implement the "recognition" called for in the David be taken up again by the CSP at its meeting in Tampa this II Report. (4) Statement of Principles; the three presidents March. should appoint an ad hoc committee to develop a short Another topic of the Washington meeting was the ques­ "statement of principles" for professional mathematicians. tion of alternate modes of funding by the Federal Agencies. The Committee on Science Policy welcomes com­ "Alternate modes" refers to any mechanism of support for ments from members of the Society on any of the research, normally from Federal Agencies, which does not above topics or suggestions of issues for the Committee follow the traditional pattern of two months summer salary to take up at future meetings. Comments and sugges­ plus a small to moderate amount of additional funds (travel, tions can be made to any member of the Committee: page charges, computers) for individual investigators. The Michael Artin, James Donaldson, Ramesh Gangolli, Rhonda traditional pattern is being questioned because the number Hughes, William Jaco, Joseph Kohn, Joel Lebowitz, Jerrold of principal investigators (Pis) is slowly decreasing and Marsden, Cathleen Morawetz, Michael Reed (chair), Oscar everyone acknowledges that there are large numbers of Rothaus, Paul Sally, Jr., David Vogan, Jr., Frank Warner, excellent researchers with no support at all. One way to deal Mary Wheeler.

112 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

Edwin Floyd ered an address at the Special Ses­ Utrecht University; there he remained 1924-1990 sion on Differential Topology at the until his retirement in 1975. Edwin Earl Floyd, a former vice pres­ Joint Mathematics Meetings in Denver In his scientific work Freudenthal ident and provost of the University of and, in 1976, an AMS Invited Address has always shown a restlessness and Virginia, died December 9, 1990 at the at the Joint Mathematics Meetings in broadness that were typical of his age of 66. San Antonio. He served on the AMS personality. This resulted in a var­ Floyd was born May 8, 1924 in Nominating Committee (1961, 1962, ied collection of mathematical gems Eufala, Alabama. He received his bach­ 1972) and the AMS Program Com­ that exerted considerable influence on elor's degree in 1943 from the Univer­ mittee (1976-1978). He was also an the mathematics of half a century. To sity of Alabama and his doctorate in associate editor for Proceedings of the mention a few: the theory of ends 1948 from the University of Virginia. AMS and served on its Editorial Com­ (starting with his dissertation "Uber He was an instructor at Princeton Uni­ mittee (1960-1962). die Enden topologischer Raume und versity (1948-1949) before joining the Floyd's early work was in ana­ Gruppen", Math. Z. 33 (1931), 692- faculty at Virginia. In 1966, he was lytic topology, and later he became 713), the suspension theorems ("Uber appointed to the Robert C. Taylor pro­ interested in group actions. From the die Klassen der Spharenabbildungen fessorial chair, a position he held until mid-1960s until the mid-1970s he and I", Compositio Math. 5 (1937), 299- his death. He served as chair of the Pierre Conner developed the subject of 314), a spectral theorem for Riesz mathematics department from 1966 to equivariant cobordism. After his years spaces ("Teilweise geordnete Moduln'", 1969 and was appointed dean of the in administration, Floyd returned to re­ Nederl. Akad. Wetensch. Proc. A 39 faculty of arts and sciences in 1974. In search and worked on the construction (1936), 641-651), the algebraic char­ 1981, he was named vice president and of classifying spaces. acterization of the topology of the real provost. He resigned from that position semisimple Lie groups (Ann. Math. 42 in 1986 to return full-time to research Hans Freudenthal (1941), 1051-1074), work on the char­ and teaching. He was also a member 1905-1990 acters of the semisimple Lie groups of the Institute for Advanced Study Hans Freudenthal died on October 13, (Nedcrl. Akad. Wetensch. lndag. Math., (1958-1959 and 1963-1964) and was a 1990. Sitting on a bench in the park 1954--1956), octonion planes and other Sloan research fellow (1960-1964). near his home on a sunny October geometries connected with the excep­ In 1981, Floyd received the Uni­ morning, he peacefully passed away. tional simple Lie groups (work done versity of Virginia's highest honor, the He was born in 1905 in Lucken­ over a long period in the fifties), the Thomas Jefferson Award for contribu­ walde, Germany, where he grew up and design of a language for cosmic inter­ tions to the University. In that same attended the gymnasium. He studied in course: "Lincos" (1957-1960). year, he also received the Imps Distin­ Berlin from 1923 to 1930, interrupted Besides being an excellent mathe­ guished Professor Award. The author by a stay in Paris during the summer matician, Freudenthal had a broad and of more than forty papers, he served semester of 1927. In 1931 he obtained vivid interest in such matters as, e.g .. on mathematics panels for the National his doctoral degree at Berlin with Heinz the social impact and educational as­ Science Foundation, the Office of Naval Hopf. In the meantime, he had come pects of mathematics, or of science Research, the Council for the Interna­ to Amsterdam (1930) on the invitation in general. Numerous articles in vari­ tional Exchange of Scholars, and the of L. E. J. Brouwer, where he was ous periodicals show that he did not Conference Board of the Mathematical appointed instructor at the Mathemati­ want to be confined to the proverbial Sciences. cal Institute of the University. With an ivory tower. He was the founder and Floyd presented a half-hour address interruption during the German occu­ for a long time the enthusiastic leader at the 1962 International Congress of pation, he held this position until 1946, of the Institute for the Development Mathematicians. In 1965, he deliv- when he was appointed full professor at of Mathematical Instruction in Utrecht

FEBRUARY 1991. VOLUME 38, NUMBER 2 113 ·············-····-·----·-·---·-·-·-·····-········--·-··-···-·"·"--.. --··············-·-·-···-···········-·-····------··-···--.. ---·-·-·"--·-·-··-·---·-·--·-···-·--·-····---·-·---··-·---·...... _...... News and Announcements

(formerly IOWO, nowadays a Univer­ orem of de Rham was most probably geometric context. These vector spaces sity Research Group on Mathematical believed to be true by Poincare and was Hq(M) constitute the singular homol­ Education named OW&OC). His book certainly conjectured (and even used!) ogy of M. By its very nature a q-form Mathematics as an Educational Task in 1928 by E. Cartan. But in 1931 de w can be integrated over a q-chain (1973) and other publications on the Rham set out to give a rigorous proof. Cq to yield a number fc wq1 so that q didactics of mathematics are the fruits The technical difficulties were consid­ these two complexes naturally stand in of a restless activity in this direction, enible at that time, as both the general a duality relation. Stokes' theorem now which lasted till the very last days theory of manifolds and the "singular takes the form: of his life. Just recently the National theory" were in their early formative Science Foundation (NSF) awarded a stages. r dwq-1 = r wq-1 grant to OW&OC in collaboration with In his early version, the theorem as­ lc• lac• the University of Wisconsin at Madi­ serts the following. Let Qq(M) denote and so extends this duality to a pairing son to develop new high school pro­ the space of smooth q-forms on M, so of Hf,R(M) and Hq(M) to~. grams in mathematics for the U.S.A. that Q0(M) denotes the C00 functions, In short, we have maps: Could one think of a more beautiful Q1(M) the line integrands I: ai dxi posthumous homage to Freudenthal's and so on. The exterior derivative, d, Hf,R(M)- Hom(Hq(M); R) pioneering contributions to didactics of extends the notion of the differential of Hq(M)- Hom(Hf,R(M); R) school mathematics, once incensed in a function to give rise to what we now and de Rham's theorem is precisely part by his vehement opposition to the call the de Rham complex of M. By that these maps are isomorphisms onto. new math wave? this we mean the sequence of vector This theorem is then a sort of topolog­ Many people who have known spaces and differential operators: ical form of the particle-wave equiva­ Freudenthal will recall his vivid and lence of quantum mechanics; and the inspiring personality. It was a privilege 0 1 0--+ Q (M) ~ Q (M) quest for "truly" understanding these and a pleasure to work with him, as and analogous dualities has been one a student, as a colleague, or in any ... ~Qn(M)--+0. of the great motivating forces in the of the various organizations in which mathematics of the last fifty years. In­ he was active. Let us remember Hans Because rJ2 = 0 by construction, it makes sense to measure the failure of deed, one of the early triumphs of sheaf Freudenthal in gratitude. theory was to give a completely new Ferdinand D. Veldkamp exactness of this sequence; thus one understanding of this duality, an un­ University of Utrecht defines: derstanding which was extended to the Hf,R(M) = kerd in Qq jdnq-l, complex and algebraic domains with such great success by Weil, Cartan, Georges de Rham and these vector spaces are called the Serre, Grothendieck, and many others. 1901-1990 cohomology groups of M in the sense In algebraic topology Chen's and Sul­ Georges de Rham died on October 9, of de Rham. livan's approach to the rational homo­ 1990 in Lausanne, a city he loved and On the other hand, the "singular topy of a space is related to these ideas which had been his home since the theory" which grew out of the triangu­ and in its most recent reincarnation it early thirties. He was eighty-nine. The lation concept, was at that time con­ reappears in the intersection cohomol­ great passions of de Rham 's life were structed out of p-chains Cp(M) con­ ogy of Goresky and McPherson. In mathematics and mountaineering, and sisting of formal linear combinations analysis the de Rham complex is the he excelled in both of them with a of oriented smooth polyhedra in M most perfect example of what Atiyah characteristic charm and modesty. with coefficients in ~ . Thus a 0-chain and I called an "elliptic complex" and In some sense the famous theorem is simply a finite sum I: riPi· where this leads yet in another direction with that bears his name dominated his math­ ri E ~,PiE M. fruitful consequences. ematicallife, as indeed it dominates so The geometric notion of boundary All these are by and large "pure" much of the mathematical life of this extends linearly to give rise to a new instances of the motivating force of whole century. When I met de Rham sequence of vector spaces: the de Rham theory. On the physics in 1949 at the Institute in Princeton he side, one can say even more: there is was lecturing on the Hodge theory in 8 +-- Co(M) j!_ C1 (M) hardly any aspect of modem field the­ the context of his "currents". These are ory which is not in some sense related +-- · · · j!_ Cn(M) +-- 0 the natural extensions to manifolds of to the de Rharn complex and its gen­ the distributions which had been intro­ which again has 82 = 0 so that eralization. Indeed, the electromagnetic duced a few years earlier by Laurent force is mathematically described by Schwartz, and of course it is only in this Hq(M) = ker8/Im8 at Cq the 2-form: extended setting that both the de Rham theorem and the Hodge theory become provides one with a measure of the F =Ex dx dt + Ey dy dt + Ez dz dt especially complete. The original the- failure of exactness in this new more +Hxdydz- Hydxdz+Hxdxdy

114 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------····-·········-··--·······-···············-·-·······················--··········--·-·····--·············-····-······-······-·.. ·.. -··-·········- News and Announcements and the equations of Maxwell-Einstein he never boasted of his mountaineer­ topics. Past recipients are: Nicholas that govern it in vacuo are expressed ing exploits and it was only at second Varopoulos (1968), Richard Hunt most succinctly in terms of the de hand that the daredevil in him be­ (1969), Yves Meyer (1970), Charles Rham and Hodge theory. Indeed, the came apparent, like when he turned up Fefferman (1971), Thomas Komer equations fall into two parts: at his seminar at Princeton at 3 p.m. (1972), E. M. Nikisin (1973), Hugh and calmly announced that he had left Montgomery (1974), William Beckner dF=O and d*F=O, Boston earlier that day at 10 a.m., or (1975), M. R. Herman (1976), S. B. some other preposterously late time. Bockarev (1977), Bjorn E. Dahlberg the first condition therefore being com­ He drove fast! Yet he walked at a (1978), Gilles Pisier (1979), Stylianos pletely topological, the second one in­ steady pace, which he could keep up Pichorides (1980), Peter Jones (1981), volving the space time metric. And of for days, crossing glaciers and exhaust­ Alexei B. Aleksandrov (1982), Jean course the nonabelian generalizations ing his younger comrades. But let me Bourgain (1983), Carlos Kenig (1984), of the electromagnetic force associated end with a potrait so eloquently and Th. H. Wolff (1985), N. G. Makarov with the compact Lie groups are gov­ precisely drawn by K. Chandrasekha­ (1986), Guy David and Jean Lin Jounre erned by the corresponding nonlinear ran on the occasion of the colloquium (1987), and A. L. Vol'berg and J. C. Hodge equation: in honour of Georges de Rham. After Yoccoz (1988). The jury consisted of J. speaking of the importance of his work, Bourgain, V. Havin, Y. Katznelson, and Chandrasekharan adds: E. M. Stein. "But the distinction of his person­ with F now being a 2-form with values ality makes him even taller. Tough History of Women in the Lie algebra g of G, and related as steel in his adherence to prin­ in Science Award to the g-valued 1-form A by ciple, resilient, placable, self-less Ann Hibner Koblitz has received the 1 and generous beyond the dictates History of Women in Science Award F = dA+ 2:[A,A]. of fashion, steadfast in friendship, from the History of Science Society. but not at the price of reason, de The $500 award, presented at the So­ In short, then, it is not surprising Rham strides the world of mathe­ ciety's annual meeting in Seattle in that de Rham had much work to do matics a happy warrior." October 1990, honors original research to build the foundations of this edifice, We mourn his passing but celebrate that explores the issues faced by women and his book on these matters is a his life. in science, the ways that science has masterpiece of rigour, as well as style. dealt with gender, and the ways that Bibliography science has dealt with women. Of course de Rham's work was [I] de Rham, G., Sur 1' Analysis situs des no way confined to this topic. His Re­ varietes a n dimensions (These de doctorat, Koblitz, who currently teaches Rus­ ducibility Theorem for Riemann Spaces Paris). Journal de math. X, 115-200 (1931). sian history at Hartwick College in is a cornerstone of Riemannian geome­ [2] de Rham, G., Varietes differentiables, Oneonta, New York, received the award try as is his work related to Reidemeis­ formes, courants, formes harmoniques. Pub­ for her article, "Science, Women, and ter torsion the starting point of much lications de l' Institut math. de l' Universite de the Russian Intelligentsia," (/sis, 1988, Nancago, III. Paris: Hermann 1955. 79:208-226). The article focuses on the further development. For instance, us­ [3] de Rham, G., Sur Ia reductibilite d'un ing these methods he proved that two espace de Riemann. Commentarii Math. Helv. political, social, and individual contexts diffeomorphic rotations of a sphere are 26, 328-344 (1952). of a group of female members of the necessarily isometric. In fact, de Rham [4] de Rham, G., Complexes a automor­ intelligentsia in Russia in the 1860s and was interested in every aspect of ge­ phismes et homeomorphismes differentiables. 1870s. ometry and topology and worked for Annates de l'Institut Fourier 2, 51--67 (1950). Koblitz is perhaps best known for the good of the world of mathematics [5] Collected Papers of G. DeRham. Oeu­ her writings on the mathematician Sofia vres Mathematiques, Universite de Genf\ve, Kovalevskaia, and particularly for her steadfastly and selflessly all his life. L'Enseignement Mathematique Geneve, 1981. book A Convergence of Lives. Sofia As president of the International Math­ Raoul Batt Kovalevskaia: Scientist, Writer, Revolu­ ematical Union he did his utmost to Harvard University bring together all branches of mathe­ tionary. matics, the East and the West and the 1990 Salem Prize young and the old. The Salem Prize for 1990 was awarded AMS Sponsors de Rham had a subtle charm which to S. V. Konyagin of Moscow State High School Lectures drew younger people to him immedi­ University for his solution of a fa­ On December 10, 1990 the AMS spon­ ately. In those early days at Princeton mous problem on trigonometric series. sored a special day of lectures on he would easily mingle with the bois­ The prize, established in 1968, is given mathematics for high school students terous postdocs, his exquisite manners every year to a young mathematician in San Diego. The purpose of the lec­ contrasting amusingly with our rude who is judged to have done outstanding tures was to bring the students into ways. He was always lean and one work in the field of Raphael Salem­ contact with working mathematicians could feel the steel in his sinews, but primarily Fourier series and related and to expand the students' horizons

FEBRUARY 1991, VOLUME 38, NUMBER 2 115 -·······-··----·····---·····-····"··-"·"-""-""""""-----········------·--·------·-·-·--"---·-·-·········"""""""""""""·"······-·····-·-···----·---··-··------·-- News and Announcements about the nature of mathematics and ing held the same day accounts in part Kelly, Program Manager, Graduate As­ mathematical research. for the low attendance. Both Smale and sistance in Areas of National Need, The lecturers, Michael H. Freed­ Freedman said they felt that the pro­ U.S. Department of Education, 400 man of the University of California gram would have been more valuable Maryland Avenue, SW, Washington, at San Diego and Stephen Smale of had it been on a larger scale. Better DC 20202-5251; telephone 202-708- the University of California at Berke­ publicity, and perhaps a 2-day program 8870. ley, were chosen for their ability to with school credit available, might help communicate sophisticated mathemat­ to increase attendance. Report Calls for Changes ical concepts to nonmathematicians. This was the second time the So­ in Reward Structure Freedman spoke on the connections be­ ciety has sponsored such an event; the The Carnegie Foundation for the Ad­ tween topology and electromagnetism, first took place at the Boston Museum vancement of Teaching has issued a while Smale lectured on chaos. Both of Science in 1988 and featured as report that calls for expanding the def­ speakers felt that the event was suc­ speakers William P. Thurston of Prince­ inition of academic faculty scholarship cessful and that the students were very ton University and Raoul H. Bott of to include teaching and other activi­ responsive. Harvard University. Support for the San ties. According to a news piece in the Joe Schanberger of San Diego Mesa Diego event was made possible by in­ December 5, 1990 issue of the Chron­ College teaches a calculus class for high come from the Waldemar J. Trjitzinsky icle of Higher Education, the report school students and he took a group of Memorial Fund, which was established has appeared amid discussions of the them to the hear the talks. "The lectures through a bequest of Barbara G. Tr­ need to improve undergraduate teach­ were very good, the students enjoyed jitzinsky (see Notices, February 1989, ing and a growing dissatisfaction with them," Schanberger remarked. "One of page 152). However, in compliance an academic rewards system that places my students later told me the lecture on with the terms of the bequest, the fund research above teaching. chaos was 'really cool, it's the coolest will in the future be used for awards The report, entitled "Scholarship thing I've ever seen."' Schanberger said to needy mathematics students to as­ Reconsidered: Priorities of the Pro­ that student later made a presentation to sist them in pursuit of their careers in fessoriate," proposes a definition of the class summarizing Smale's lecture. mathematics. The AMS is considering scholarship comprising the discovery "Both of the lectures were very well alternative ways to support a continu­ of new knowledge, the integration of done and they were excellent in terms ing series of high school mathematics knowledge, the application of knowl­ of relating to the audience and making lectures. edge, and teaching. Such a definition of them feel welcome." scholarship would improve the faculty­ Schanberger feels that one of the Education Department Announces rewards system and boost morale, the most valuable things about this kind of Graduate Fellowship Awards report said. In addition, the report rec­ program is that it exposes students to The Department of Education has an­ ommends that institutions carve out research mathematics. In addition, the nounced five new awards in its Grad­ niches for themselves, rather than try­ personal element is important. "Seeing uate Assistance in Areas of National ing to imitate more prestigious insti­ a professional mathematician, seeing Need program. The program provides tutions, and that graduate students be the work they do, being able to rub three-year grants to educational insti­ required to take teaching seminars. elbows with them, is very beneficial," tutions to establish graduate fellowship Copies of the report are available he notes. "The students that were there programs in mathematics, chemistry, for $8 from: Princeton University Press, appreciated very much the effort put physics and engineering. 3175 Princeton Pike, Lawrenceville, NJ forth by the speakers, and I did too." The institutions receiving awards in 08648; telephone 609-896-1344. During the question and answer ses­ mathematics, followed by the amount sion that followed the lectures, the stu­ of each grant and the number of fellow­ News from the dents asked the speakers about a wide ships each grant covers are: University Institute for Mathematics range of topics in science. "We were of Chicago, $240,000, 15; University and its Applications 'mined' for information across a wide of Wisconsin, $115,812, 7; Renssalaer University of Minnesota field," said Freedman, though in several Polytechnic Institute, $216,667, 13; The ongoing 1990--1991 academic year cases the questions fell outside of their Rice University, $113,920, 8; and Uni­ program at the Institute for Mathemat­ expertise. "We were asked about many versity of Minnesota, $136,800, 12. The ics and its Applications (IMA) is Phase problems in physics and astronomy." In grants involve cost-sharing on the part Transitions and Free Boundaries. The addition, the students asked questions of the institutions. organizers are R. Fosdick, M.E. Gurtin, about topics from the lectures, as well At the time of this writing, the com­ W.-M. Ni, and L.A. Peletier. The ad­ as about what mathematicians do and petition for the fiscal year 1991 funds visory committee is: H. Brezis, L.A. possible careers involving mathematics. was under way; awards are expected to Caffarelli, D. Kinderlehrer, and J. Ser­ About sixty students were present, be announced in March 1991. Those in­ rin. The aim of the program is to though about twice as many were origi­ terested in more information about this understand certain types of physical be­ nally expected. A science olympiad be- program may contact Carolyn Proctor havior which occur in phase transitions

116 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements and in phenomena which involve free Preference will be given to those who mation: Institute for Mathematics and boundaries. The February-June portion participate in the entire program. For its Applications, University of Min­ of the program was discussed in the details write to A. Freidman, Director. nesota, 514 Vincent Hall, 206 Church November 1990 issue of Notices; it The IMA Postdoctorates in Indus­ St., S.E., Minneapolis, MN 55455- will focus on free-boundary problems trial Mathematics program which began 0436; 612-624-6066; Fax: 612-626- and on diffusion problems involving a in September 1990 with four positions 7370; ima_staff%csfsa.cs. umn.edu@ singular mechanism, such as a degen­ is expanding to seven positions dur­ cs.umn.edu. eracy and free boundaries. Here the ing summer and fall of 1991. These physical areas to be considered will one to two year appointments are in News from the include porous flow, jets, cavities, lu­ addition to the regular IMA postdoc­ Mathematical Sciences Institute brication, combustion, plasma, coating toral program and are funded jointly by Cornell University flows, and the dispersal of biological the National Science Foundation (NSF) The Mathematical Sciences Institute populations. and by Honeywell, Inc. and 3M (4 po­ (MSI), in conjunction with the Univer­ On June 10-13, 1991 the IMA and sitions), jointly by the IMA and Cray sity of Maryland Institute for Advanced the Army High Performance Comput­ Research (2 positions) and jointly by Computer Studies, will sponsor the ing Research Center (AHPCRC) will the IMA and Siemens A. G. (1 po­ First International Workshop on Logic cosponsor the workshop Graphics and sition). They are designed to prepare Programming and Non-Monotonic Rea­ Visualization issues in Computational mathematicians for research careers in­ soning. The workshop is scheduled to Fluid Dynamics. P. Woodward chairs volving industrial interaction. Postdoc­ meet July 22-24, 1991 at the Capi­ the organizing committee. The first two torates spend 50% effort working in the tol Holiday Inn, Washington, DC. A. days will be a graphics tutorial in the regular IMA program and 50% effort Nerode from the MSI (607-255-8005), AHPCRC graphics laboratory, meant working with industrial scientists on a W. Marek from the University of Ken­ for CFD researchers who are inter­ specific project. tucky (606-257-3961), and V.S. Subrah­ ested in using computer graphics. The On October 7-11, 1991 the IMA manian from the University of Mary­ last two days will consist of research will host the workshop Transfer of land (301-405-2711) are organizers for talks and demonstrations on graphics Mathematics to Industry in the U.S. the meeting and can supply additional for CFD. and France, co-sponsored by the Insti­ information. Topics to be discussed in­ From July 15 - August 9, 1991 the tut National de Recherche en Informa­ clude: stable semantics, default logic, IMA will present a summer program on tique et en Automatique (INRIA). Both auto-epistemic logic, truth maintenance Semiconductors. The organizers are F. institutes have considerable, but dif­ systems, implementation issues, diag­ Odeh (Chair), J. Cole, W.M. Coughran, fering, experience in relating academic nosis, probabilistic non-monotonic the­ Jr., P. Lloyd, and J. White. The goal mathematics to industrial application. ories, applications, meta-programming of this program is to foster interac­ The workshop will bring together some and non-monotonicity, inheritance net­ tion in this interdisciplinary field which of the key people from industry and works, inconsistency and non-monoton­ involves electrical engineers, computer from universities in France and the icity, and logics of belief. scientists, semiconductor physicists and U.S. who are playing roles in building The MSI Special Program in Par­ mathematicians. from both university bridges between the two communities. tial Differential Equations will con­ and industry. The program will particu­ The goals of the workshop are: To dis­ tinue this Spring with talks by E. larly encourage the participation of nu­ seminate experience gained by mathe­ DiBenedetto from Northwestern Uni­ merical and mathematical analysts with matical scientists in industry, in univer­ versity (Porous Media Type Equations, backgrounds in ordinary and partial dif­ sities and in government agencies; to Feb. 1st), J.L. Bona from Pennsylva­ ferential equations and help get them facilitate transfer of mathematical prob­ nia State University (Dispersive Blow­ involved in the mathematical aspects lems of present interest to industry, and up of Nonlinear Wave Equations, Feb. of semiconductor models and circuits. mathematical knowledge applicable to 3-5), D. Hoff from Indiana Univer­ Leading engineers in semiconductors industry; to outline future mathematical sity (Discontinuous Solutions of the will be invited to present the signif­ research directions in industry; and to Navier-Stokes Equations for Compress­ icant industrial issues as well as to discuss the ways and means as to how ible Flow, Feb. 8-15), M. Avellaneda concentrate on those models which are best to educate mathematics graduate from the Courant Institute (Scaling most relevant to mathematicians. The students to be successful in industry, Properties and Phase Diagrams for main topics of the program are pro­ while doing good mathematics. There Long-time Turbulent Transport, March cessing modeling (July 15-19), device will be ten speakers from French in­ 7-14), J.-C. Saut from Universite Paris­ modeling (July 22-30), quantum effects dustry and from INRIA; ten speakers Sud (Linear and Nonlinear Dispersive (July 31-August 2), and circuit analysis from U.S. industry, government agen­ Waves, March 25-April 12), and C. (Aug. 5-9). Some partial support will cies and universities; overview talks by Foias from Indiana University (Normal be available for researchers (including A. Bensoussan (President of INRIA) Form of the Navier-Stokes Equations graduate students) who are, or wish and A. Freidman (Director of IMA); as and the Connection to Turbulence, June to become, familiar with the subject. well as round table discussions. Infor- 5-15). For details contact B.S. Titi at

FEBRUARY 1991, VOLUME 38, NUMBER 2 117 ••••••••••-••-•••••oo•••••oo•-•••oo••••••""""•"•""""•""-•"•""_" __••••••-••••·-•--··---·---·••--•••"••• ______••••••·-·-••••••-•••••••••••••••••••••-••••••-••••••••••••••••••••••••-•••••••••••••••••••••••••••••••••••••••••••••-••••••••••••••••••• News and Announcements

607-255-8005 or P. Holmes at 607- physics and mathematics. For example, modynamics has not yet been con­ 255-4267 or the Mathematical Sciences advances in knot theory have involved structed, and this remains the outstand­ Institute at 409 College Ave., Ithaca, ideas from statistical mechanics; and ing challenge. Similar processes occur NY 14850; Fax: 607-255-9003. important progress in four-dimensional in thermonuclear fusion containment geometry has been based on concepts devices (e.g. JET, the Joint European News from the from gauge theory, the field theory Torus, at Culham). An understanding of Isaac Newton Institute used to describe the interactions of fun­ these magneto-fluid dynamic processes The Isaac Newton Institute came into damental particles. The program will is thus of central importance if energy existence on November 2, 1990 when encourage further progress by bring­ from fusion (rather than fission) is ever Michael Atiyah took office as director. ing together mathematicians and physi­ to become a reality. Organized by U. The Scientific Steering Committee for cists working in interrelated areas such Frisch (Nice), H. K. Moffatt (Cam­ the Institute, which consists of leading as statistical physics, string theory, bridge), A.M. Soward (Newcastle). mathematical scientists from universi­ topology, and geometry. Organized by A brief description of the Institute ties all over the United Kingdom and E. Corrigan (Durham), M. B. Green appears in Notices, September 1990, from overseas, have received twenty­ (QMW, London), W. B. R. Lickorish page 882. For further information, con­ three proposals for scientific programs (Cambridge). tact: P. V. Landshoff, DAMTP, Uni­ at the Institute. Two have been cho­ Dynamo theory. This program will versity of Cambridge, Silver Street, sen as the Institute's first programs and be concerned with the fundamental Cambridge, England CB3 9EW; tele­ they will run simultaneously in 1992 problem of the origin of magnetic phone 0223-337880; electronic mail from July until December. They are fields in cosmic bodies, particularly [email protected]. described below. stars and planets. Electromagnetic in­ Low-dimensional topology and quan­ duction in a conducting fluid in motion Biodegradable Bags tum field theory. This program will fo­ can give rise to spontaneous growth of for Notices cus on the spectacular developments magnetic field, a phenomenon whose Readers will be pleased to learn that that have occured in recent years as basic character is now well understood. the Society has recently switched to a result of the increasingly fruitful in­ A self-consistent theory incorporating biodegradable plastic bags for mailing teractions between areas of theoretical the relevant fluid dynamics and ther- Notices.

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118 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Funding Information for the Mathematical Sciences

Research Careers plexity of the proposed project. Grants lowing two categories: 1) atmospheric for Minority Scholars will normally be awarded for up to five sciences (including climate dynamics The National Science Foundation spon­ years. and atmospheric chemistry), earth sci­ sors a program entitled Research Ca­ For more information, contact: Roo­ ences, geography and regional science, reers for Minority Scholars (RCMS) sevelt Johnson, RCMS Program Di­ oceanography; and 2) statistics, proba­ designed to assist in the implementa­ rector, Room 1225, National Science bility, computational mathematics, ap­ tion of research and academic enrich­ Foundation, 1800 G Street, NW, Wash­ plied mathematics. ment programs for minority students ington, DC 20550; telephone 202-357- Before sending a formal proposal, (defined to be Blacks, American Indi­ 5054. investigators are urged to send letters ans, Hispanics, Alaskan Natives, and of interest or to contact an appropriate Native Pacific Islanders). Opportunities for Joint program director at the NSF. Letters The RCMS program is directed at Research in Geosciences, should be brief (no longer than three minority graduate and undergraduate Geography, and Mathematics pages), but should provide a basis for students in all areas of mathemat­ The National Science Foundation feedback on the development of a full ics, science, and engineering. Projects (NSF) wishes to stimulate development proposal. should emphasize factors that will con­ of new collaborative, cross-disciplinary Awards are expected to be for tribute to entry and retention of mi­ research programs involving quanti­ twenty-four months at a total level norities, such as: early research expe­ tative modeling in the geosciences. of $50,000 to $100,000 and are to be rience with dedicated mentors and role Projects are expected to include cross­ non-renewable. (Subsequent collabora­ models; academic enrichment, men­ disciplinary training or enhancement tive research proposals will be handled taring, and counseling; partnerships for faculty participants. through regular joint award mecha­ among institutions; and greater inter­ The Division of Mathematical action among parents, educators, scien­ nisms.) Cost-sharing may be appropri­ Sciences (DMS) believes that the ate where faculty training or enhance­ tists, engineers, and school counselors. government-wide focus on Global Among the activities supported by ment is involved. Several awards are Change provides unique opportunities expected for fiscal year 1991, with ad­ RCMS are: programs for entering fresh­ for cooperation between the mathemati­ ditional awards in fiscal year 1992. men; participation in special seminars, cal sciences and geosciences. Effective colloquia, and individualized skill de­ cooperation calls for innnovative ap­ Researchers in the mathematical velopment sessions; conference partici­ proaches to collaborative research and sciences should contact DMS staff in pation; regular interaction with faculty intensive cross-disciplinary training so the relevant program areas for more and other talented students; and per­ that investigators can speak a com­ information; a list of DMS program sonal and career counseling and men­ mon language as they address in-depth officers and their telephone numbers taring. In addition to the other coordi­ problems involving more than one dis­ may be found in Notices, September nated activities, student research expe­ cipline. 1990, page 883. The mailing address riences are to be provided for all partic­ The research will be conducted is Division of Mathematical Sciences, ipating students. The proposed duration by teams of faculty in two or more Room 339, National Science Founda­ for which support is requested should of the target disciplines, including at tion, 1800 G Street, NW, Washington, be consistent with the nature and com- least one area from each of the fol- DC 20550.

FEBRUARY 1991, VOLUME 38, NUMBER 2 119 For Your Information

Oklahoma Conference Provides and work together well as a team. "You don't have to have Model for Mathematics Renewal connections like these for such a conference to work," he says. The chancellor agreed to host the conference and sent The following article describes an activity that grew out of the letters of invitation to the presidents, chief academic officers, update of the David Report, "Renewing U.S. Mathematics: A Plan for the 1990s." In order to disseminate information about and mathematical sciences department heads of the twenty­ these kinds of exemplary activities, the editors of Notices will seven state-supported higher education institutions. All of consider publishing descriptions of other successful programs. the state's independent colleges and universities were also The descriptions may be sent to: Managing Editor, Notices, invited. The group of department chairs did the bulk of the American Mathematical Society, P.O. Box 6248, Providence, work organizing the conference. Bernard L. Madison of the Rl 02940. University of Arkansas, the main force behind "A Challenge of Numbers," and Kenneth M. Hoffman, executive director Oklahoma mathematicians have taken an unusual tack for of the Mathematical Sciences Education Board (MSEB) of focusing state-wide attention on the task of renewing the the National Research Council, also agreed to speak at mathematics profession and teaching in the state. Building the conference. In addition to individual presentations, the on the recommendations in the report "Renewing U.S. speakers held a panel discussion on specific actions for Mathematics: A Plan for the 1990s" and the picture of the Oklahoma to take in renewing the mathematical sciences in mathematical sciences painted in "A Challenge of Numbers" the state. (both published by the National Research Council in 1990), The conference, called "Renewing Oklahoma Mathemat­ this group took a top-down approach to marshalling support ics: A State Responds to the National Challenge," was held for change. The story of how this activity was organized December 10, 1990. Each state-supported higher education may help mathematicians in other states to launch similar institution was asked to send three representatives, and about initiatives. eighty people attended. After what Magid describes as "very The idea for the conference surfaced during an informal supportive" introductory remarks by the chancellor, Jaco de­ meeting last May of a group of mathematical sciences livered the keynote address, speaking on some of the strong department chairs from a variety of Oklahoma higher forces for change now at work in the mathematical sciences education institutions. The group came up with the idea community. McDonald discussed federal funding in the for the conference as a way for mathematical sciences mathematical sciences, and Madison spoke on demographic departments to come into direct contact with higher education and workforce issues confronting the mathematical sciences. administration at the state level. Gaining the support of the The panel discussion followed Hoffman's presentation on state's higher education chancellor seemed crucial, so the the massive challenges presented by mathematical sciences group wrote to the chancellor and asked for sponsorship and education reform. support for the conference. Shortly after the conference, Magid met with the chan­ Before writing to the chancellor, the group lined up as cellor to discuss followup actions. The first is to issue a speakers two mathematicians prominent in national policy report on the conference to all participants. Second, there circles who had ties to Oklahoma: Bernard R. McDonald, will be a survey of departmental missions, instructional deputy director of the Mathematical Sciences Division of activities, and staffs, to provide a "snapshot" of what the the National Science Foundation, and William H. Jaco, state's departments are currently doing. Finally, efforts will executive director of the AMS. Andy Magid, chair of the be made to develop a state-wide, systemic approach to iden­ department of mathematics at the University of Oklahoma tify ways in which Oklahoma can revitalize its mathematical and one of the main conference organizers, points out that sciences enterprise and enhance the performance of students although Oklahoma is fortunate to have such connections, and educators alike. To support the latter, work is under the main consideration is that the speakers be well-informed way on an MSEB-sponsored state coalition for mathematics,

120 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------······························-··············For Your Information

CAMEO (Coaltion for the Advancement of Mathematical "Everyone came away from this conference feeling really Education in Oklahoma). good," Magid notes. "The mathematicians felt they were Magid points to the "top-down" approach of the confer­ being listened to. And the presenters felt they weren't just ence as a way to highlight issues facing the mathematical preaching to the choir, but were reaching people who could sciences. "Rather than having departments approaching their really effect change." Magid believes that other states could administrations from below and describing the needs of hold similar conferences as a way to bring attention to the mathematics, we thought it might be better to get the upper issues of renewing the profession discussed in the update of administration in direct contact with the national experts on the David Report. "This kind of conference is a good way to the challenges facing mathematics," he explains. Magid feels bring attention to these issues," he remarks. Magid says he that the sJpport of the chancellor was crucial in helping to would be happy to help others organize similar conferences. gain state-wide attention for the conference and to insure that He can be reached at: Department of Mathematics, 601 Elm, it received serious attention from university administrators. PHSC 423, University of Oklahoma, Norman, OK 73019. "When the chief fiscal officer for higher education in the Allyn Jackson state says that mathematics is a priority, people listen." Staff Writer

PROCEEDINGS OF THE hand is still discernible in them. In addition to the historical and research oriented articles, the book contains other material that provides some colorful background on Gibbs and his world. Focusing on Gibbs and the teaching of science, the final article is a commentary, embellished GIBBS with personal reminiscences, on what to do and what to avoid in S Y MP 0 S I U M the education of prospective scientists. In the appendix, the editors have included a transcription of the Yale Physical Club (which YALE UNIVERSITY, MAY 15-17,1989 continues to this day as the Physics Club) for the meeting following D. G. Caldi and G. D. Mostow, Editors the death of Gibbs in 1903. The minutes provide a flavor of the esteem in which Gibbs was held by his colleagues and a vivid This volume, a joint publication with the American Insti­ glimpse of the Yale Physics Department at the time. The appendix tute of Physics, contains the proceedings of a symposium held May also has a section presenting a number of examples of various 15-17, 1989, at Yale University. The symposium was organized Gibbsian surfaces generated by computer graphics, for the graphi­ to honor the memory of Josiah Willard Gibbs, one of the giants of cal presentation of Gibbs's concepts dates back to Gibbs himself. theoretical physics, on the 150th anniversary of his birth. The Readers will appreciate the variety in this well-rounded range of the topics covered in the symposium reflects the extraor­ volume, and it would make an excellent addition to any library. It dinary versatility of Gibbs's ideas. Despite their widely separated is a fitting tribute to Josiah Williard Gibbs, a towering figure in expertises, the symposium speakers made an effort to present their American science and mathematics. lectures in a way that would be understandable to all the partici­ pants. The result was a genuine exchange of ideas across 1980 Mathematics Subject Classification: 01A55, 11D09, 11E45. disciplines that is captured in this volume. 11F66, 11F67,11F70, 11G05. 11G40, 11R39, 22E50, 22E55. Three of the articles in the book provide perspectives on 60G15, 76N15, 80-02, 80-03 {01A55), 80A10, 80A50, 82A15. 82A25, 82A30, 82A97, 86A15, 90-02, 90-03 {01A99) Gibbs, the man, and on the place his work occupies in the history ISBN 0-8218-0157-0 {hardcover), September 1990 of science. There are also contributions from leading scientists who Individual member $41, List price $65. assess the state of the art in those areas of physics and mathematics Institutional member $52 in which Gibbs worked, primarily those having to do with statistical To order, please specify GIBBS/NA mechanics and thermodynamics. To underscore the great generality of Gibbs's methods and the broad applicability his work, contribu­ All prices subject to change. Free shipment by surface; for air delivery, tions were also solicited from distinguished investigators in a please add $6.50 per title. Prepayment required. Order from number of different fields, such as geophysics, number theory, American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS {321- general relativity, and economics. Some of these fields are far 4267) in the continental U.S. and Canada to charge with VISA or removed from those to which Gibbs contributed directly, but Gibbs's MasterCard.

FEBRUARY 1991, VOLUME 38, NUMBER 2 121 1991 AMS Elections Nominations by Petition

-······-·····----·--····------·-·--·---···-·-········-·······-····-··-·· ········------·---··-----·-----·------·------·------···--- Vice-President or Member-at-Large The new members will be elected in a preferential ballot. The Pres­ One position of vice-president and member of the Council ex officio ident will name at least six candidates for these three places, among for a term of two years is to be filled in the election of 1991. The whom may be candidates nominated by petition in the manner de­ Council intends to nominate at least two candidates, among whom scribed in the rules and procedures. may be candidates nominated by petition as described in the rules and The candidate's assent and petitions bearing at least 100 valid sig­ procedures. natures are required for a name to be placed on the ballot. In addition, Five positions of member-at-large of the Council for a term of three several other rules and operational considerations, described below; years are to be filled in the same election. The Council intends to nomi­ should be followed. nate at least ten candidates, among whom may be candidates nominated by petition in the manner described in the rules and procedures. Petitions are presented to the Council, which, according to Section Rules and Procedures 2 of Article VII of the bylaws, makes the nominations. The Council Use separate copies of the form for each candidate for vice-president, of 23 January 1979 stated the intent of the Council of nominating all member-at-large, or member of the Nominating and Editorial Boards persons on whose behalf there were valid petitions. Committees. 1. To be considered, petitions must be addressed to Robert M. Prior to presentation to the Council, petitions in support of a can­ Fossum, Secretary, P. 0. Box 6248, Providence, Rhode Island 02940, didate for the position of vice-president or of member-at-large of the and must arrive by 28 February 1991. Council must have at least 50 valid signatures and must conform to 2. The name of the candidate must be given as it appears in the several rules and operational considerations, which are described be­ Combined Membership List. If the name does not appear in the list, as low. in the case of a new member or by error, it must be as it appears in the mailing lists, for example on the mailing label of the Notices. If the name does not identify the candidate uniquely, append the member code, which may be obtained from the candidate's mailing label or the Providence office. Editorial Boards Committee 3. The petition for a single candidate may consist of several sheets Two places on the Editorial Boards Committee will be filled by elec­ each bearing the statement of the petition, including the name of the tion. There will be four continuing members of the Editorial Boards position, and signatures. The name of the candidate must be exactly the Committee. same on all sheets. The new members will be elected in a preferential ballot. The Pres­ 4. On the next page is a sample form for petitions. Copies may be ident will name at least four candidates for these two places, among obtained from the Secretary; however, petitioners may make and use whom may be candidates nominated by petition in the manner de­ photocopies or reasonable facsimiles. 5. A signature is valid when it is clearly that of the member whose scribed in the rules and procedures. name and address is given in the left-hand column. The candidate's assent and petitions bearing at least 100 valid sig­ 6. The signature may be in the style chosen by the signer. However, natures are required for a name to be placed on the ballot. In addition, the printed name and address will be checked against the Combined several other rules and operational considerations, described below, Membership List and the mailing lists. No attempt will be made to match should be followed. variants of names with the form of name in the CML. A name neither in the CML nor on the mailing lists is not that of a member. (Example: The name Robert M. Fossum is that of a member. The name R. Fossum appears not to be.) 7. When a petition meeting these various requirements appears, the Nominating Committee Secretary will ask the candidate whether he is willing to have his name on Three places on the Nominating Committee will be filled by election. the ballot. Petitioners can facilitate the procedure by accompanying the There will be six continuing members of the Nominating Committee. petitions with a signed statement from the candidate giving his consent.

122 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... _...... -...... ------·············-···-·------········-····-················-·······--··············-·······-··········-···-·-····--·····-----·················-···-·--···

NOMINATION PETfi10N FOR 1991 ELECTION

The undersigned members of the American Mathematical Society propose the name of

as a candidate for the position of (check one): D Vice-President D Member-at-Large of the Council D Member of the Nominating Committee D Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 January, 1992.

Name and Address (printed or typed)

Signature

Signature

Signature

Signature

Signature

Signature

FEBRUARY 1991, VOLUME 38, NUMBER 2 123 South Bend, Indiana Indiana University at South Bend March 15-16

Second Announcement

------··-···-····------·-···------· ------The eight-hundred-and-sixty-fourth meeting of the American Noncommutative ring the01y, Gail R. Letzter, Peter Mathematical Society will be held at Indiana University at Malcolmson, and Frank Okoh, Wayne State University. South Bend, South Bend, Indiana on Friday, March 15, and Hilbert spaces of analytic function, John E. McCarthy, Saturday, March 16, 1991. All special sessions will be held Indiana University at Bloomington. in Northside Hall and all invited addresses will be in Room Probability and prediction the01y, Mohsen Pourahmadi, 113 of Northside Hall. Northern Illinois University. Abstracts for consideration for these sessions should have been submitted by the December deadline. Invited Addresses 13, 1990 This deadline was previously published in the Calendar of By invitation of the Central Section Program Committee, AMS Meetings and Conferences and in the Invited Speakers there will be four invited one-hour addresses. The speakers, and Special Sessions section of Notices. their affiliations, and the titles of their talks are: Leonid G. Makar-Limanov, Wayne State University, Contributed Papers Infinite-dimensional skew fields. There will also be sessions for contributed ten-minute Donald G. Saari, Northwestern University, Dynamics papers. Abstracts for consideration of these sessions should and symmetry: Explanations of paradoxes from statistics, have been submitted by the January 3, 1991 deadline voting, and economics. previously published in the Calendar of AMS Meetings and Stephen D. Smith, University of Illinois at Chicago Conferences. Late papers will not be accommodated. and California Institute of Technology, Simplicial complexes associated to finite groups and their representations. Deane Yang, Columbia University, Questions relating Registration Riemannian geomet1:v and the topology of3 -manifolds. The meeting registration desk will be located in the south wing (main entrance) of Northside Hall and will be open Special Sessions from 8:00a.m. to 5:00p.m. on Friday, March 15, and from 8:00a.m. to noon on·saturday, March 16. The registration By invitation of the same committee, there will be eight fees are $30 for members of the AMS, $45 for nonmembers, special sessions of selected twenty-minute papers. The and $10 for students or unemployed mathematicians. topics of these sessions, and the names and affiliations of the organizers, are as follows: Petition Table Mathematical economics and dynamical systems, C. D. Aliprantis, Indiana University and Purdue University, and A petltwn table will be set up in the registration area. Carl P. Simon, University of Michigan, Ann Arbor. Additional information about petition tables can be found in Simplicial complexes associated to finite groups and a box in the San Francisco meeting announcement in the their representations, Jonathan L. Alperin, University of October 1990 issue of Notices. Chicago, and Stephen D. Smith. Model theory, Steven A. Buechler, University of Notre Accommodations Dame. Rooms have been blocked for participants at The Works Geometric topology, Frank X. Connolly, University of Hotel, the Holiday Inn - Downtown, and the Ramada Inn. Notre Dame. Participants should make their own reservations and directly Algebraic topology, William G. Dwyer, University of mention the AMS meeting to obtain the rates listed below. Notre Dame, and Anthony D. Elmendorf, Indiana Univer­ All rates are subject to a ten percent tax. The AMS is sity at South Bend. not responsible for rate changes or the accommodations

124 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY --···-···············-·········-·-·········-·············-·-·········--···············-·--····-·······························- ._ ,_, ,,_, ,_, ,_,,_,_,,_ ...... ______...... __ .. ______...... -...... --.... -...... _,_, __ ,,...... Meetings offered by these hotels/motels. Parking Other motels located on U.S. Route 31/33 North near the Free parking will be available in the student lot Ramada Inn are: Budgeteer Motor Inn (219-272-9000); Best (P1) located north of Northside Hall. Inns of America (219-277-7000); Days Inn (219-277-0510); Knights Inn (219-277-2960); and Motel 6 (219-277-2960). Holiday Inn - Downtown (2.8 miles from campus) Travel and Local Information 213 W. Washington Street, South Bend, IN 46601 Michiana Regional Airport is served by several major Telephone: 219-232-3941 airlines. Free shuttle service is available to the Holiday The deadline for reservations is February 27. Inn - Downtown and the Works Hotel. Transportation to Flat rate $55 Single, Double, Triple the Ramada Inn or other accommodations can be arranged Restaurant/lounge, indoor pool, and free parking. For through United Limo or cab service at the airport. free van transportation from airport, dial 6 from courtesy TRANSPO buses serve the IUSB campus from the phone located at baggage pick-up. downtown area of South Bend. Bus #9 leaves the downtown transfer center at approximately ten minutes before the hour The Works Hotel (2.5 miles from campus) (Monday-Friday), and every half-hour (Monday-Saturday) 475 N. Niles Avenue, South Bend, IN 46617 beginning at 5:00 a.m. The bus ride from downtown to Telephone: 219-234-1954 the IUSB bus stop at Mishawaka Avenue and Greenlawn Deadline for reservations is March 1. Avenue takes about ten minutes. Bus #10 for the return trip Single $48 Each additional adult $7 leaves the comer of Mishawaka and Greenlawn Avenues Free continental breakfast, restaurant adjacent, and free at approximately five minutes before the hour (Monday­ parking. For free van transportation from airport, call motel. Saturday). TRANSPO bus service back to the downtown area ends at 9:33 p.m. on Friday and 6:26 p.m. on Saturday. The Ramada Inn (6.3 miles from campus) TRANSPO service is not available to or from the Ramada 52890 U.S. Route 33 North, South Bend, IN 46637 Inn area. Telephone: 219-272-5220 The deadline for reservations is February 22. Single $51 Double $59 Weather Restaurant/lounge, indoor pools, sauna, jacuzzi. A wide range of weather is possible in the Michiana area in March. Participants are advised to note regional forecasts Food Service near the time of the meeting. The IUSB Cafeteria (UC2) will be serving breakfast and lunch on Friday, March 15. Other restaurants are located Andy Roy Magid within 1.5 miles of the campus. Complete listings will be Associate Secretary available at the meeting registration desk. Norman, Oklahoma

Positive Definite Unimodular Lattices with Etsuko Bannai Trivial Automorphism Groups ----·------(Memoirs of the AMS, Number 429) In this book, the author proves that there exists a lattice with trivial automorphism group in every genus of positive definite unimodular Z-lattices of rank m (with m;;::: 43 for the odd unimodular case and m;;::: 144 for the even unimodular case). Siegel's mass formulas for lattices (for both orthogonal and hermitian cases) are used in the proof. In addition, the author shows that, for those positive definite unimodular Z-lattices in the given genus and of rank m, the ratio of the mass of classes with nontrivial automorphisms to the mass of all classes approaches 0 very rapidly as m increases. The book is intended for researchers and advanced graduate students in the areas of number theory and quadratic forms.

1980 Mathematics Subject Classification: 10 All prices subject to change. Free shipment by surface; for air ISBN 0-8218-2491-0, LC 90-31824. ISSN 0065-9266 delivery, please add $6.50 per title. Prepayment required. 70 pages (softcover). May 1990 Order from American Mathematical Society, P.O. Box 1571, Individual member $10. List price $16. Annex Station, Providence. RI 02901-1571, or call toll free Institutional member $13 800-321-4AMS (321-4267) in the continental U.S. and Canada To order. plea~e specify MEM0/429NA to charge with VISA or MasterCard.

FEBRUARY 1991, VOLUME 38, NUMBER 2 125 Tampa, Florida University of South Florida, Tampa March 22-23

Second Announcement

··-·-·---·····-··-·-··-·············-·····--········-··-········----·------·-·------·---.. --.. -·-·-·------··--·.. -.. ------.. ------The eight-hundred-and-sixty-fifth meeting of the American Graves, and L. Senechal, Institute for Academic Com­ Mathematical Society will be held at the University of South puting, University of North Carolina, Chapel Hill. Florida (USF), Tampa, Florida, on Friday, March 22, and Probability on algebraic and topological structures, Saturday, March 23, 1991. All scientific sessions will be held Joseph Glover and Arunava Mukherjea, University of in the Chemistry, Engineering and Math/Physics buildings. South Florida, Tampa. Fractal and spectral geometry, Michel J. Lapidus; and Invited Addresses Robert S. Strichartz, Cornell University. By invitation of the Southeastern Section Program Com­ Operator methods for control problems, Sung J. Lee and mittee, there will be four invited one-hour addresses. The Y. C. You, University of South Florida, Tampa. speakers, their affiliations, and the titles of their talks are: Nonlinear boundary value problems, R. Kent Nagle and Josefina Alvarez, New Mexico State University, The Mary E. Parrott, University of South Florida, Tampa. Weyl functional calculus. Ronald A. DeVore, University of South Carolina, Hypergeometric functions on domains of positivity, Jack, Columbia, Wavelet compression. polynomials, and applications, Donald St. P. Richards. Michel L. Lapidus, University of California, Riverside Abstracts for consideration for these sessions should and Yale University, Can one hear the shape of a fractal have been submitted by the December 13, 1990 deadline. drum? From the Weyl-Beny conjecture to the Riemann This deadline was previously published in the Calendar of hypothesis. AMS Meetings and Conferences and in the Invited Speakers Donald St. P. Richards, University of Virginia, Hyper­ and Special Sessions section of the Notices. geometric functions on domains ofpositivity and applications. Contributed Papers Special Sessions There will also be sessions for contributed ten-minute By invitation of the same committee, there will be twelve papers. Abstracts for consideration for these sessions should special sessions of selected twenty-minute papers. The have been submitted by the January 3, 1991 deadline topics of these sessions, and the names and affiliations of previously published in the Calendar of AMS Meetings and the organizers, are as follows: Harmonic analysis and applications, Josefina Alvarez. Conferences. Late papers will not be accommodated. Mathematical issues in biologically motivated computing, W. Edwin Clark, Joseph L. Liang, Gregory L. McColm, Council John F. Pedersen, and W. Richard Stark, University of The Council of the Society will meet at 7:00 p.m. on South Florida, Tampa. Approximation the01y, Ronald A. Devore; Edward B. Thursday, March 21, 1991, at the Holiday Inn - Busch Saff and B. Shekhtman, University of South Florida, Tampa. Gardens, 2701 E. Fowler Avenue, Tampa, FL 33612. Finite groups and related topics, David A. Drake, Chat Yin Ho, and Geoffrey R. Robinson, University of South Registration Florida, Tampa. The registration desk will be located in the lobby of the Differential geometry and mathematical physics, Paul E. Ehrlich and Stephen J. Summers, University of Florida. Math/Physics building and will be open from 8:00 a.m. to Several complex variables, Paul M. Gauthier, University 5:00p.m. on Friday, March 22, and from 8:00a.m. to noon of Montreal. on Saturday, March 23. The registration fees are $30 for Microcomputers and workstations in mathematics: Teach­ members of the AMS, $45 for nonmembers, and $10 for ing and research, Ladnor D. Geissinger, William H. students or unemployed mathematicians.

126 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -··--··-·------·--··-··--·······---····-·············-··············---·········-········-····-··-···.. ················-········-·········------·········-·········--····-··-······-·-··-····· ··············--·········---··-·--···-·-·--·-·-·-·-···-·-···----···-·-····-···-······ Meetings

Petition Table of the meeting rooms. The Empty Keg offers a soup and salad bar, pizza, and various sandwich platters. Also open A petition table will be set up in the registration area. in the University Center from 7:30a.m until 3:00p.m. will Additional information about petition tables can be found in be Sweet Sensations, a pastry and coffee shop. Complete a box in the San Francisco meeting announcement in the listings of other restaurants will be available at the meeting October 1990 issue of Notices. registration desk.

Accommodations Parking Rooms have been blocked for participants at the following Free parking will be available to conference participants in hotels or motels in the area. Because of the large number lots 8A and 8B on the campus of USF. These lots are in of tourists during the winter month, hotel/motel reservations close proximity to the conference site. should be made as soon as possible. Participants should make their own reservations directly and mention the AMS meeting. The AMS is not responsible for rate changes or Travel and Local Information the accommodations offered by these hotels. All rates are Tampa International Airport (TIA) is served by all major subject to a ten percent sales tax. airlines and located 15 miles from the USF campus. Travel Embassy Suites Hotel (.5 miles from campus) to the campus can be secured by calling Tampa Tours 11310 North 30th Street, Tampa, FL 33612 (telephone 813-621-6667) prior to arrival and giving the Telephone: 1-800-EMBASSY date, airline, flight number, and estimated time of arrival. Deadline for reservations is March 7. The cost is $9 for one person one-way, $7 each for two to four persons one-way, and $30 for five to ten people Single $79 Double $89 one-way. Other transportation from TIA to USF can be Complimentary full breakfast and cocktail reception, obtained through limousine service (Mannone's Limousine pool and jacuzzi, free shuttle service up to a three mile Service@ 813-932-1797 or Limo Inc.@ 1-800-282-6817) radius, and free parking. or taxi. The cost of a taxi is approximately $24. Most major car rental companies have agencies at Tampa International Holiday Inn • Busch Gardens (1/4 mile from campus) Airport. Directions for participants driving to the meeting 2701 E. Fowler Avenue, Tampa, FL 33612 are as follow: Telephone: 1-800-99-BUSCH If traveling by automobile, participants should take I-75 Deadline for reservations is March 1. around Tampa and exit west at either the Fletcher Avenue Single $65 Double $65 or the Fowler Avenue exit. The university is approximately three miles west. The campus can also be reached by taking Shoney's Inn - Tampa (2.5 miles from campus) I-275 through Tampa and exit east on either Fletcher Avenue 8602 Morris Bridge Road, Tampa, FL 33617 or Fowler Avenue. The university is approximately one-and­ Telephone: 1-800-222-2222 one-half miles to the east. Bus service is available around Deadline for reservations is March 5. the university by Hartline and bus schedules will be made One-Four People $43-$45 available at the meeting registration desk. Complimentary coffee and cocktail reception, pool, and FROM THE AIRPORT: Participants should take Memo­ free parking. rial Highway south to Interstate 275 and exit north to Fowler Avenue directly to USF. Quality Suites Busch Gardens (1/2 mile from campus) 3001 University Center Drive, Tampa, FL 33612 Weather and Local Attractions Telephone: 1-800-228-5151 Deadline date for reservations is March 1. The weather in Tampa in March is usually mild. The average maximum temperature is 76.1°F and the average minimum Suites (One-Four persons) $69 temperature is 57.2°F. The average rainfall for March is Complimentary buffet breakfast and cocktail reception, three inches. pool, and free parking. Beaches, golf courses, Busch Gardens, Disney World, and many other attractions are located within an hour's drive Food Service of the Tampa area. The University Center Food Service will keep the Empty Keg open from 11 :00 a.m. to 2:00 p.m. for conference Joseph A. Cima participants. The Empty Keg is located in the basement of Associate Secretary the University Center which is within short walking distance Chapel Hill, North Carolina

FEBRUARY 1991, VOLUME 38, NUMBER 2 127 Invited Speakers and Special Sessions

Invited Speakers Invited addresses at Sectional Meetings are selected at AMS Meetings by the Section Program Committee, usually twelve to The individuals listed below have accepted invitations to eighteen months in advance of a meeting. Members wishing address the Society at the times and places indicated. For to nominate candidates for invited addresses should send some meetings, the list of speakers is incomplete. the relevant information to the Associate Secretary for the Section who will forward it to the Section Program Committee. South Bend, IN, March 1991 Leonid G. Makar-Limanov Stephen D. Smith Donald G. Saari Deane Yang Organizers and Topics of Special Sessions Tampa, FL, March 1991 The list below contains all the information about Special Josefina Alvarez Michel L. Lapidus Sessions at meetings of the Society available at the time Ronald A. De Yore Donald St. P. Richards this issue of Notices went to the printer. The section below entitled Information for Organizers describes the timetable for announcing the existence of Special Sessions. Portland, OR, June 1991 Dinakar Ramakrishnan V. S. Varadarajan March 1991 Meeting in South Bend, Indiana Gunther A. Uhlmann Central Section Associate Secretary: Andy R. Magid Deadline for organizers: Expired Orono, ME, August 1991 Deadline for consideration: Expired H. W. Lenstra Richard M. Schoen C. D. Aliprantis and Carl P. Simon, Mathematical economics (Progress in Mathematics (Progress in. Mathematics and dynamical systems Lecture) Lecture) Jonathan L. Alperin and Stephen D. Smith, Simplicial com- plexes associated to finite groups and their representations Steven A. Buechler, Model theory Philadelphia, PA, October 1991 Frank X. Connolly, Geometric topology Michael T. Anderson Majorie Senechal William G. Dwyer and Anthony D. Elmendorf, Algebraic Abbas Bahri Panagiotis E. Souganidis topology Gail R. Letzter, Peter Malcolmson and Frank Okoh, Non­ Fargo, ND, October 1991 commutative ring theory Ian D. Macdonald Henry C. Wente John E. McCarthy, Hilbert spaces of analytic functions Harald Upmeier Sylvia M. Wiegand Mohsen Pourahmadi, Probability and prediction theory

March 1991 Meeting in Tampa, Florida Baltimore, MD, January 1992 Southeastern Section Michael E. Fisher Associate Secretary: Joseph A. Cima (Gibbs Lecture) Deadline for organizers: Expired Deadline for consideration: Expired Josefina Alvarez, Harmonic analysis and applications Cambridge, England, June 1992 Ronald A. DeVore, Edward B. Saff and B. Shekhtman, (Joint meeting with the London Mathematical Society) Approximation the01y John M. Ball Benedict H. Gross David A. Drake, Chat Yin Ho and Geoffrey R. Robinson, Lawrence Craig Evans Nigel J. Hitchin Finite groups and related topics

128 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Speakers and Special Sessions

Paul E. Ehrlich and Stephen J. Summers, Differential geom­ Boris A. Datskovsky and Marvin I. Knopp, Modularforms, etry and mathematical physics arithmetic algebraic geomet1y Paul M. Gauthier, Several complex variables James F. Davis, Ronnie Lee and Julius L. Shaneson, Surgery Ladnor D. Geissinger, William H. Graves and L. Senechal, themy and singular spaces Microcomputers and workstations in mathematics: teach­ Leon Ehrenpreis and Eric L. Grinberg, Geometric analysis ing and research Janos Galambos, Extreme value themy Joseph Glover and Arunava Mukherjea, Probability on David R. Hill, Computational experiments for numerical algebraic and topological structures analysis instruction Michel L. Lapidus and Robert S. Strichartz, Fractal and Nicholas Ranges and A. Alexandrou Himonas, Applications spectral geometry of microlocal analysis to partial differential equations Sung J. Lee and Y. C. You, Operator methods for control Bruce A. Kleiner and Robert B. Kusner, Variational problems problems in low dimensional geometry R. Kent Nagle and Mary E. Parrott, Nonlinear boundmy Martin Lorenz and Shari A. Prevost, Rings and representa­ value problems tions John F. Pedersen, W. Edwin Clark, W. Richard Stark, Joseph Doris Schattschneider and Marjorie Senechal, Tilings J. Liang and Gregory L. McColm, Mathematical issues Halil Mete Soner and Panagiotis E. Souganidis, Phase in biologically motivated computing· transitions and/or front propagation Donald St. P. Richards, Hypergeometricftmctions on domains Daniel B. Szyld, Numerical linear algebra ofpositivity, Jack polynomials, and applications

June 1991 Meeting in Portland, Oregon October 1991 Meeting in Fargo, North Dakota Western Section Central Section Associate Secretary: Lance W. Small Associate Secretary: Andy R. Magid Deadline for organi:::ers: E.lpired Deadline for organizers: Expired Deadline for consideration: March 5. 1991 Deadline for consideration: July 11. 1991 Donald G. Babbitt, Meromorphic differential equations Joseph P. Brennan and Sylvia M. Wiegand, Commutative M. Paul Latiolais, Combinatorial group themy and low algebra dimensional topology Dogan Comez, Ergodic theory M. Sergei Prishepionok, Harmonic mappings and their David B. Jaffe, Algebraic geomet1y applications Satyanad Kichenassamy, Nonlinear wave equations Dinakar Ramakrishnan, Cycles and poles of£-functions Kendall E. Nygard, Operations research Kenneth A. Ross, Fourier analysis James H. Oisen and Mark Pavicic, Mathematical foundations John Sylvester and Gunther A. Uhlmann, Inverse problems of computer graphics and applications Justin R. Peters III and Warren R. Wogen, Nonselfadjoint operator algebras August 1991 Meeting in Orono, Maine Norberto Salinas and Harald Upmeier, Multidimensional Associate Secretary: Joseph A. Cima complex analysis and operator theory Deadline for organi:::ers: Expired Deadline for consideration: May 1. 1991 Warren E. Shreve, Graph themy (Please note that this deadline has changed) Vasant A. Ubhaya, Approximation theory Joseph Arkin, Number themy Abraham Ungar, Lorentz transformations and !>pacetime Edward Bierstone and Gerald W. Schwarz, Symmet1y and geomet1y differential analysis Frank Curtis and Andrew R. Kustin, Commutative Noethe- rian rings with applications in algebraic geomet1y November 1991 Meeting in Santa Barbara, California Western Section John C. Mayer, Continuum themy and dynamical systems Associate Secretary: Lance W. Small Ali E. Ozluk and William M. Snyder, Analytic number themy Deadline for organi:::ers: February 7, 1991 Stanley Rabinowtiz, Geometric inequalities for polytopes Deadline for consideration: July 11, 1991 Chuu-Lian Terng and Karen Uhlenbeck, Variational methods and symmetry Toma V. Tonev and Keith Yale, Function algebras and January 1992 Meeting in Baltimore, Maryland Associate Secretary: Lance W. Small function spaces Deadline for organi:::ers: April 8, 1991 Deadline for consideration: September li, 1991 October 1991 Meeting in Philadelphia, Pennsylvania Eastern Section Associate Secretary: W. Wistar Comfort March 1992 Meeting in Tuscaloosa, Alabama Deadline for organi:::ers: Expired Southeast Section Deadline for consideration: July 11, 1991 Associate Secretary: Joseph A. Cima Michael T. Anderson and Jeff Cheeger, Recent progress in Deadline for organi:::ers: June 13, 1991 Ricci curvature and related topics Deadline for consideration: To be announced

FEBRUARY 1991, VOLUME 38, NUMBER 2 129 Invited Speakers and Special Sessions

March 1992 Meeting in Springfield, Missouri are sent to the Providence office of the Society, to Notices, Central Section or directed to anyone other than the Associate Secretary will Associate Secretary: Andy R. Magid have to be forwarded and may not be received in time to be Deadline for organizers: June 26, 1991 Deadline for consideration: To be announced considered for acceptance. It should be noted that Special Sessions must be an­ June 1992 Meeting in Cambridge, England nounced in Notices in such a timely fashion that any member (Joint Meeting with the London Mathematical Society) of the Society who so wishes may submit an abstract for Associate Secretary: Robert M. Fossum consideration for presentation in the Special Session before Deadline for organi=ers: September 28, 1991 the deadline for such consideration. This deadline is usually Deadline for consideration: To be announced three weeks before the deadline for abstracts for the meeting January 1993 Meeting in San Antonio, Texas in question. Associate Secretary: W. Wistar Comfort Special Sessions are very effective at Sectional Meetings Deadline for organizers: April 13, 1992 and can usually be accommodated. The processing of Deadline for consideration: To be announced proposals for Special Sessions for Sectional Meetings is handled in essentially · the same manner as for Annual August 1993 Meeting in Vancouver, and Summer Meetings by the Section Program Committee. British Columbia, Canada Again, no Special Session at a Sectional Meeting may be Associate Secretary: Lance W. Small approved so late that its announcement appears past the Deadline for organi::ers: November 11, 1992 deadline after which members can no longer send abstracts Deadline for consideration: To be announced for consideration for presentation in that Special Session. January 1994 Meeting in Cincinnati, Ohio The Society reserves the right of first refusal for the Associate Secretary: Joseph A. Cima publication of proceedings of any Special Session. These Deadline for organi::ers: April 5, 1993 proceedings appear in the book series Contemporary Math­ Deadline for consideration: To be announced ematics. More precise details concerning proposals for and orga­ January 1996 Meeting in Orlando, Florida nizing of Special Sessions may be found in the "Rules for Associate Secretary: Lance W. Small Special Sessions" or may be obtained from any Associate Deadline for organizers: April 12, 1995 Deadline for consideration: To be announced Secretary. Information for Organizers Pr,oposals for Special Sessions to the Special Sessions at Annual and Summer Meetings are held Associate Secretaries under the supervision of the Program Committee for National The programs of Sectional Meetings are arranged by the Meetings (PCNM). They are administered by the Associate Associate Secretary for the section in question: Secretary in charge of that meeting with staff assistance Western Section from the Meetings and Editorial Departments in the Society Lance W. Small. Associate Secretary Department of Mathematics office in Providence. University of California, San Diego According to the "Rules for Special Sessions" of the La Jolla, CA 92093 Society, Special Sessions are selected by the PCNM from Electronic mail: [email protected] a list of proposed Special Sessions in essentially the same (Telephone 619-534-3590) manner as Invited Speakers are selected. The number Central Section of Special Sessions at a Summer or Annual Meeting Andy R. Magid, Associate Secretary Department of Mathematics is limited. The algorithm that determines the number of University of Oklahoma Special Sessions allowed at a given meeting, while simple, 601 Elm PHSC 423 is not repeated here, but can be found in "Rules for Special Norman, OK 73019 Electronic mail: [email protected] Sessions'' on page 614 in the April 1988 issue of Notices. (Telephone 405-325-6711) Each Invited Speaker is invited to generate a Special Eastern Section Session, either by personally organizing one or by having a W. Wistar Comfort, Associate Secretary Special Session organized by others. Proposals to organize a Department of Mathematics Special Session are sometimes requested either by the PCNM Wesleyan University Middletown, CT 06457 or by the Associate Secretary. Other proposals to organize a Electronic mail: [email protected] Special Session may be submitted to the Associate Secretary (Telephone 203-347-9411). in charge of that meeting (who is an ex-officio member of the Southeastern Section committee and whose address may be found below). These Joseph A. Cima, Associate Secretary proposals must be in the hands of the PCNM at least nine Department of Mathematics months prior to the meeting at which the Special Session is University of North Carolina, Chapel Hill Chapel Hill, NC 27599-3902 to be held in order that the committee may consider all the Electronic mail: [email protected] proposals for Special Sessions simultaneously. Proposals that (Telephone 919-962-1050)

130 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ______...... Invited Speakers and Special Sessions

As a general rule, members who anticipate organizing Special Sessions at convenient way, but users may also obtain the package AMS meetings are advised to seek approval at least nine months prior to the on IBM or Macintosh diskettes, available free of charge scheduled date of the meeting. No Special Sessions can be approved too late to provide adequate advance notice to members who wish to participate. by writing to: Electronic Abstracts, American Mathematical Proposals for Special Sessions at the June 29-July I, 1992, meeting in Society, Publications Division, P.O. Box 6248, Providence, Cambridge, England, only should be sent to Professor Fossum at the Department RI 02940, USA. When requesting the abstracts package, of Mathematics, University of Illinois. Urbana, IL 61801, Telephone: 217-244- users should be sure to specify whether they want the plain 1741. Electronic mail: [email protected] lFX, ~-lFX, or the rn}jX package.

Information for Speakers Number of Papers Presented A great many of the papers presented in Special Sessions at Joint Authorship meetings of the Society are invited papers, but any member Although an individual may present only one ten-minute of the Society who wishes to do so may submit an abstract contributed paper at a meeting, any combination of joint for consideration for presentation in a Special Session, authorship may be accepted, provided no individual speaks provided it is received in Providence prior to the special more than once. An author can speak by invitation in more early deadline announced above and in the announcements of than one Special Session at the same meeting. the meeting at which the Special Session has been scheduled. An individual may contribute only one abstract by title Contributors should know that there is a limitation in size in any one issue of Abstracts, but joint authors are treated of a single Special Session, so that it is sometimes true that as a separate category. Thus, in addition to abstracts from all places are filled by invitation. Papers not accepted for two individual authors, one joint abstract by them may also a Special Session are considered as ten-minute contributed be accepted for an issue. papers. Abstracts of papers submitted for consideration for pre­ sentation at a Special Session must be received b)( the Providence office (Editorial Department, American Mathe­ Site Selection for Sectional Meetings matical Society, P. 0. Box 6248, Providence, RI 02940) by Sectional Meeting sites are recommended by the Associate the special deadline for Special Sessions, which is usually Secretary for the Section and approved by the Committee of three weeks earlier than the deadline for contributed papers Associate Secretaries and Secretary. Recommendations are for the same meeting. The Council has decreed that no usually made eighteen to twenty-four months in advance. paper, whether invited or contributed, may be listed in the Host departments supply local information, ten to twelve program of a meeting of the Society unless an abstract of the rooms with overhead projectors for contributed paper ses­ paper has been received in Providence prior to the deadline. sions and special sessions, an auditorium with twin overhead Electronic submission of abstracts is available to those projectors for invited addresses, and registration clerks. The who use the 1FX typesetting system. Requests to obtain Society partially reimburses for the rental of facilities and the package of files may be sent electronically via the equipment, and for staffing the registration desk. Most host Internet to [email protected]. Requesting the departments volunteer; to do so, or for more information, files electronically will likely be the fastest and most contact the Associate Secretary for the Section.

Proba Theory, Function Theor Mechanics

Yu. V. Prokhorov, Editor (Proceedings of the Steklov Institute, Volume 182) This is a translation of the fifth and final volume in a special cycle of"Trudy of the Steklov Mathematical Institute ofthe Academy of Sciences," published in commemoration of the 50th anniversary of the Institute. The purpose of the special cycle of publications was to present surveys of work on certain important trends and problems pursued at the Institute. Because the choice of the form and character of the surveys was left up to the authors, the surveys do not necessarily form a comprehensive overview, but rather represent the authors' perspectives on the important developments.

The survey papers in this collection range over a variety of areas, including: probability theory and mathematical statistics, metric theory of functions, approximation of functions, descriptive set theory, spaces with an indefinite metric, group representations, mathematical problems of mechanics, and spaces of functions of several real variables and some of its applications.

/980 Mathematics Subject Classifications: 01, 04. 22, 34, All prices subject to change. Free shipment by surface; for air 41. 42, 46. 62, 73, 76. 93 and others delivery, please add $6.50 per title. Prepayment required. ISBN 0-8218-3132-1. ISSN 0081-5438 Order from American Mathematical Society. P.O. Box 1571, LC 90-513; 318 pages (hardcover), May 1990 Individual member $92, List Price $153. Annex Station, Providence, RI 02901-1571, or call toll free Institutional member $122 800-321-4AMS (321-4267) in the continental U.S. and Canada To order, please specify STEKL0/182NA to charge with VISA or MasterCard.

FEBRUARY 1991, VOLUME 38, NUMBER 2 131 Mathematics Sessions at the AAAS Annual Meeting Washington, DC, February 14-19, 1991

The annual meeting of the American Association for the Owens, David E. Rowe, and Sanford L. Segal), Monday, Advancement of Science (AAAS), February 14-19, 1991, in February 18, 8:30 a.m. Washington, DC, will feature many outstanding expository • Mathematics and mathematics education: Beyond reports, talks by prominent mathematicians. These talks include organized by Ronald G. Douglas, SUNY at Stony the following symposia (three-hour sessions) and invited Brook. (William Bowen, Ernest L. Boyer, Edward E. address cosponsored by Section A (Mathematics) of the David, Jr., Ralph E. Gomory, Mary Good, Philip A. AAAS and the Society. In addition, there will be special Griffiths, William E. Kirwan, II, Frank Press and Alvin events during the meeting to celebrate the 20th anniversary W. Trivelpiece), Friday, February 15, 8:30a.m. and 2:30 of the Association for Women in Mathematics, including the p.m. symposium, "Mathematics in the public policy arena" listed below. • Calculus reforms: Some examples, organized by Thomas The AMS helps to support mathematical activities at W. Thcker, Colgate University. (James Callahan, Edward the AAAS meetings by contributing to the sponsorship of D. Gaughan, Deborah Hughes Hallet, David A. Smith, speakers in mathematical symposia it cosponsors with the and J. Jerry Uhl, Jr.), Saturday, February 16, 8:30a.m. AAAS. In addition, the Society has a committee to act as • Frontiers of physical sciences: A mathematics lecture a liaison with AAAS. The AMS believes that strengthening by Neil J. A. Sloane, AT&T Bell Laboratories. Friday, its ties with AAAS helps to create new opportunities for February 15, 8:30 a.m. and 2:30 p.m. mathematicians to interact with scientists from all disciplines. The names and affiliations of the organizers follow ln addition, Section A of the AAAS will sponsor various (speakers' names are given in parentheses): symposia that will especially interest mathematicians and mathematics educators. These symposia include: • Robotics and mathematics, organized by Bhubaneswar Mishra, New York. (Jerrold E. Marsden, Bhubaneswar • Science and mathematics education in the United States: Mishra, and Jacob T. Schwartz), Tuesday, February 19, A report from the Longitudinal Study ofAmerican Youth 2:30p.m. • Structuring the college environment for success in team­ • The geometry and topology ofDNA, organized by DeWitt ing science and mathematics L. Sumners, Florida State University. (Nicholas R. • Urban initiatives in precollege science and mathematics: Cozzarelli, DeWitt L. Sumners, and James H. White), A model program Monday, February 18, 2:30 p.m. • Minority mathematics and science education: Successful • Mathematics in the public policy arena, organized by programs at community colleges Mary W. Gray, American University, Jill P. Mesirov, Thinking Machines Corporation, and Mary • Implications ofmathematics curriculum reform for science Beth Ruskai, University of Lowell. (Ingrid Daubechies, education Mary W. Gray, Barbara J. Grosz, Fern Y. Hunt, and • Sophisticated uses of single computers Mary Wheeler), Monday, February 18, 2:30p.m. • Global initiatives in high-peJformance computing and • Voting: Mathematical foundations and political realities, neflt>orking organized by Alan D. Taylor, Union College. (Steven J. Brams, Samuel Merrill III, and William Zwicker), The above symposia represent only a few of the ap­ Monday, February 18, 8:30 a.m. proximately 150 AAAS program offerings that will broaden the perspectives of students and professionals alike. Indeed, • Mathematics in the material sciences, organized by David AAAS annual meetings showcase American science and S. Kinderlehrer, Carnegie-Mellon University. (Morton deserve greater mathematical participation. The Section A Gurkin, Richard James, Robert V. Kohn, and Mitchell B. Committee seeks organizers and speakers who can present Luskin), Sunday, February 17, 2:30p.m. substantial new material in understandable ways. This task • Mathematics in times of social upheaval, organized by is not easy, but the outstanding success of the mathemat­ Sanford L. Segal, University of Rochester. (Charles ics symposia at last year's AAAS annual meeting in New Edwin Ford, Charles Gillespie, Aleskey Levin, Larry Orleans proved that effort and inspiration can accomplish

132 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AAAS Meeting wonders. That year's mathematics program demonstrated For details about the symposia, see the September 7, that first-rate mathematical researchers can also effectively 1990, issue of Science. Participants are invited to attend reach a broad and diverse scientific audience. the Section A Committee meeting, 6:00p.m. to 8:00 p.m., Section A of the AAAS knows that increasing the February 16, 1991, in the Presidential Room of the Shoreham representation and participation of mathematicians at AAAS Hotel. The committee meeting is open to all who wish to annual meetings offers an important means for deepening stimulate interest in activities of the mathematical sciences public awareness and appreciation of the manifold ways within the AAAS. Symposia proposals for future AAAS that mathematics contributes to science and society. The meetings should be sent to: Warren Page, Secretary of Secretary of Section A welcomes suggestions for symposia Section A, AAAS, Department of Mathematics, New York topics and individuals who might organize them. City Technical College of the City University of New York, 300 Jay Street, Brooklyn, NY 11201.

[][JJ A. J. Lohwater's [][] RUSSIAN-ENGLISH Dictionary of the Mathematical Sciences Second Edition Edited by Ralph P. Boas Revised and expanded with the assistance of Alana I. Thorpe This long-awaited update of the popular Lohwater dictionary is the most complete and up-to-date resource for reading and translating mathematical literature written in Russian. Hundreds of new words have been added, and existing entries have been amplified, corrected, and brought up-to-date to reflect current mathematical usage (though some obsolete terms were retained for users who need to consult older literature). The grammar section has been rewritten, and an appendix contains complete paradigms of a large number of selected words. In addition, at the request of many users of the dictionary, stress markings on Russian words have been added. Intended primarily for those whose first language is English, this dictionary will prove a useful tool for researchers, editors, and translators working with Russian mathematical literature.

1980 Mathematics Subject Classification: 00 All prices subject to change. Free shipment by surface; for ISBN 0-8218-0160-0 (hardcover), air delivery, please add $6.50 per title. Prepayment 0-8218-0133-3 (softcover), LC 90-290 required. Order from 343 pages, July 1990 American Mathematical Society P.O. Box 1571, Annex Station Price $50 (hardcover), Price $35 (softcover) Providence, RI 02901-1571 To order please specify REDH/NA (hardcover), or call toll free 800-321-4AMS (321-4267) in the continental REDS/NA (softcover) U.S. and Canada to charge with VISA or MasterCard.

FEBRUARY 1991, VOLUME 38, NUMBER 2 133 Joint Summer Research Conferences in the Mathematical Sciences University of Washington, Seattle, June 22 to August 2, 1991

The 1991 Joint Summer Research Conferences in the Math­ Please type or print the following: ematical Sciences will be held at the University of Wash­ 1. Title and dates of conference desired ington, Seattle, from June 22 to August 2. It is anticipated 2. Full name that the series of conferences will be supported by grants from the National Science Foundation and other agencies. 3. Mailing address 4. Telephone number and area code for office, home and There will be eight conferences in eight different areas electronic-mail address of mathematics. The topics and organizers for the confer­ ences were selected by the AMS, Institute of Mathematical 5. Member of AMS, IMS, or SIAM? If AMS, please give Statistics (IMS), and the Society for Industrial and Applied member code Mathematics (SIAM) Committee on Joint Summer Research 6. Your scientific background relevant to the topic of the Conferences in the Mathematical Sciences. The selections conference were based on suggestions made by the members of the 7. Financial assistance requested; please estimate cost of committee and individuals submitting proposals. The com­ travel mittee considered it important that the conferences represent 8. Indicate if support is not required and if interested in diverse areas of mathematical activity, with emphasis on attending even if support is not offered. areas currently especially active, and paid careful attention The deadline for receipt of applications is March to subjects in which there is important interdisciplinary 1, 1991. Requests to attend will be forwarded to the activity at present. Organizing Committee for each conference for consideration The conferences emulate the scientific structure of those after the deadline of March 1. All applicants will receive held throughout the year at Oberwolfach. These conferences a formal invitation and notification of financial assistance are intended to complement the Society's program of annual from the AMS. Requests received past the deadline will be Summer Institutes and Summer Seminars, which have a returned. Funds available for these conferences are limited larger attendance and are substantially broader in scope. The and individuals who can obtain support from other sources conferences are research conferences and are not intended should do so. Women and members of minority groups are to provide an entree to a field in which a participant has not encouraged to apply and participate in these conferences. already worked. Any questions concerning the scientific portion of the It is expected that funding will be available for a limited conference should be directed to the chair or any member number of participants in each conference. Others, in addition to those funded, will be welcome, within the limitations of of the Organizing Committee. the facilities of the campus. In the spring a brochure of The Joint Summer Research Conferences in the Mathe­ information will be mailed to all who are requesting to attend matical Sciences are under the direction of the AMS-IMS­ the conferences. The brochure will include information on SIAM Committee on Joint Summer Research Conferences room and board rates, the residence and dining hall facilities, in the Mathematical Sciences. The following committee travel, local information, and a Residence Housing Form to members chose the topics for the 1991 conferences: John A. use to request on-campus accommodations. Information on Bums, Fan R. K. Chung, Leonard Evens, Martin Golubitsky, off-campus housing will also be included in the brochure. Anthony W. Knapp, Ingram Olkin, Emanuel Parzen, Stewart Participants will be responsible for making their own housing B. Priddy, Stephen Simpson and Gregg J. Zuckerman. and travel arrangements. Each participant will be required Descriptions of the subject matter of each of the 1991 to pay nominal registration and social fees. conferences appeared in the November issue of Notices, Those interested in attending one of the conferences pages 1278 -1279; they were accompanied by lists of should send the following information to the Summer members of the respective Organizing Committees. Research Conference Coordinator, Meetings Department, American Mathematical Society, Post Office Box 6887, Prov­ N.B. Lectures begin on Sunday morning and run idence, RI 02940 or by E-Mail: [email protected] through Thursday. on the Internet.

134 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------··-···········-···········--··-··-·····-···-·-··-··-Joint Summer Research Conferences

Saturday, June 22 to Friday, June 28 Saturday, July 6 to Friday, July 12 Biojluiddynamics Stochastic modeling and statistical inference for selected problems in biology A.Y. Cheer (University of California, Davis), Chair Charles Smith (North Carolina State University), C.P. van Dam (University of California, Davis), Co-Chair Co-Chair, Grace L. Yang (University of Maryland, College Park), Saturday, July 13 to Friday, July 19 Co-Chair No conference scheduled

Saturday, June 22 to Friday, July 5 Saturday, July 20 to Friday, August 2 Graph minors Motives Neil Robertson (Ohio State University), Co-Chair Steven Kleiman (Massachusetts Institute of Technology), P.D. Seymour (Bell Communications Research), Co-Chair Co-Chair Kari Vilonen (Brandeis University), Co-Chair Saturday, June 29 to Friday, July 5 Saturday, July 20 to Friday, July 26 Theory and applications of multivariate time series Mathematical aspects of classical field theory analysis Mark J. Gotay (United States Naval Academy), Co-Chair Robert H. Shumway (University of California, Davis), Co-Chair Jerrold E. Marsden (University of California, Berkeley), Co-Chair Ruey S. Tsay (University of Chicago), Co-Chair Vincent E. Moncrief (Yale University), Co-Chair

Saturday, July 6 to Friday, July 12 Saturday, July 27 to Friday, August 2 Stochastic inequalities Systems of coupled oscillators Moshe Shaked (University of Arizona), Co-Chair D. G. Aronson (University of Minnesota, Minneapolis) Y.L. Tong (Georgia Institute of Technology), Co-Chair Chair

COMBINATORIAL GROUP THEORY Benjamin Fine, Anthony Gaglione and Francis C.Y. Tang, Editors Contemporary Mathematics, Volume 109 The AMS Special Session on Combinatorial Group Theory-Infinite Groups, held at the University of Maryland in April 1988, was designed to draw together researchers in various areas of infinite group theory, especially combinatorial group theory, to share methods and results. The session reflected the vitality and interests in infinite group theory, with eighteen speakers presenting lectures covering a wide range of group-theoretic topics, from purely logical questions to geometric methods. The heightened interest in classical combinatorial group theory was reflected in the sheer volume of work presented during the session. This book consists of eighteen papers presented during the session. Comprising a mix of pure research and exposition, the papers should be sufficiently understandable to the nonspecialist to convey a sense of the direction of this field. However, the volume will be of special interest to researchers in infinite group theory and combinatorial group theory, as well as those interested in low-dimensional (especially three-manifold) topology. 1980 Mathematics Subject Classifications: 20 All prices subject to change. Free shipment by ISBN 0-8218-5116-0, LC 90-40475, surface: for air delivery, please add $6.50 per title. ISSN 0271-4132 Prepayment required. Order from American 191 pages (softcover), October 1990 Mathematical Society, P.O. Box 1571, Annex Individual member $22, List price $37, Station, Providence, RI 02901-1571, or call toll free Institutional member $30 800-321-4AMS (321-4267) in the continental U.S. To order, please specify CONM/l09NA and Canada to charge with Visa or MasterCard.

FEBRUARY 1991, VOLUME 38, NUMBER 2 135 1991 Summer Research Institute Algebraic Groups and Their Generalizations Pennsylvania State University, University Park, July 8-28

The thirty-ninth Summer Research Institute sponsored by of functions on a Lie group. This has inspired the devel­ the American Mathematical Society will be devoted to Al­ opment of the theory of quantum groups particularly by gebraic groups and their generali=ations and will take place Drinfel' d. Lusztig has formulated arithmetic quantizations at the Pennsylvania State University, University Park, Penn­ of the Kostant Z-forms of semi-simple Lie algebras which sylvania. Members of the Organizing Committee are: Igor allow the formulation of statements concerning the represen­ Frankel, Yale University; Eric Friedlander, Northwestern tation theory of semi-simple groups which have the theory University; William Haboush (chair), University of Illinois, over fields of positive characteristic as a specialization. Urbana-Champaign; Jens Jantzen, University of Oregon, Through these developments a major reformulation of Eugene; and Brian Parshall, University of Virginia. the vocabulary of algebraic group theory has taken place. It is anticipated that the institute will be partially Though conferences on various aspects of the theory of supported by a grant from the National Science Foundation. algebraic groups have taken place, no conference has focused Proceedings of the institute will be published in the AMS on the general theory for some time. The summer institute series Proceedings of Symposia in Pure Mathematics. will attempt to present this new knowledge as a corpus This topic was selected by the 1989 AMS Committee on stressing overall structure, both common elements and Summer Institutes and Special Symposia whose members at special features that mark off one area from another. Thus the time were: Steven L. Kleiman (chair), Haynes R. Miller, certain topics, such as Kazhdan-Lusztig theory and the idea Raghavan Narasimhan, Brian Parshall, and Thomas C. of induced representation as well as the higher derived Spencer. functions of induction viewed as expressions of the structure While several recent conferences have been devoted to of homogeneous spaces, are common threads while other the theory of algebraic groups, it has been some time since topics such as vertex operators and related matters are there has been an extended conference devoted to the core based on unique aspects of special situations. Both types of subject itself. Meanwhile, the subject has undergone a most ideas should be studied and juxtaposed. Similarly, certain remarkable expansion and transformation. quantization theories couched in analytic terms can be compared to the Lusztig quantization. It is hoped that these The first of these developments is the one that be­ juxtapositions can be organized to result in fertile exchanges gan with observations by Jantzen and Deodhar that certain of ideas. composition factors in Verma modules occurred with mul­ There are plans for major lecture series on quantum tiplicity. This led to the work of Kazhdan and Lusztig groups, Kac-Moody Lie algebras and groups, Heeke alge­ relating these multiplicities to the representative theory of bras, and on the representation theories associated to these Weyl groups and Heeke algebras and the intersection ho­ objects. In addition, a series of talks will be devoted to mology of generalized Schubert cells, work culminating induction in its various guises and to the geometry of ho­ in the Kazhdan-Lusztig conjectures. The solutions to these mogeneous spaces and their compactifications, especially as conjectures by Bernstein and Bielenson and by Kashiwara they relate to representation theory. Directly related topics have made algebraic analysis and the theory of the derived such as transformation spaces and quotients might also be category part of the substance of representation theory which discussed particularly in so far as they can be applied to has led to a new way of understanding the subject as a or viewed as applications of the main topics. For example, whole. transformation spaces can be related to orbit methods and to The second major development begins with the obser­ questions concerning the intersection homology of homoge­ vation by Kac and Moody that relaxation of the positivity neous spaces which in turn might bear on the combinatoric conditions on the Cartan matrix leads to a new class of aspects of representation theory. infinite dimensional simple Lie algebras and the subsequent A tentative list of the topics to be addressed follows. exploitation of this fact by Kac, Lepowsky, and others to Please note, however, that the program is subject to change. develop a representation theory and a group theory for these Lie algebras. This has led to the development of a mean­ Week One: ingful infinite dimensional group theory by Kac, Peterson, General theory of quantum groups and algebras, Kac­ Matthieu, and others. Moody Lie algebras and root systems, basic Kac-Moody The third major change begins with Woronowicz's dis­ group theory, finite dimensional representations in positive covery of a "non-commutative" deformation of the algebra characteristic, infinitesimal structures, flag varieties, Bruhat

136 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Summer Research Institute

decompostion and generalized Schubert cells in the finite and Information on housing, dining, travel, and the local infinite dimensional cases, standard bases for representations, area will be sent to invited participants in the spring. Each and loop groups. participant will pay a registration fee and a social fee to cover the costs of social events scheduled during the Week Two: institute. Theory of quantum groups and algebras continued, Those interested in receiving an invitation to participate Kac-Moody groups, the representation theory of quantum in the institute should send the following information to groups and of Kac-Moody groups and algebras, character Summer Institute Conference Coordinator, American Math­ formulae, Heeke algebras and Weyl groups, triangulated ematical Society, Post Office Box 6887, Providence, RI categories and derived categories in representation theory, 02940, prior to April 1, 1991 or through electronic mail to D-modules induced representations, the derived functors [email protected]. of induction, homogeneous spaces, transformation spaces, Please type or print the following: almost homogeneous spaces, infinitesimal analogues, loop l. Full name; groups and affine Kac-Moody groups, and vertex operators. 2. Mailing address; Week Three: 3. Telephone number and area code for office and home; 4. Which week or weeks you wish to attend; Arithmetic quantizations (the Lusztig quantization), quan­ 5. Your scientific background relevant to the institute tum groups and representation theory in positive characteris­ topic; tic, Kazhdan-Lusztig polynomials and their generalizations, 6. Financial assistance requested; the intersection homology of Schubert cells and its relation 7. Indicate if support is not required, and if interested in to Kazhdan-Lusztig theory, infinite dimensional analogues, attending even if support is not offered. D-modules and orbit methods, D-modules in positive char­ acteristic and other models of infinite dimensional theory Requests for invitations will be forwarded to the Orga­ and quantum group theory. nizing Committee for consideration up to the deadline of Accommodations will be available in the campus res­ April 1, and applicants selected will receive formal invi­ idence halls for participants; cafeteria style meals will be tations and notification of financial assistance beginning in available. All facilities will be accessible to the handicapped. mid-May.

CRYPTOLOGY AND COMPUTATIONAL NUMBER THEORY Carl Pomerance, Editor Proceedings of Symposia in Applied Mathematics, Volume 42

In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But fornow, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principle advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudo-random number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at non-experts, including graduate students and advanced undergraduates in mathematics and computer science.

All prices subject to change. Free shipment by surface; for 1980 Mathematics Subject Classification: 11, 94 air delivery, please add $6.50 per title. Prepayment ISBN 0-8218-0155-4, LC 90-1248, required. Order from American Mathematical Society, ISSN 0160-7634 P.O. Box 1571, Annex Station, Providence, RI 171 pages (hardcover), December 1990 02901-1571, or call toll free 800-321-4AMS (321- Individual member $34, List price $57, 4267) in the continental U.S. and Canada to charge with Institutional member $46 VISA or MasterCard. To order, please specify PSAPM/42NA

FEBRUARY 1991, VOLUME 38, NUMBER 2 137 Mathematical Sciences 5-7. Association for Computing Machinery 1991 Computer Science Conference, San Antonio Convention Center, San Antonio, Meetings and Conferences TX. (May/Jun. 1990, p. 611) 7-8. Twenty-second ACM SIGCSE Tech­ nical Symposium on Education in the Com­ puting Sciences, San Antonio, TX. (May/Jun. 1990, p.612) 7-10. International Conference on Dif­ ferential Equations, Cadi Ayyad University, Marrakech, Morocco. (May/Jun. 1990, p.612) 10-14. International Conference on In­ verse Problems: Computational Algorithms, Texas A&M University, College Station, TX. THIS SECTION contains announcements of meetings and conferences of interest to some (Nov. 1990, p. 1284) segment of the mathematical public, including ad hoc, local, or regional meetings, and 10-16. Mathematische Stochastik, Ober­ meetings or symposia devoted to specialized topics, as well as announcements of regularly wolfach, Federal Republic of Germany. (Apr. scheduled meetings of national or international mathematical organizations. (Information on 1990, p. 500) meetings of the Society, and on meetings sponsored by the Society, will be found inside the front cover.) 11-15. NSF-CBMSRegionalResearchCon­ AN ANNOUNCEMENT will be published in Notices if it contains a call for papers, and specifies ference on Nonlinear Dispersive Wave Sys­ the place, date, subject (when applicable), and the speakers; a second full announcement tems, University of Central Florida, Orlando, will be .Published only if there are changes or necessary additional information. Once an FL. (Jui/Aug. 1990, p. 742) announcement has appeared, the event will be briefly noted in each issue until it has been 11-15. IMA Workshop on Free Boundaries held and a reference will be given in parentheses to the month, year, and page of the issue in which the complete information appeared. Asterisks (*) mark those announcements containing in Viscous Flows, University of Minnesota, new or revised information. Minneapolis, MN. (Sep. 1990, p. 934) IN GENERAL, announcements of meetings and conf~rences held in North America carry 11-15. William H. Roever Lectures in only date, title of meeting, place of meeting, names of speakers (or sometimes a general Geometry, Washington Univ., St. Louis, MO. statement on the program), deadlines for abstracts or contributed papers, and source of (Jan. 1991, p. 44) further information. Meetings held outside the North American area may carry more detailed information. In any case, if there is any application deadline with respect to participation in 13. The Emergence of Abstract Harmonic the meeting, this fact should be noted. All communications on meetings and conferences Analysis: 1930-1950, Institut Henri Poincare, in the mathematical sciences should be sent to the Editor of Notices, care of the American Paris. (Jan. 1991, p. 44) Mathematical Society in Providence. 13-15. IMACS Workshop on Decision DEADLINES for entries in this section are listed on the inside front cover of each issue. In Support Systems and Qualitative Reason­ order to allow participants to arrange their travel plans, organizers of meetings are urged to ing, LAAS-Toulouse, France. (May/Jun. 1990, submit information for these listings early enough to allow them to appear in more than one issue of Notices prior to the meeting in question. To achieve this, listings should be received p. 612) in Providence SIX MONTHS prior to the scheduled date of the meeting. 13-16. Twenty-Second Annual Iranian EFFECTIVE with the 1990 volume of Notices, the complete list of Mathematical Sciences Mathematics Conference, Ferdowsi Univer­ Meetings and Conferences will be published only in the September issue. In all other issues, sity of Mashhad, Iran. (Sep. 1990, p. 934) only meetings and conferences for the twelve-month period following the month of that issue will appear. As new information is received for meetings and conferences that will occur later 14-16. Sixth S.E.A. Meeting, Southeastern than the twelve-month period, it will be announced at the end of the listing in the next possible Approximation Theorists Annual Meeting, issue. That information will not be repeated until the date of the meeting or conference falls Memphis State Univ., Memphis, TN. (Sep. within the twelve-month period. 1990, p. 934) 14-16. Bundles in Complex Differential Geometry, Idaho State Univ., Pocatello, ID. 1991. IMACS Symposium on Parallel and ematics, KTH, S-100 44 Stockholm, Swe­ (Jan. 1991, p. 44) Distributed Computing in Engineering Sys­ den, or D. Laksov, Institut Mittag-Leffler, 14-20. Probability and Bayesian Statistics tems, Athens, Greece. (Jul./Aug. 1990, p. 741) Auraviigen 17, S-182 62 Djursholm, Swe­ in Medicine and Biology, Erice (Trapani), Spring 1991. IMACS International Sympo­ den. Sicily, Italy. (Dec. 1990, p. 1452) sium on Iterative Methods in Linear Alge­ 15-16. Central Section, Indiana University, bra, Brussels Free Univ., Brussels, Belgium. South Bend, IN. (Mar. 1990, p. 334) March 1991 INFORMATION: W. Drady, American Math­ * 1991-1992. Mittag-Leffler Institute Aca­ ematical Society, P.O. Box 6887, Provi­ demic Program for 1991-1992: Combina­ March 1991. Computational Number The­ dence, RI 02940. torics, Djursholm, Sweden. ory, Rutgers University, New Brunswick, NJ. (Oct. 1990, p. 1136) 16-23. Sixth Conference in Geometric PROGRAM: Emphasis will mainly be on 3-9. PartielleDitl'erentialgleichungen, Ober­ Rigidity and Hyperbolic Dynamics, Penn algebraic and geometric aspects. wolfach, Federal Republic of Germany. (Apr. State Univ., State College, PA. (Jan. 1991, CALL FOR PAPERS: Application dead­ 1990, p. 500) p. 44) line for postdoctoral fellowships: April 1, 4-15. Workshop on Mathematical Physics 17-23. Elementare und Analytische 1991. and Geometry, Trieste, Italy. (Sep. 1990, Zahlentheorie, Oberwolfach, Federal Re­ INFORMATION: A. Bjomer, Dept. of Math- p. 934) public of Germany. (Apr. 1990, p. 500)

138 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------·························································································... ································································································· Meetings and Conferences

17-24. Sixth International Conference gebraic geometry, mathematical biology. include title, abstract (one page). duration on Geometry, University of Haifa, Israel. number theory, quantitative methods, gen­ of presentation and description of special (May/Jun. 1990. p. 612) eral. equipment needed. 21-28. Mathematical Aspects of Human INFORI\IATION: P. Blass. Ulam Mathe­ INFORI\IATION: J. Haataja, VTKK/TLP, Diseases, Erice (Trapani), Sicily, Italy. (Dec. matics Conference, Palm Beach Atlantic P.O. Box 40, 02101 Espoo, Finland: 1990, p. 1453) College, MacArthur School of Continu­ email: [email protected] or K. Elo­ 22-23. Southeastern Section, University of ing Education, P.O. Box 3353, West Palm ranta, Dept. of Math.. Helsinki Univ. South Florida, Tampa, FL. Beach, FL 33402-3353; 407-835-4353. of Tech., 02150 Espoo, Finland: email: [email protected]. INFORMATION: W. Drady, American Math­ 7-13. Algebraische Gruppen, Oberwolfach, ematical Society, P.O. Box 6887, Provi­ Federal Republic of Germany. (Apr. 1990, 18-20. Determinantal Ideals and Repre­ dence, Rl 02940. p. 500) sentation Theory, University of Arkansas, 8-12. Seventh International Conference on Fayetteville, Arkansas. (Sep. 1990, p. 935) 22-24. Fifth SIAM Conference on Par­ Data Engineering, Kobe, Japan. (Apr. 1990, 20--21. Wabash Extramural Modern Anal­ allel Processing for Scientific Computing. p. 500) ysis Miniconference. Indiana University-Pur­ Houston, TX. (Mar. 1990, p. 334) 8-12. NASECODE VII, The Seventh In­ due University, Indianapolis. IN. (Dec. 1990, 24-29. Mathematical Approaches to DNA ternational Conference on the Numerical p. 1453) II (The Genome: DNA to Protein Structure). Analysis of Semiconductor Devices and Inte­ 21-24. SUPER!: Supercomputing by Uni­ Santa Fe, NM. (Dec. 1990, p. 1453) grated Circuits, Copper Mountain, Colorado. versity People for Education and Research, 24-30. Gewohnliche Differentialgleichun­ (May/Jun. 1990, p. 612) Park City, UT. (Nov. 1990, p. 1284) gen, Oberwo1fach, Federal Republic of Ger­ 10--12. Fourth International Conference 21-27. Numerical Linear Algebra, Oberwol­ many. (Apr. 1990, p. 500) on Rewriting Techniques and Applications fach, Federal Republic of Germany. (Jul./Aug. 25-27. Fifth SIAM Conference on Par­ (RTA-91), Como, Italy. (Jul./Aug. 1990, 1990, p. 743) allel Processing for Scientific Computing, p. 743) 21-May 4. NATO ASI Finite and Infinite Houston, TX. (Jul./Aug. 1990, p. 742) 11-13. Twenty-Fifth Annual Spring Topol­ Combinatorics in Sets anJ. Logic, Banff, 25-28. International Conference on Math­ ogy Conference, California State University, Canada. (Dec. 1990. p. 1453) ematical Linguistics - ICML '91, Barce­ Sacramento, CA. (Oct. 1990, p. 1137) 23-26. Mathematical and Numerical As­ lona, Spain. (Jul./Aug. 1990, p. 742) 11-16. Assessment in Mathematics Educa­ pects of Wave Propagation Phenomena, 25-29. Forty-Third British Mathematical tion and Its Effects, Calonge (Costa Brava), Strasbourg, France. (Jul./Aug. 1990, p. 743) Colloquium, Univ. of Batb, Claverton Down, Spain. (Sep. 1990, p. 935) Batb, U.K. (Jan. 1991, p. 44) * 26-28. Similarity Solutions of Differen­ * 13. Workshop on Differential Geometry tial Equations, University of Pittsburgh, PA. 25-April 12. Linear and Nonlinear Disper­ and Mathematical Physics, Arkansas State (Please note changes from Oct. 1990, p. 1137) sive Waves, Mathematical Sciences Institute, University. Jonesboro. AR. Cornell University, Ithaca, NY. (Jan. 1991, PROGRAI\1: The meeting will be partially p. 45) PROGRAI\1: Organized around differential supported by the National Science Foun­ 29-30. 1991 Association for Symbolic Logic geometry and its applications to mathe­ dation. Partial support is available for Spring Meeting (in conjunction with a meet­ matical physics. a limited number of participants. Please ing of the American Philosophical Asso­ INVITED SPEAKERS: R. Fisher, R. Fulp. contact S. Hastings. Dept. of Math., Univ. ciation), San Francisco, CA. (Dec. 1990, J. Glazebrook, G. Jensen, X. Mo. of Pittsburgh, [email protected]. p. 1453) INFORMATION: R. Bowman, A. Talmadge INVITED SPEAKERS: [REVISED]: M. 31-April 6. Arbeitsgemeinschaft mit Ak­ or K. Yang, Math. Dept., Box 70, State Ablowitz. G.l. Barenblatt, G. Bluman. P. tuellum Thema, Oberwolfach, Federal Re­ Univ., AR 72467; 501-972-3090. Clarkson. A. Fokas. N. Goldenfeld. J.-S. public of Germany. (Apr. 1990, p. 500) Guo, M.-K. Kwong. R. Kohn, P. Olver, 14-20. Brauer Groups and Representa­ L.A. Peletier. tion Theory of Finite Groups, Oberwolfach. 26-28. First Eugene Lukacs Symposium, April1991 Federal Republic of Germany. (Apr. 1990, p. 500) Bowling Green State University, Bowling 1-4. Eighth International Conference on 15-19. IMA Workshop on Variational Prob­ Green. OH. (Dec. 1990, p. 1453) Mathematical and Computer Modeling, Uni­ lems, University of Minnesota, Minneapolis. 28-May 4. Deductive Systems, Oberwolfach, versity of Maryland, College Park, MD. (Oct. MN. (Sep. 1990, p. 935) Federal Republic of Germany. (Apr. 1990. 1990, p. 1137) p. 501) * 17-18. Workshop on Cellular Automata. 1-7. JAMI Workshop and Conference on Center for Scientific Computing, Helsinki. 29-May 2. Joint U.S.-French Workshop on Algebraic and Complex Geometry, Johns Finland. Applied Stochastic Analysis. Rutgers Uni­ Hopkins Univ., Baltimore, MD. (Jan. 1991, versity. New Brunswick, NJ. (Nov. 1990, p. 45) CONFERENCE TOPICS: General theory p. 1285) of cellular automata and related dynami­ 2-4. IMACS International Symposium on 29-May 10. NATO Advanced Study In­ cal systems, applications to computational * Iterative Methods in Linear Algebra, Brus­ stitute on Approximation Theory, Spline science, physics and other natural sciences sels Free Universities, Belgium. (May/Jun. Functions and Applications, Maratea, Italy. 1990, p. 612) and engineering. INVITED SPEAKERS: P. Bak, B.M. INFORMATION: Partial financial support 3-5. Second Annual Ulam Mathematics * Boghosian, D. Griffeath, C. Pickover. is available for participants. Contact: S.P. Conference, Palm Beach Atlantic College, CALL FOR PAPERS: Time will be al­ Singh, Dept. of Math., Memorial Univ., West Palm Beach, Florida. located to 15-30 minute presentations. St. John's, NF. Canada A1C 5S7; email: SPECIAL SESSIONS: Probability, com­ which can include video, slide or com­ bitnet spsingh@mun: Fax: 709-737-3010; puter science, artificial intelligence, al- puter demonstrations. Submissions should Tel: 709-737-8795.

FEBRUARY 1991, VOLUME 38, NUMBER 2 139 ------···············-·················-···········...... --...... _...... - ...... _, __ ...... --...... _ Meetings and Conferences

17-20. Conference/Workshop on Contin­ tionsrechnung-Optimal Control, Ober­ uum Theory and Dynamical Systems, Uni­ wolfach, Federal Republic of Germany. (Apr. May 1991 versity of Southwestern Louisianna, Lafayette, 1990, p. 501) May/June 1991. Summer Workshop on LA. (Dec. 1990, p. 1454) * 27-June 4. Workshop on Probabilistic Calculus, Computer, Concepts, and Coop­ 19-25. Differentialgeometrie im Grossen, Methods in Differential Equations, Tech­ erative Learning, Purdue University, West Oberwolfach, Federal Republic of Germany. nion, Haifa, Israel. Lafayette, IN. (Nov. 1990, p. 1285) (Apr. 1990, p. 501) ORGANIZER: R.G. Pinsky. May/June 1991. IMACS Workshop on Deci­ 20-24. Eleventh International Conference INVITED SPEAKERS: M. Berger, I. Chavel, sion Support Systems and Qualitative Rea­ on Distributed Computing Systems, Arling­ M. Cranston, R. Darling, J.D. Deuschel, soning, Toulouse, France. (Mar. 1990, p. 334) ton, TX. (Sep. 1990, p. 936) E.B. Dynkin, M. Emery, W. Fleming, M. 2-3. Twenty-Second Annual Pittsburgh 21-24. Quantization and Microlocal Anal­ Freidlin, R.Z. Hasminskii, E.P. Hsu, I. Conference on Modeling and Simulation, ysis. Reims, France. (Jan. 1991, p. 46) Karatzas, L. Karp, G. Kersting, H. Kunita, University of Pittsburgh, PA. (Sep. 1990, 22-24. Second International Conference on T. Kurtz, T.Y. Lee, P. March, B. Oksendal, p. 935) Algebraic Methodology and Software Tech­ G. Papanicolaou, M. Pinsky, U. Rosier, D. 2-4. International Conference on Poly­ nology, (AMAST), Iowa City, Iowa. (Apr. Stroock, M. van den Berg, S.R.S. Varad­ nomials with concentration at low degrees: 1990, p. 501) han, S. Watanabe, J. Watkins, V. Wihstutz, From Analysis and Number Theory to Com­ R. Williams, and Z. Zhao. * 23-24. Thirteenth Symposium on Mathe­ INFORMATION: Institute for Advanced puter Science and Symbolic Computation, matical Programming with Data Perturba­ Paris, France. (Nov. 1990, p. 1285) Studies in Mathematics, Dept. of Math., tions, George Washington Univ., Washington, Technion - Israel Institute of Technology, 5-11. Darstellungstheorie Endlich-Di­ DC. Haifa, Is. 32000. mensionaler Algebren, Oberwolfach, Fed­ eral Republic of Germany. (Jul./Aug. 1990, PROGRAM: The symposium is designed to bring together practitioners who use 29-June 1. Eighth Biennial Conference of p. 743) the Association of Christians in the Mathe­ mathematical programming optimization 6--8. Fifth SIAM International Sympo­ models and deal with questions of sensi­ matical Sciences, Wheaton College, Wheaton, IL. (Jul./Aug. 1990, p. 743) sium on Domain Decomposition Methods tivity analysis, with researchers who are for Partial Differential Equations, Norfolk, developing techniques applicable to these 29-June 1. Methods in Module Theory, VA. (Jul./Aug. 1990, p. 743) problems. University of Colorado, Colorado Springs, 7-10. IMACS Symposium on Modelling CALL FOR PAPERS: Contributed papers CO. (Sep. 1990, p. 936) and Simulation of Control Systems, Casa­ in mathematical programming are solicited 30-31. Special Session on Polymer Config­ blanca, Morocco. (Mar. 1990, p. 334) in the folllowing areas: Sensitivity and urations: Nonlinear and Nonlocal Diffusion 7-14. Singapore Number Theory Work­ stability analysis results and their ap­ Problems, University of Minnesota, Min­ shop, National Univ. of Singapore, Kent plications; solution methods for problems neapolis, MN. (Nov. 1990, p. 1286) Ridge, Singapore. (Jul./Aug. 1990, p. 743) involving implicitly defined problem func­ 31-June 2. CMS Summer Meeting 1991, 9-11. A Conference on History, Geometry, tions and for problems involving deter­ Universite de Sherbrooke, Sherbrooke, Quebec. and Pedagogy in honor of the 80th b!rth­ ministic or stochastic parameter changes; (Dec. 1990, p. 1454) day of Howard Eves, University of Central solution approximation techniques and er­ Florida, Orlando, FL. (Nov. 1990, p. 1285) ror analysis. "Clinical" presentations that describe problems in sensitivity or stabil­ 12-18. Nichtlineare Evolutionsgleichungen, ity analysis encountered in applications are June 1991 Oberwolfach, Federal Republic of Germany. also invited. Abstracts of papers intended (Apr. 1990, p. 501) 2-8. Diskrete Geometrie, Oberwolfach, Fed­ for presentation should be sent in tripli­ eral Republic of Germany. (Apr. 1990, p. 501) 13-17. Conference in Harmonic Analysis cate and should provide a good technical in Honor ofE.M. Stein, Princeton University, summary of key results, avoid the use 3-7. 1991 Annual Meeting of the Statistical Princeton, NJ. (Mar. 1990, p. 334) of mathematical symbols and references, Society of Canada, Toronto, Ontario, Canada. 13-18. IMA Workshop on Degenerate Dif­ not exceed 500 words, and include a title (Mar. 1990, p. 334) fusions, University of Minnesota, Minneapo­ and the name and full mailing address of 3-7. NSF-CBMS Regional Research Con­ lis, MN. (Sep. 1990, p. 935) each author. Deadline: March 9, 1991. 30 ferences in the Mathematical Sciences: Har­ 15-17. Third IEEE Conference on Com­ minutes will be allocated for each paper. monic Analysis and Partial Differential puter Workstations: Accomplishments and INFORMATION: A.V. Fiacco, Organizer, Equations, University of Missouri, St. Louis, Challenges, Falmouth (Cape Cod), MA. (Sep. School of Engineering and Applied Sci­ MO. (Dec. 1990, p. 1455) 1990, p. 936) ence, The George Washington University, 3-8. International Singularity Conference, 15-18. International Conference on Theory Washington, DC 20052; 202-994-7511. Lille, France. (Nov. 1990, p. 1286) and Applications of Differential Equations, 3-13. Fifth International Workshop in 23-25. Sixth Annual Lehigh University Analysis and its Applications, Kupari­ University of Texas-Pan American, Edinburg, Geometry and Topology Conference, Beth­ Dubrovnik, Yugoslavia. (Nov. 1990, p. 1286) TX. (Dec. 1990, p. 1454) lehem, PA. (Dec. 1990, p. 1454) 16-21. NSF-CBMS Regional Research 5-7. Conference in Honor ofMoshe Zakai, Conferences in the Mathematical Sciences: 26--29. Twenty-first International Sym­ Haifa, Israel. (Jan. 1991, p. 46) New Trends in Nonlinear Control Theory, posium on Multi-Valued Logic, Victoria, 5-15. A Normal Form for the Navier­ Louisiana State University, LA. (Dec. 1990, Canada. (Dec. 1990, p. 1454) Stokes Equations and Its Connection to p. 1454) Turbulence, Mathematical Sciences Institute, 2~31. Signal Theory and Image Process­ 17-18. Annual Regional Group Theory ing, Cetraro, Italy. (Sep. 1990, p. 936) Cornell University, Ithaca, NY. (Jan. 1991, Conference, Bucknell Univ., Lewisburg, PA. p. 46) (Jan. 1991, p. 45) 26--June 1. Optimalsteuerung und Varia- 9-12. International Workshop on Ele-

140 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

mentary Operators and Applications, Hein­ forum for presentation of recent progress Conferences in the Mathematical Sciences: rich Fabri-Institut der Universitat Tiibingen, in the mathematical modeling of renew­ Multigrid and Multilevel Adaptive Methods Blaubeuren/Ulm, Federal Republic of Ger­ able resources. Particular emphasis will for Partial Differential Equations, George many. (Nov. 1990, p. 1286) be given to the modeling of biologi­ Washington University, Washington, DC. (Dec. 9-14. Second International Conference cal processes, population dynamics and 1990, p. 1455) on Fixed Point Theory and Applications, bioeconomics, especially as they relate 24-29. Geometry Conference in Honour Dalhousie University, Halifax, Nova Scotia, to problems in fisheries, forestry, pest and of Claude Godbillon and Jean Martinet, Canada. (Oct. 1990, p. 1138) wildlife management, and water resources. University of Strasbourg, France. (Dec. 1990, 9-15. Singuliire Storungsrechnung, Ober­ INVITED SPEAKERS: C. Clark, Univ. of p. 1455) wolfach, Federal Republic of Germany. (Apr. British Columbia; A. Charles, St. Mary's * 24-29. Workshop on Algebraic and Topo­ Univ.; J. Conrad, Cornell Univ.; R. Lande, 1990, p. 50 I) logical Methods in Graph Theory, Slovenia, Univ. of Oregon; M. Mangel, Univ. of Yugoslavia. 9-28. NSF Faculty Workshop on Computer­ California, Davis. Aided Instruction in Linear Algebra and CALL FOR PAPERS: Those who wish INVITED SPEAKERS: P. Cameron, F. Differential Equations, University of New to present a paper (20 minutes) should Jaeger, B. Jackson, I. Rival, C. Thomassen, Hampshire, Durham, NH. (Jan. 1991, p. 46) submit an abstract by May I, 1991. T.W. Tucker. 10-14. Bernoulli Society Twentieth Con­ INFORMATION: R. Lamberson or C. Biles, CALL FOR PAPERS: Deadline for reg­ ference on Stochastic Processes and their Math. Dept., Humboldt State Univ., Ar­ istration and abstracts: April 15, 1991. Applications, Nahariya, Israel. (Nov. 1989, cata, CA 95521; 707-826-4926; 707-826- Conference fee $100, $50 for students. p. 1254) 4251; email: rollie@calstate or charlie@ INFORMATION: B. Mohar, IMFM, Dept. I 0-14. Trent Homotopy Theory Confer­ calstate. of Mathematics, Jadranska 19, 61111 ence, Trent Univ., Peterborough, Ontario, Ljubljana, Yugoslavia; email: mohar@ Canada. (Jan. 1991, p. 46) 19-July I. Nonsmooth Optimization­ uni-lj.ac.mail.yu. 11-July 5. Miniworkshop on Nonlinearity: Methods and Applications, Erice (Trapani), Sicily. (Jan. 1991, p. 47) 24-July 2. Topological Methods in the Fractals, Pattern Formation, Trieste, Italy. Theory of Ordinary Differential Equations 20-25. Curves, Surfaces, CAGD, and Image (Jan. 1991, p. 46) * in Finite and Infinite Dimensions, Villa "La Processing, Biri, Norway. 13-15. Western Sectional Meeting, Portland Querceta", Montecatini Terme. State University, Portland, Oregon. PROGRAM: Focus will be on the classical DIRECTORS: M. Furi and P. Zecca of the topics of Computer Aided Geometric De­ INFORMATION: W. Drady, American Math­ Univ. de Firenze. sign such as spline and Bezier methods for ematical Society, P.O. Box 6887, Provi­ LECTURERS: H. Amann (Univ. Zurich), curve and surface modeling, visualization, dence, RI 02940. P. Fitzpatrick (Univ. of Maryland, Col­ and data fitting, as well as connections lege Park), M. Martelli (California State with wavelets and fractals, and their ap­ 14-17. Symposium on Lattice Theory and Univ. at Fullerton), J. Mawhin (Univ. plications in image processing. The con­ its Applications, in Honor of the 80th Birth­ Catholique, Louvain-La-Neuve, Belgio), ference will include I 0 one-hour survey day of Garrett Birkhoff, Darmstadt, Federal R. Nussbaum (Rutgers Univ.). Republic of Germany. (Oct. 1990, p. 1138) lectures and about 50 research lectures. INFORMATION: P. Zecca, Secretary, CIME, 16--19. Bar-Han Symposium on the Foun­ INVITED SPEAKERS: M. Bamsley, C. Dipartimento di Matematica "U. Dini", deBoor, P. Brunet, P. de Casteljau, C. dations of Artificial Intelligence, Ramat Gan, viale Morgagni 67I A, 50134 Firenze, Israel. (Nov. 1990, p. 1286) Chui, M. Daehlen, A. DeRose, N. Dyn. Italy; email: [email protected]; +39-55- R. Farouki, T. Foley, R. Goldman, J. 16-22. Mathematische Methoden in der 434975. Hoschek, B. Lucier, C. Micchelli, M.J. Robotik, Oberwolfach, Federal Republic of Pratt, C. Rabut, P. Sablonniere, R. Sch­ Germany. (Jan. 1991, p. 46) * 24-July 2. Arithmetic Algebraic Topology, abach, T. Sederberg, and H. -P. Seidel. Villa "Madruzzo", Trento. 17-19. Seventeenth International Work­ INFORMATION: T. Lyche, lnstitutt for ln­ shop on Graph-Theoretic Concepts in Com­ formatikk, P.O. Box 1080, Blindern, 0316 DIRECTOR: E. Ballico (Univ. di Trento). puter Science, Fischbachau near Munich, Oslo 3, Norway; email: [email protected]; or LECTURERS: J. L. Colliot-Thelen (Univ. Federal Republic of Germany. (Jan. 1991, L.L. Schumaker, Dept. of Math., Vander­ de Paris Sud), K. Kato (Univ. Tokyo), C. p. 46) bilt Univ., Nashville, TN 37235; email: Soule (IHES), P. Vojta (Univ. of Califor­ 17-21. 1991 International Symposium on schumake@ctrvax. vanderbilt.edu. nia, Berkeley). the Mathematical Theory of Networks and INFOR!VIATION: P. Zecca, Secretary, CIME, Systems (MTNS-91), International Confer­ 20-27. NP-Completeness: The First 20 Dipartimento di Matematica "U. Dini", ence Center Kobe, Kobe, Japan. (Nov. 1989, Years, Erice (Trapani), Sicily. (Jan. 1991. viale Morgagni 67/A, 50134 Firenze, p. 1254) p. 47) Italy; email: [email protected]; +39-55- 17-21. European Conference on Elliptic 23-29. Mathematische Methoden des VLSI­ 434975. and Parabolic Problems, Pont a Mousson, Entwurfs und des Distributed Computing, 25-28. Eighth International Conference France. (May/Jun. 1990, p. 613) Oberwolfach, Federal Republic of Germany. on Logic Programming, Paris, France. (Jan. * 19-21. The Tenth Pacific Coast Resource (Jul./Aug. 1990, p. 744) 1991, p. 47) Modeling Conference, Humboldt State Univ., 23-30. International Category Theory Meet­ 26-28. Third IMACS International Sympo­ Arcata, CA. ing, Montreal, Quebec, Canada. (Jan. 1991, sium on Computational Acoustics, Harvard p. 47) SPONSORS: Resource Modeling Associa­ University, Cambridge, MA. (Jul./Aug. 1990, tion, Humboldt State Univ. Colleges of 24-27. Barsotti Memorial Symposium on p. 744) Science and Natural Resources, U.S. For­ Algebraic Geometry, Abano Terme, Italy. 26-28. Local Communications Systems: est Service, Redwood Sciences Lab. (Jan. 1991, p. 47) LAN and PBX, Palma, Balearic Islands, PURPOSE: The purpose is to provide a 24-28. NSF-CBMS Regional Research Spain. (Jan. 1991, p. 47)

FEBRUARY 1991, VOLUME 38, NUMBER 2 141 ------····················-···-·-·-... ··-... ·-·········-···················-·· ... ··---· ... ··-········ ...... ·---···... ···-··········· Meetings and Conferences

* 26-29. Sunimer Conference on General PROGRAM: A series of ten lectures by J. Topology and Applications, Univ. of Wis­ Harrison, Mathematical Sciences Research consin, Madison. July 1991 Institute, plus related lectures. Support for 1-5. The Mathematics of Nonlinear Sys­ travel, lodging, and stipends expected from INVITED SPEAKERS: M.E. Rudin (Univ. tems, University of Bath. United Kingdom. NSF. of Wisconsin), A. Beslagic (George Ma­ (Dec. 1990. p. 1455) INFORMATION: Dynamical Systems Insti­ son Univ.), A. Dow (York Univ., Toronto), tute, Dept. of Math., Boston Univ., 111 W. Fleissner (Univ. of Kansas), G. Gruen­ * 1-19. Symposium on Geometric Group Theory, University of Sussex, Brighton, Eng­ Cummington St., Boston, MA 02215. hage (Auburn Univ.), J. Kennedy (Univ. land. of Delaware). S. Koppelberg (Free Univ., 7-12. Fifth Gregynog Symposium on Differ­ Berlin), K. Kunen (Univ. of Wisconsin), PROGRAM: This 3-week symposium cov­ ential Equations, University of Wales, UK. K. Magill (State Univ. of NY, Buffalo), ering geometric methods in group theory (Nov. 1990, p. 1287) P. Nyikos (Univ. of South Carolina), will consist of a 2-week workshop at the 7-13. Computational Number Theory, B.E. Shapirovskii (Moscow), M. Starbird Univ. of Sussex followed by a conference Oberwolfach, Federal Republic of Germany. (Univ. of Texas), F. Tall (Univ. of Toronto), at the nearby Isle of Thoms. The workshop (Jul./Aug. 1990, p. 744) S. Todorcevic (York Univ., Toronto), S. will be informal, allowing seminars. short 7-20. Eighth International Conference on Watson (York Univ., Toronto), W. Weiss reading courses and problem sessions on Probability in Banach Spaces, Bowdoin Col­ (Univ. of Toronto). the areas of special interest to the par­ lege, Brunswick, ME. (Jan. 1991, p. 47) CALL FOR PAPERS: Participants are in­ ticipants. The conference will be centered 8-12. Second International Conference on vited to present shorter talks (25 minutes). around a series of key note lectures given Industrial and Applied Mathematics, Wash­ Abstract Deadline: May 1. 1991. These by invited speakers; participants will be ington, DC. (Apr. 1990, p. 501) free to give talks on their own particular should be 7.5 inches by 5 inches, 1 1/2 8-12. NATO Advanced Research Work­ developments if time permits. space (4 lines/inch). Registration fee $40 shop: Approximation by Solutions of Partial INVITED SPEAKERS: M. Bestvina (Prince­ before June 1, $50 after. Differential Equations, Quadrature Formu­ ton), R. Bieri (Frankfurt), K. Brown lae, and Related Topics, Hanstholm, Den­ INFORMATION: Fees, Abstracts, Gen­ (Ithaca), A. Casson (Berkeley). D. Ep­ mark. (Jan. 1991, p. 48) eral: R. Kopperman, City College of stein (Warwick), S. Gersten (Utah), M. NY, New York. NY 10031; mathrdk@ Gromov (IHES). J. Howie (Heriot Watt), 8-12. Thirty-Fifth Annual Conference of ccnyvme.bitnet; Fax: 212-6560-6970; Ab­ P. Kropholler (QMW). J. Morgan (Co­ the Australian Mathematical Society, Mel­ stracts, General: F. Tall, Univ. of Toronto, lumbia), E. Rips (Jerusalem), P. Scott bourne, Australia. (Oct. 1990, p. 1139) Toronto, Ontario M5S 1A4, Canada: (Michigan), J. Stallings (Berkeley), W. * 8-12. Thirteenth British Combinatorial [email protected]; Fax: 416-978-4107; Thurston (Princeton). Conference, Guildford, England. Student Nominations: M. Henriksen. Har­ INFORMATION: G.A. Niblo. M. Roller, INVITED LECTURES: J.A. Bondy (Water­ vey Mudd College. Claremont, CA 91711; School of Mathematical and Physical Sci­ henriksen@ hmcvax.ed. loo) - Graph reconstruction: the state of ences, Univ. of Sussex, Brighton BNI the art; Z. Furedi (Budapest) - Turan type 9QH, England: email: mmfe6@ problems; S.W. Golomb (Los Angeles) * 29-July 5. Nineteenth International Collo­ uk.ac.sussex.cluster; Fax: (0273) 678097. quium on "Group Theoretical Methods in - Radar signal patterns from combinato­ Physics", Salamance, Spain. 1-26. NSF Geometry Institute- Geometry rial designs; G. Korchmaros (Potenza) - in the Machine Age, Mount Holyoke College, Old and new results on ovals of finite INFORlVIATION: L.J. Boya. Chairman, South Hadley, MA. (Jan. 1991, p. 47) projective planes; I.G. MacDonald (Lon­ don) - Schubert polynomials; R. Mathon Depto. Fisica Teorica, University of 2-5. European Control Conference, Greno­ (Toronto) - Computational methods in de­ Zaragoza, 50.009.Zaragoza (Spain). Tel: ble, France. (Jul./Aug. 1990, p. 744) sign theory; J. Nesetril (Prague)- Unprov­ 34-76-554214; FAX: 34-76-567920; 2-5. International Conference on Com­ email: [email protected]. able combinatorial statements; 0. Pretzel plexity: Fractals, Spin Glasses and Neural (London) - Orientations and edge func­ Networks, Trieste, Italy. (Jan. 1991, p. 47) 30-July 3. Sixth Annual Conference on tions on graphs; and P. Rowlinson (Stir­ Structure in Complexity Theory, University 4-11. International Conference on Alge­ ling) - Graph perturbations. braic Topology, Oaxtepec, Mexico. (Nov. of Chicago, Chicago, IL. (Nov. 1990, p. 1287) INFORMATION: A.D. Keedwell and P.J. 1990, p. 1287) Owens, Dept. of Mathematical and Com­ * 30-July 3. Chaos and Catastrophes, Dy­ * 6-13. Transition to Chaos in Classical puting Sciences. Univ. of Surrey, Guild­ namical Systems Institute, Boston University, and Quantum Systems, Villa "La Querceta", ford, Surrey, GU2 5XH, United Kingdom. Boston, MA. Montecatini Terme. 8-14. ICOR '91 International Conference PROGRAJI.I: A series of eight lectures DIRECTOR: S."Graffi (Univ. di Bologna). on Radicals, Szekszard, Hungary. (Apr. 1990, by E. Christopher Zeeman, Oxford Univ., LECTUREHS: J. Bellisard (Wissenschaft­ p. 502) plus related lectures. Support for travel, skolleg zu Berlin), J.N. Mather (Prince­ * 14-18. Complex Analytic Dynamics, Dy­ lodging, and stipends expected from NSF. ton Univ.), A. Katok (Pennsylvania State namical Systems Institute, Boston University, Univ.). Boston, MA. INFORMATION: Dynamical Systems Insti­ INFORl\IATION: P. Zecca, Secretary, CIME, tute, Dept. of Math., Boston Univ., Ill Dipartimento di Matematica "U. Dini", PHOGRAl\-1: A series of ten lectures by B. Cummington St., Boston, MA 02215. viale Morgagni 67/A, 50134 Firenze. Branner, Technical Univ. of Denmark, and Italy; email: [email protected]; +39-55- J. Milnor, SUNY, Stony Brook, plus re­ 30-July 6. Elliptische Operatoren auf 434975. lated lectures. Support for travel, lodging, Singuliiren und Nichtkompakten Manilig­ and stipends expected from NSF. faltigkeiten, Oberwolfach, Federal Republic * 7-11. Fractal Geometry, Dynamical Systems INFORMATION: Dynamical Systems Insti­ of Germany. (Apr. 1990, p. 50 1) Institute, Boston University, Boston, MA. tute, Dept. of Math., Boston Univ., 111

142 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------··············-·--·------·----··------··------·----··------·---- Meetings and Conferences

Cummington St., Boston, MA 02215. ORGANIZERS: A. Nerode (MSI), W. Marek University of Hawaii. (Univ. of Kentucky), V.S. Subrahmanian INFORMATION: P. Shiue, Dept. of Math­ 14--20. Dynamische Systeme, Oberwolfach, (Univ. of Maryland). ematical Sciences, Univ. of Nevada, Las Federal Republic of Germany. (Apr. 1990, CONFERENCE TOPICS: Stable seman­ Vegas, NV 89154; 702-739-3748; Fax: p. 502) tics, default logic, auto-epistemic logic, 702-597-4343; email: [email protected]: 14--20. International Conference on Near­ truth maintenance systems, implementa­ or G.L. Mullen, Mathematics Dept., Penn rings and Near-fields, Linz, Austria. (Jan. tion issues, diagnosis, probabilistic non­ State Univ., University Park, PA 16802; 1991, p. 48) monotonic theories, applications, meta­ 814-865-9413; mullen@ math. psu.edu. 14--27. 1991 NATO Advanced Study In­ programming and non-monotonicity, in­ stitute: Probabilistic and Stochastic Meth­ heritance networks, inconsistency and non­ 7-14. 1991 ASL European Summer Meet­ ods in Analysis, with Applications, Castel­ monotonicity, and logics of belief. ing (Logic Coloquium '91) in conjunction vecchio Pascoli (Lucca), Italy. (Jan. 1991, INFORMATION: J. Chiment, Mathemati­ with the Ninth International Congress of p. 48) cal Sciences Institute (MSI), 409 College Logic, Methodology and Philosophy of Sci­ Ave., Ithaca, NY 14850; 607-255-8911. 15-17. Fifth IFAC/IMACS Symposium on ence, Uppsala, Sweden. (Dec. 1990, p. 1456) Computer Aided Design in Control and 22-26. Thirteenth IMACS World Congress 8-11. Joint Mathematics Meetings, Uni­ Engineering Systems, Swansea, UK. (Mar. on Computation and Applied Mathematics, versity of Maine, Orono, ME. (including the 1990, p. 334) Trinity College, Dublin University, Dublin, summer meetings of the AMS, AWM, MAA, 15-17. International Symposium on Sym­ Ireland. (Apr. 1990, p. 502) and PME) bolic and Algebraic Computation (ISSAC 28-August 2. Conference on Symbolic Dy­ INFORMATION: H. Daly, AMS, P.O. Box '91), Bonn, Germany. (Jan. 1991, p. 48) namics and its Applications, Yale University, 6887, Providence, RI 02940. 15-18. Sixth Annual IEEE Symposium on New Haven, CT. (Nov. 1990, p. 1287) Logic in Computer Science, Amsterdam, The 28-August 2. SIGGRAPH-Eighteenth In­ ll-15. Eleventh Annual Crypto Conference Netherlands. (Sep. 1990, p. 937) * ternational Conference on Computer Graph­ (Crypto '91), University of California, Santa 15-18. The Fourth Interdisciplinary Con­ ics and Interactive Techniques, Las Vegas, Barbara. ference on Natural Resource Modelling and Nevada. (Jan. 1991, p. 49) Analysis, University of Barcelona, Spain. 28-August 3. Gruppen und Geometrien, CALL FOR PAPERS: Original research (Jan. 1991, p. 48) Oberwolfach, Federal Republic of Germany. papers and technical expository talks are 15-August 2. Conference on Recent Devel­ (Apr. 1990, p. 502) solicited on all practical and theoretical opments in Differential Equations a1,1d Eco­ 29-August 9. SMS-NATO ASI: Universal aspects of cryptology. These aspects in­ logical Modeling, University of Wyoming, Algebra and Orders, Universite de Montreal, clude, but are not limited to, theoretical Laramie, WY. (Jan. 1991, p. 48) Montreal, Canada. (Dec. 1990, p. 1456) computer science, information and cod­ ing theory, number-theoretic algorithms, 15-August 9. IMA Summer Program in tools for the development and analysis Semiconductors, University of Minnesota, of cryptographic protocols, cryptanalysis, Minneapolis, MN. (Dec. 1990, p. 1456) August 1991 software, hardware, operating system se­ 20-21. 1991 Summer Institute of the Lin­ * 3-7. Interamerican Conference on Math­ curity, crypto systems engineering, and guistics Society of America, University of ematics Education, Univ. of Miami, Coral key management. Authors are strongly California, Santa Cruz. Gables, FL. (Apr. 1990, p. 502) encouraged to consolidate their ideas into INFORMATION: W. Ladusaw, Dept. of 4--10. Effiziente Algorithmen, Oberwol­ one or two submissions. Submissions must Linguistics, Univ. of California, Santa fach, Federal Republic of Germany. (Jul./Aug. be anonymous: they must start with a title Cruz, CA 95064. 1990, p. 744) page that contains only the title of the paper and the author's names and affili­ * 21-25. Renormalization and Rigidity, Dy­ 5-8. ICMI-China Regional Conference ations; this title page should be the only namical Systems Institute, Boston University, on Mathematics Education, Beijing, China. place that the names and affiliations ap­ Boston, MA. (Jul./Aug. 1990, p. 744) pear. There is a limit of 10 pages of 12 5-9. Fourteenth International Symposium pt type. Authors are instructed to send 15 PROGRAM: A series of ten lectures by C. on Mathematical Programming, Amster­ copies of a detailed abstract by April 10, McMullen, Univ. of California, Berkeley, dam, The Netherlands. (Jul./Aug. 1990, p. 745) 1991. Send submissions to the program and D. Sullivan, CUNY Graduate Center 5-10. NSF-CBMS Regional Research Con­ chair: J. Feigenbaum, Crypto '91, AT&T and IHES, plus related lectures. Support ferences in the Mathematical Sciences: K­ Bell Labs, Room 2C473, 600 Mountain for travel, lodging, and stipends expected Homology and Index Theory, University of Ave., Murray Hill, NJ 07974; 908-582- from NSF. Colorado, CO. (Dec. 1990, p. 1456) 6910; internet [email protected]. INFORMATION: Dynamical Systems Insti­ tute, Dept. of Math., Boston Univ., Ill * 7-10. Conference on Finite Fields, Coding lNFORl\-IATION: B. Kaliski, Crypto '91, Cummington St., Boston, MA 02215. Theory, and Advances in Communication RSA Data Security, Inc., 10 Twin Dolphin and Computing, University of Nevada, Las Drive, Redwood City, CA 94065; 415- 21-26. SPIE's International Symposium on Vegas. 595-8782: Fax: 415-595-1873; internet: Optical Applied Science and Engineering, PROGRAM: The two main speakers will [email protected]. San Diego, CA. (Jan. 1991, p. 49) each give a series of one-hour lectures sur­ 11-17. European Young Statisticians Meet­ 21-27. Halbgruppentheorie, Oberwolfach, veying recent developments. There will be ing, Oberwolfach, Federal Republic of Ger­ Federal Republic of Germany. (Jul./Aug. sessions for 15 minute contributed papers many. (Jul./Aug. 1990, p. 745) 1990, p. 744) and a refereed conference proceedings will * 22-24. First International Workshop on be published. * 12-16. Workshop on p-adic Monodromy Logic Programming and Non-Monotonic INVITED SPEAKERS: Harald Niederreiter, and the Birch-Swinnerton-Dyer Conjecture, Reasoning, Washington, DC. Austrian Academy of Sciences: Shu Lin, Boston University, Boston, MA.

FEBRUARY 1991, VOLUME 38, NUMBER 2 143 ···································-·········································································-···········-········································------Meetings and Conferences

ORGANTZFms: G. Stevens, Boston Univ.; Method International Conference, Tulsa, 1, 1991 and submitted to address below. B. Mazur, Harvard Univ. OK. (Nov. 1990, p. 1288) INFORMATION: Major M. Welch, U.S. INFORMATION: A. Thayer, Dept. of Math., 21-24. Colloquium on Differential Equa­ Army Cost and Economic Analysis Center, Boston Univ., Boston, MA 02215; 617- tions and Applications, Budapest, Hungary. 1900 Half St., S.W., Washington, DC 353-2560. (Dec. 1990, p. 1457) 20324-2300. 12-17. NSF-CBMS Regional Research 21-25. The International Conference on 4-10. IMA Tutorial, University of Min­ Conferences in the Mathematical Sciences: the Theory of Rings, Algebras, and Modules nesota, Minneapolis, MN. (Oct. 1990, p. 1139) Higher Order Asymptotics with Applica­ in Honor of A.l. Shirshov, Barnaul, U.S.S.R. (Jul./Aug. 1990, p. 745) 7-9. International Workshop on Software tions to Statistical Inference, University of for Automatic Control Systems, Irkutsk, North Carolina, NC. (Dec. 1990, p. 1456) 25-31. Klassifikation Komplex-Aigebrai­ USSR. (Oct. 1990, p. 1139) scher Varietiiten, Oberwolfach, Federal Re­ 14-16. Short Conference on Uniform public of Germany. (Jul./Aug. 1990, p. 745) 8-14. NiedrigidimensionaleTopologie, Ober­ Mathematics and Applications (Interna­ wolfach, Federal Republic of Germany. 25-31. Conference on Classifying Spaces tional Conference on Quasi-Uniformities (Jul./Aug. 1990, p. 745) of Compact Lie Groups and Finite Loop and Related Structures), Bern, Switzerland. 8-14. Knoten und Verschlingungen, Ober­ (Sep. 1990, p. 937) Spaces, Gottingen University. (Nov. 1990, p. 1288) wolfach, Federal Republic of Germany. 18-24. The Navier-Stokes Equations: The­ (Jul./Aug. 1990, p. 745) ory and Numerical Methods, Oberwolfach, * 26-31. International Conference on Differ­ ential Equations: EQUADIFF 91, 9-13. Journees Arithmetiques, Geneva, Federal Republic of Germany. (Jul./Aug. Switzerland. (Dec. 1990, p. 1457) 1990, p. 745) Barcelona, Spain. (Please note changes from Dec. 1990, p. 1457) 9-13. ICMTA 5 Teaching Mathematics by 18-24. The Third Conference of the Cana­ Applications, Noordwijkerhout, The Nether­ INVITED SPEAKERS: The following speak­ dian Number Theory Association, Queen's lands. (Jan. 1991, p. 50) University, Kingston, Ontario. (Sep. 1990, ers are to be added to the previously pub­ p. 938) lished list. V.S. Afraimovich, J.I. Diaz, D. 9-27. School on Dynamical Systems, Trieste, Italy. (Sep. 1990, p. 938) 18-September 4. Twenty-first Summer Ecole Henry, J.S. llyashenko. de Calcul des Probabilites, Saint Flour, 10-13. IFACIIMACS Symposium on Fault France. (Jul./Aug. 1990, p. 745) Detection, Supervision and Safety for Tech­ September 1991 nical Processes-SAFEPROCESS '91, Baden­ 19-22. 1991 Joint Statistical Meetings, Baden, Federal Republic of Germany. (Apr. Atlanta, GA. (Mar. 1988, p. 466) 1-7. Topologie, Oberwolfach, Federal Re­ 1990, p. 502) 19-23. NSF-CBMS Regional Research public of Germany. (Jul./Aug. 1990, p. 745) 11-13. IFACIIFIPIIMACS Symposium on Conferences in the Mathematical Sciences: 3-6. Seventeenth International Conference Robot Control (SYROCO '91), Vienna, Aus­ Qualitative and Structured Matrix Theory, on Very Large Data Bases (VLDB '91), tria. (Oct. 1990, p. 1140) Georgia State University, GA. (Dec. 1990, Barcelona (Catalonia, Spain). (Jan. 1991, p. 1456) 11-14. Fourth SIAM Conference on Ap­ p. 49) plied Linear Algebra, Univ. of Minnesota, 19-23. The Seventh Prague Topological 3-6. Functional Integration and its Appli­ Minneapolis, MN. (Nov. 1990, p. 1288) Symposium, Prague, Czechoslovakia. (Dec. cations, Trieste, Italy. (Jan. 1991, p. 50) 1990, p. 1456) 13-15. Representation Theory Conference, 3-10. Applied Mathematics in the Aerospace University of Oregon, Eugene, OR. (Nov. 19-30. Course in Functional Integration Field, Brice (Trapani), Sicily. (Jan. 1991, 1990, p. 1288) and its Applications, Trieste, Italy. (Jan. p. 50) 1991, p. 49) * 14-27. An International Conference on * 4-6. Twenty-fifth Annual DOD Cost Anal­ Theoretical Aspects of Computer Software, 19-September 6. College on Singularity ysis Symposium, Xerox International Center Tohoku University, Sendai, Japan. Theory, Trieste, Italy. (Sep. 1990, p. 938) for Training and Management Development, '20-24. Second Colloquium on Differential Leesburg, VA. INFORMATION: A. Meyer (Co-chair), MIT Equations, Plovdiv, Bulgaria. Lab for Computer Science, 545 Technol­ CONFERENCE THEME: Cost Analysis: A ogy Square, NE43-315, Cambridge, MA CONFERENCE TOPICS: Ordinary dif­ quarter century of progress-challenges for 02139; email: [email protected]; ferential equations: general, functional, the future. Fax: 617-253-3480 or T. Ito, Dept. of impulsive, stochastic, integra-differential CONFERENCE TOPICS: Cost estimating Information Engineering, Tohoku Univ., equations, dynamical systems and sym­ artificial intelligence/expert systems, au­ Sendai, Japan 980; email: ito@ plectic geometry; applications: control tomated information systems, software, ito.ecei.tohoku.ac.jp; Fax: 81 22 267 4404. theory, theoretical mechanics, applied me­ space/SDI, cost methodology, risk analy­ chanics, physical and chemical, biological, sis, acquisition strategy, strategic systems, 15-20. DMV-Jahrestagung 1991, Biele­ technical; partial differential equations: tactical systems, reporting systems/data­ feld, Federal Republic of Germany. (Jul./Aug. linear and nonlinear. bases, C3, cost considerations in COEAs, 1990, p. 746) CALL FOR PAPERS: Abstracts for con­ O&S cost analysis, visibility and main­ 15-21. Geometrie der Banachraume, Ober­ tributed papers should be received by tenance of O&S costs, weapons system wolfach, Federal Republic of Germany. April 30, 1991. costing, training and professional devel­ (Jul./Aug. 1990, p. 746) INFORMATION: Secretary S. Zlatev, Math­ opment, BASOPS/commercial activities. * 16-20. Summer School on Minimal Models, ematical Faculty of Plovdiv University, CALL FOR PAPERS: Papers are invited Lie Groups and Differential Geometry, Uni­ Tsar Assen Str. 24, Plovdiv 4000, Bul­ from all government agencies, Federal versidad de Santiago de Compostela, Spain. garia; or Drumi Bainov, P.O. Box 45, Contractor Research Centers, universities, 1504 Sofia, Bulgaria. non-profit organizations, and nonhardware PROGRAM: The theme of the school will research organizations under DoD con­ be applications of the theory of minimal 21-23. Thirteenth Boundary Element tract. Abstracts must be received by April models to differential geometry, including:

144 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

actions of groups. homogeneous spaces and programming language environments. ministic Models, Trieste, Italy. (Sep. 1990, and Kahler manifolds. enclosure methods, interval arithmetic al­ p. 938) INVITED SPEAKERS: L. Cordero-Rego. gorithms. 7-11. IMA-INRIA Workshop on Transfer Y. Felix. S. Halperin. D. Tanre. J.C. CALL FOR PAPERS: Contributors are of Mathematics to Industry in the U.S. and Thomas. invited to submit abstracts of one page France, University of Minnesota, Minneapo­ INFOR:\IATION: A. Gomez Tato, Dept. in length for short communications (20 lis, MN. (Dec. 1990. p. 1458) de Xeometrla e Topoloxfa. Facultad de minutes) prior to April 30, 1991. 12-13. Eastern Section, Temple University, Matematicas, Univ. de Santiago de Com­ INFORl\IATION: J. Herzberger, Fachbere­ Philadelphia, PA. postela, 15705 Santiago de Compostela ich Mathematik, Univ. Oldenburg, W-2900 (Spain); email: [email protected]. Oldenburg, Germany. INFORMATION: W. Drady, American Math· The number of participants is limited: ematical Society, P.O. Box 6887, Provi­ preference will be given to younger math­ 6-12. Arbeitsgemeinschaft mit Aktuellem dence, RI 02940. ematicians, including graduate students. Thema (wird in den Mitteilungen der DMV 13-19. Geometrie, Oberwolfach, Federal Application deadline: May I, 1991. Heft 3/1991 bekanntgegeben), Oberwolfach, Federal Republic of Germany. (Jul./Aug. Republic of Germany. (Jul./Aug. 1990, p. 746) 22-28. Nonlinear and Random Vibrations, 1990, p. 746) 14-18. IMA Workshop on Sparse Matrix Oberwolfach, Federal Republic of Germany. * 7-9. Second Symposium on High Perfor- Computations: Graph Theory Issues and (Jul./Aug. 1990, p. 746) mance Computing, Montpellier, France. Algorithms, University of Minnesota, Min­ 23-29. Sixth Symposium on Classical Anal­ neapolis, MN. (Oct. 1990, p. 1140) ysis. Kazimierz Dolny, Poland. (Apr. 1990, PROGRAl\1: This is the second in a series 16-18. SIAM Workshop on Micromechan­ p. 502) of biennial symposia, the goal being an ics. Leesburg, VA. (Nov. 1990, p. 1288) overview of innovations in the high per­ 24-27. International Conference on Theo­ 18-19. Differential and Delay Equations, formance. computing field. During the last retical Aspects of Computer Software, To­ Iowa State University, Ames, Iowa. (Jan. decade. intensive computing (paralellism, hoku Univ., Sendai, Japan. (Sep. 1990, p. 938) 1991, p. 50) vectorization, and schalar) has drawn a 25-27. Ninth GAMM Conference on Nu­ large audience in the world of engineers 20-26. C* -Aigebren, Oberwolfach, Federal merical Methods in Fluid Mechanics, Lau­ and researchers, particularly in the field of Republic of Germany. (Jan. 1991, p. 50) sanne, Switzerland. (May/Jun. 1990, p. 613) classical computations. This has opened 21-26. Third International Workshop­ 29-0ctober 5. Kombinatorik Geordneter several new perspectives which were im­ Conference on Evolution Equations, Con­ Mengen, Oberwolfach, Federal Republic of possible to realize or conceptualize previ­ trol Theory, and Biomathematics, Han-sur­ Germany. (Jul./Aug. 1990, p. 746) ously. The main purpose of this meeting Lesse, Belgium. (Nov. 1990, p. 1288) * 3D-October 2. First International Confer­ is to bring scientists from various fields 27-November 2. Statistische Entscheidungs­ ence of the Austrian Center for Parallel together in order to investigate areas such theorie, Oberwolfach, Federal Republic of Computation (ACPC), Salzburg, Austria. as Architectures of supercomputers, com­ Germany. (Jan. 1991, p. 50) pilers, algorithms. computational methods, 27-November 2. Convergence Structures in PFRPOSE: The ACPC is a cooperative numerical applications, etc. research organization founded in 1989 to Topology and Analysis, Oberwolfach. Federal CONFERENCE TOPICS: Architectures and Republic of Germany. {Jan. 1991, p. 50) promote research and education in the field parallel algorithms, tools and numerical of software for parallel computer systems. methods oriented or adapted to paral­ This first conference is intended as a lel/vector computations. applications on November 1991 forum for both researchers and practioners supercomputers. in the field. CALL FOR PAPERS: Contributors are in­ 3-9. Mengenlehre, Oberwolfach, Federal CALL FOR PAPERS: Submissions of pa­ vited to submit an original non-published Republic of Germany. (Jul./Aug. 1990, p. 746) pers are sought presenting original re­ paper (not exceeding 12 pages) in 5 copies 4-8. Second SIAM Conference on Geomet­ search in topics including: Algorithms, before February 28, 1991. Authors will ric Design, Tempe. AZ. (Nov. 1990, p. 1289) languages, compilers, programming envi­ have 25 minutes for presentations with 5 9-10. Western Sectional Meeting, University ronments, applications. Contributors are minutes for questions. Proposed articles of California, Santa Barbara. invited to send five copies of a full pa­ should be preceded by a front page in­ per not exceeding 12 pages in English to INFORMATION: W. Drady, American Math· cluding the paper's title, the name(s) and addrress below. Submissions must arrive ematical Society, P.O. Box 6887, Provi­ affiliation of the authors, a 200 word ab­ before March 1, 1991. dence, RI 02940. stract and the complete address (tel., fax, INFORMATION: H.P. Zima. lnst. for Stats. email) of the author responsible for further ·and Comp. Science, Univ. of Vienna, 11-15. IMA Workshop on Combinatorial correspondence with the organizers. Rathausstrasse 19/3, A-1010 Vienna, Aus­ and Graph-Theoretic Problems in Linear INFORl\IATION: CNUSC, SHPC Secre­ tria; tel: +43-1-401032788; Fax: +43-1- Algebra, University of Minnesota, Minneapo­ tariat. 950, rue de Saint Priest, BP 7229, 4089250; a4424daj@awiuni !!.bitnet. lis, MN. (Oct. 1990, p. 1140) 34184 Montpellier Cedex 4, France; tel: 17-23. Singularitiiten der Kontinuums­ country code 33 67.14.14.14; Fax: coun­ mechanik: Numerische und Konstruktive try code 33 67.52.37.63; email: shpc@ Methoden zu Ihrer Behandlung, Oberwol­ October 1991 frmop II. bitnet. fach, Federal Republic of Germany. (Jul./Aug. * 1-4. SCAN-91 IMACS-GAMM Interna­ 1990, p. 746) tional Symposium on Computer Arithmetic 7-10. The Ninth International Symposium 18-22. Supercomputing '91, Albuquerque, and Scientific Computation, Universitiit Old­ on Applied Algebra, Algebraic Algorithms, NM. (Jan. 1990, p. 62) enburg. Germany. and Error Correcting Codes, New Orleans, LA. (Dec. 1990. p. 1458) 20-26. C* -Aigebren, Oberwolfach, Federal CONFERENCE THEl\IES: Contemporary Republic of Germany. (Jul./Aug. 1990. p. 746) computer arithmetic. computer arithmetic 7-11. Workshop on Stochastic and Deter- 24-30. Numerische Methoden der Approx-

FEBRUARY 1991, VOLUME 38, NUMBER 2 145 -········--·······················--····-······-············--·····...... ______...... -...... ·-···-······-· .. ··········-········ ... ······-······"······-··-·--·····-···-··················--······-······-·· Meetings and Conferences

imationstheorie, Oberwolfach, Federal Re­ Markov Chains, and Queuing Models, Uni­ INFORMATION: Mathematisches For­ public of Germany. (Jul./Aug. 1990, p. 746) versity of Minnesota, Minneapolis, MN. (Oct. schungsinstitut Oberwolfach Geschlift­ 25-26. Central Section, North Dakota State 1990, p. 1141) sstelle: Alberstrasse 24 D-7800 University, Fargo, ND. 19-25. Modelltheorie, Oberwolfach, Federal Freiburg im Breisgau. Republic of Germany. (Jan. 1991, p. 51) INFORMATION: W. Drady, American Math­ * 19-25. Arbeitsgemeinschaft mit Aktuellem ematical Society, P.O. Box 6887, Provi­ 26-February 1. Applied and Computational Thema, Oberwolfach, Federal Republic of dence, Rl 02940. Convexity, Oberwolfach, Federal Republic of Germany. Germany. (Jan. 1991, p. 51) * 27-29. Third ACM-SIAM Symposium on INFORMATION: Mathematisches For­ Discrete Algorithms, Orlando, FL. schungsinstitut Oberwolfach Geschiift­ December 1991 sstelle: Alberstrasse 24 D-7800 1-7. Statistik Stochastischer Prozesse, Ober­ CALL FOR PAPERS: Abstract Deadline: Freiburg im Breisgau. wolfach, F.R.G. (Jul./Aug. 1990, p. 746) June 10, 1991. INFORMATION: SIAM Conference Dept., * 26-May 2. Gruppentheorie, Oberwolfach, *Fourth International Conference on Numer- 3600 University City Science Center, Federal Republic of Germany. ical Combustion, St. Petersburg, FL. Philadelphia, PA 19104-2688; 215-382- CHAIRMEN: O.H. Kegel, Freiburg; W. ORGANIZER: J.D. Buckmaster, Univ. of 9800; Fax: 215-386-7999; email: siam@ Plesken, Aachen; G. Stroth, Berlin. Illinois, Urbana. wharton.upenn.edu. INFORMATION: Mathematisches For­ CALL FOR PAPERS: Abstract deadline: schungsinstitut Oberwolfach Geschiift­ June 24, 1991. sstelle: Alberstrasse 24 D-7800 Freiburg im Breisgau. 2-6. Workshop on Statistical Methods in February 1992 Imaging, Mathematical Sciences Research 2-8. Thermodynamische Materialtheorien, Institute, Berkeley, CA. (Oct. 1990, p. 1140) Oberwolfach, Federal Republic of Germany. May 1992 2-9. SIAM Conference on Combustion, St. (Jan. 1991, p. 51) Petersburg, FL.· (Nov. 1990, p. 1289) * 3-9. Wavelett (Signalverarbeitung), Ober- 9-15. Numerical Methods for Parallel Com­ wolfach, Federal Republic of Germany. 7-10. Canadian Mathematical Society Win­ puting, Oberwolfach, Federal Republic of ter Meeting, Victoria, B.C., Canada. (Oct. Germany. (Jan. 1991, p. 51) CHAIRMEN: A. Louis, Berlin; Y. Meyer, 1990, p. 1141) 16-22. Funktiontheorie, Oberwolfach, Fed­ Paris. 8-14. Stochastic Geometry, Geometric eral Republic of Germany. (Jan. 1991, p. 51) INFORMATION: Mathematisches For­ schungsinstitut Oberwolfach Geschiift­ Statistics, Stereology, Oberwolfach, Federal 23-29. p-Adische Analysis und Anwen­ sstelle: Alberstrasse 24 D-7800 Republic of Germany. (Jul./Aug. 1990, p. 746) dungen, Oberwolfach, Federal Republic of Freiburg im Breisgau. 15-21. Quantenstochastik, Oberwolfach, Germany. (Jan. 1991, p. 51) Federal Republic of Germany. (Jul./Aug. 24--28. IEEE Computer Society COMP­ * 10-16. Geschichte der Mathematik, Ober- 1990, p. 746) CON Spring '92, San Francisco, CA. (Jan. wolfach, Federal Republic of Germany. 23-26. International Conference on Gen­ 1990, p. 62) eralized Functions and Their Applications, CHAIRMEN: C.J. Scriba, Hamburg; W. 24--March 1. IMA Workshop on Iterative WuBing, Leipzig. Banaras Hindu University, Varanasi, India. Methods for Sparse and Structured Prob­ (Dec. 1990, p. 1458) INFORMATION: Mathematisches For­ lems, University of Minnesota, Minneapolis, schungsinstitut Oberwolfach Geschiift­ 27-31. Holiday Symposium on the Impact MN. (Oct. 1990, p. 1141) sstelle: Alberstrasse 24 D-7800 of Software Systems in Mathematical Re­ Freiburg im Breisgau. search, New Mexico State Univ., Las Cruces, The following new announcements will not NM. (Jul./Aug. 1990, p. 746) be repeated until the criteria in the last * 11-13. Fourth SIAM Conference on Opti- paragraph in the box at the beginning of mization, Chicago, IL. this section are met. ORGANIZERS: J. More, Argonne Nat'l January 1992 Labs and J. Nocedal, Northwestern Univ. 1-11. Mathematische Optimierung, Ober­ CALL FOR PAPERS: Abstract Deadline: wolfach, Federal Republic of Germany. (Jan. October 11, 1991. April1992 1991, p. 51) INFORMATION: SIAM Conference Dept., 5-8. Second Caribbean Conference on * 5-11. Algebraische K-Theorie, Oberwol- 3600 University City Science Center, the Fluid Dynamics, University of the West fach, Federal Republic of Germany. Philadelphia, PA 19104-2688; 215-382- Indies, St. Augustine, Trinidad. (Jan. 1991, 9800; Fax: 215-386-7999; email: siam@ CHAIRMEN: R.K. Dennis, Ithaca; U. Reh­ wharton.upenn.edu. p. 51) mann, Bielefeld. 8-11. Joint Mathematics Meetings, Balti­ INFORMATION: Mathematisches For­ * 17-23. Quadratische Formen, Oberwolfach, more, MD. (including the annual meetings of schungsinstitut Oberwolfach Geschiift­ Federal Republic of Germany. the AMS, AWM, MAA and NAM) sstelle: A1berstrasse 24 D-7800 CHAIRMEN: M. Knebusch, Regensburg; Freiburg im Breisgau. INFORMATION: H. Daly, AMS, P.O. Box A. Pfister, Mainz; W. Scharlau, Miinster. 6248, Providence, RI 02940. * 12-18. Mathematische Logik, Oberwolfach, INFORMATION: Mathematisches For­ schungsinstitut Oberwolfach Geschiift­ 12-18. Applied Dynamics and Bifurcation, Federal Republic of Germany. sstelle: Alberstrasse 24 D-7800 Oberwolfach, Federal Republic of Germany. CHAIRMEN: W. Felscher, Tiibingen; H. Freiburg im Breisgau. (Jan. 1991, p. 51) Schwichtenberg, Miinchen; A.S. Troelstra, 13-17. IMA Workshop on Linear Algebra, Amsterdam. * 24--30. Kommutative Algebra und Alge-

146 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ______Meetings and Conferences

braische Geometrie, Oberwolfach, Federal of computers in regular and distance teach­ * 26--August 1. Variationsrechnung, Ober- Republic of Germany. ing of science and humanities including wolfach, Federal Republic of Germany. areas such as language learning, medicine, CHAIRMEN: E. Kunz, Regensburg; H.J. CHAIRMEN: J. Jost, Bochum; L. Modica, computer science, business, engineering, Nastold, Miinster; L. Szpiro, Paris. Pisa; E. Zeidler, Leipzig. and others. Workshops and tutorials will INFORMATION: Mathematisches For­ INFORMATION: Mathematisches For­ also be offered. schungsinstitut Oberwolfach Geschaft­ schungsinstitut Oberwolfach Geschaft­ CALL FOR PAPERS: Deadline for sub­ sstelle: Alberstrasse 24 D-7800 sstelle: Alberstrasse 24 D-7800 mission of papers: September 20, 1991. Freiburg im Breisgau. Freiburg im Breisgau. INFORMATION: I. Tomek, Jodrey School * 31-June 6. Singularitaten, Oberwolfach, of Computer Science, Acadia Univ., Wolf­ Federal Republic of Germany. ville, Nova Scotia BOP lXO, Canada. Tel: 902-542-2201, ext. 467; Fax: 902-542- CHAIRMEN: G.-M. Greuel, Kaiserslautern; 7224; email: Bitnet [email protected]. J. Kollar, Salt Lake City; H.M. Steenbrink, Nijmegen. * 21-27. Porous Media, Oberwolfach, Federal INFORMATION: Mathematisches For­ Republic of Germany. August 1992 schungsinstitut · Oberwolfach Geschiift­ CHAIRMEN: J. Douglas, West Lafayette; August 1992. The International Confer­ sstelle: Alberstrasse 24 D-7800 * C.J. van Duijn, Delft; U. Hornung, Neu­ ence Lobachevsky and Modern Geome­ Freiburg im Breisgau. biberg. try devoted to the 200th Anniversary of * 31-June 6. Free Resolutions in Alge- INFORMATION: Mathematisches For­ Lobachevsky's birthday, Kazan, USSR. schungsinstitut Oberwolfach Geschiift­ braic Geometry and Representation Theory, PROGRAM: There will be three sections: sstelle: Alberstrasse 24 D-7800 Oberwolfach, Federal Republic of Germany. Geometry and topology, the theory of Freiburg im Breisgau. CHAIRMEN: W. Bruns, Osnabriick; D. relativity and gravitation, and the history Eisenbud, Waltham; J. Herzog, Essen. * 28-July 4. Hyperbolic Systems of Conser­ of mathematics. INFORMATION: Mathematisches For­ vation Laws, Oberwolfach, Federal Republic INFORMATION: V.V. Vishnevsky, Dept. schungsinstitut Oberwolfach Geschaft­ of Germany. of Geometry, Kazan Univ., 18 Lenin St., sstelle: Alberstrasse 24 D-7800 Kazan, 420008-USSR. CHAIRMEN: C.M. Dafermos, Providence. Freiburg im Breisgau. INFORMATION: Mathematisches For­ * 2-8. Algebraische Zahlentheorie, Oberwol- schungsinstitut Oberwolfach Geschaft­ fach, Federal Republic of Germany. sstelle: Alberstrasse 24 D-7800 June 1992 Freiburg im Breisgau. CHAIRMEN: G. Frey, Essen; H.-W. Leo­ poldt, Karlsruhe; P. Roquette, Heidelberg. * 7-13. Computational Group Theory, Ober- INFORMATION: Mathematisches For­ wolfach, Federal Republic of Germany. July 1992 schungsinstitut Oberwolfach Geschiift­ CHAIRMEN: J. Neubiiser, Aachen; C. sstelle: Alberstrasse 24 D-7800 12-18. Arithmetic Algebraic Geometry, Sims, New Brunswick. * Freiburg im Breisgau. Oberwolfach, Federal Republic of Germany. INFORMATION: Mathematisches For­ * 9-15. Jordan-Algebren, Oberwolfach, Fed- schungsinstitut Oberwolfach Geschiift­ CHAIRMEN: G. Faltings, Princeton; G. eral Republic of Germany. sstelle: Alberstrasse 24 D-7800 Harder, Bonn; N. Katz, Princeton. Freiburg im Breisgau. INFORMATION: Mathematisches For­ CHAIRMEN: K. McCrimmon, Charlottes­ schungsinstitut Oberwolfach Geschiift­ ville; W. Kaup, Tiibingen; H. Petersson, * 14-20. Freiformkurven und Freiform- sstelle: Alberstrasse 24 D-7800 Hagen. flachen, Oberwolfach, Federal Republic of Freiburg im Breisgau. INFORMATION: Mathematisches For­ Germany. schungsinstitut Oberwolfach Geschiift­ 19-24. SIAM Annual Meeting (SIAM's CHAIRMEN: R.E. Barnhill, Tempe; W. * sstelle: Alberstrasse 24 D-7800 40th Anniversary), Los Angeles, CA. Boehm, Braunschweig; J. Hoschek, Darm­ Freiburg im Breisgau. stadt. CALL FOR PAPERS: Abstract deadline: * 23-29. Mathematical Finance, Oberwolfach, INFORMATION: Mathematisches For­ January 6, 1992. Federal Republic of Germany. schungsinstitut Oberwolfach Geschaft­ INFORMATION: SIAM Conference Dept., sstelle: Alberstrasse 24 D-7800 3600 University City Science Center, CHAIRMEN: D. Duffie, Stanford; E. Eber­ Freiburg im Breisgau. Philadelphia, PA 19104-2688; 215-382- lein, Freiburg; S.R. Pliska, Chicago. 9800; Fax: 215-386-7999; email: siam@ INFORMATION: Mathematisches For­ * 17-20. Fourth International Conference wharton. upenn.edu. schungsinstitut Oberwolfach Geschaft­ on Computers and Learning, ICCAL '92, sstelle: Alberstrasse 24 D-7800 Acadia University, Nova Scotia, Canada. * 19-25. Lower-Dimensional Theories and Freiburg im Breisgau. Domain Decomposition Methods in Me­ PROGRAM: ICCAL is devoted to the pre­ chanics, Oberwolfach, Federal Republic of * 30-September 5. Komplexe Analysis, Ober- sentation of new results in the theory Germany. wolfach, Federal Republic of Germany. and practice of computers and learning. Areas proposed include theoretical top­ CHAIRMEN: P. Ciarlet, Paris; K. Kirchgass­ CHAIRMEN: W. Barth, Erlangen; H. ics and their applications such as student ner, Stuttgart. Grauert, Gottingen; R. Remmert, MUnster. models, cognitive science, user interfaces, INFORMATION: Mathematisches For­ INFORMATION: Mathematisches For­ computer learning environments (includ­ schungsinstitut Oberwolfach Geschiift­ schungsinstitut Oberwolfach Geschiift­ ing hypermedia), and intelligent tutoring sstelle: Alberstrasse 24 D-7800 sstelle: Alberstrasse 24 D-7800 systems, as well as innovative applications Freiburg im Breisgau. Freiburg im Breisgau.

FEBRUARY 1991, VOLUME 38, NUMBER 2 147 Meetings and Conferences

* 8-14. Numerische Integration, Oberwol- fach, Federal Republic of Germany. September 1992 October 1992 CHAIRMEN: H. BraB, Braunschweig; G. * 6-12. Topologie, Oberwolfach, Federal Re- * 4-10. Funktionalanalysis, Oberwolfach, Fed- Hiimmerlin, Miinchen. public of Germany. eral Republic of Germany. INFORMATION: Mathematisches For­ CHAIRMEN: M. Kreck, Mainz; A.A. Ran­ CHAIRl\lEN: K.-D. Bierstedt, Paderbom; schungsinstitut Oberwolfach Geschiift­ icki, Edinburgh; L. Siebenmann, Paris. R. Meis, DUsseldorf,; D. Vogt, Wuppertal. sstelle: Alberstrasse 24 D-7800 INFORMATION: Mathematisches For­ INFORMATION: Mathematisches For­ Freiburg im Breisgau. schungsinstitut Oberwolfach Geschiift­ schungsinstitut Oberwolfach Geschiift­ 15-21. Komplexitatstheorie, Oberwolfach, D-7800 sstelle: Alberstrasse 24 D-7800 * sstelle: Alberstrasse 24 Federal Republic of Germany. Freiburg im Breisgau. Freiburg im Breisgau. CHAIRMEN: J. von zur Gathen, Toronto; * 13-19. 4-Dimensional Manifolds, Oberwol- * 11-17. Arbeitsgemeinschaft mit Aktuellem V. Strassen, Konstanz. fach, Federal Republic of Germany. Thema, Oberwolfach, Federal Republic of INFORMATION: Mathematisches For­ Germany. CHAIRMEN: S. Donaldson, Oxford; M. schungsinstitut Oberwolfach Geschiift­ Kreck, Mainz; R.J. Stem, Irvine. INFOR~IATION: Mathematisches For­ sstelle: Alberstrasse 24 D-7800 INFORMATION: Mathematisches For­ schungsinstitut Oberwolfach Geschiift­ Freiburg im Breisgau. schungsinstitut Oberwolfach Geschiift­ sstelle: Alberstrasse 24 D-7800 29-December 5. Theory of Large Devia­ sstelle: Alberstrasse 24 D-7800 Freiburg im Breisgau. * tions, Oberwolfach, Federal Republic of Ger­ Freiburg im Breisgau. * 18-24. Geometrie, Oberwolfach, Federal many. * 16-18. Second SIAM Conference on Con- Republic of Germany. CHAIRI\IEN: E. Bolthausen, Ziirich; J. trol in the 90s, Minneapolis, MN. CHAIRMEN: V. Bangert, Freiburg; U. Gartner, Berlin; S. Varadhan, NY. CALL FOR PAPERS: Abstract deadline: Pinkall, Berlin. INFORMATION: Mathematisches For­ February 14, 1992. INFORMATION: Mathematisches For­ schungsinstitut Oberwolfach Geschiift­ INFORMATION: SIAM Conference Dept., schungsinstitut Oberwolfach Geschiift­ sstelle: Alberstrasse 24 D-7800 3600 University City Science Center, sstelle: Alberstrasse 24 D-7800 Freiburg im Breisgau. Philadelphia, PA 19104-2688; 215-382- Freiburg im Breisgau. 9800; Fax: 215-386-7999: email: siam@ wharton. upenn.edu. * 25-31. Stochastische Analysis, Oberwolfach, Federal Republic of Germany. December 1992 20-26. Funktionalgeichungen, Oberwol- * CHAIRMEN: H. Follmer, Bonn; A.-S. * 6-12. Theory and Numerical Methods for of Germany. fach, Federal Republic Sznitrnan, NY. Initial-Boundary Value Problems, Oberwol­ fach, Federal Republic of Germany. CHAIRMEN: J. Aczel, Waterloo; W. Benz, INFORMATION: Mathematisches . For­ Hamburg; J. Ratz, Bern. schungsinstitut Oberwolfach Geschiift­ CHAIRMEN: H.-0. Kreiss, Los Angeles; INFORMATION: . Mathematisches For­ sstelle: Alberstrasse 24 D-7800 J. Lorenze, Pasadena. schungsinstitut Oberwolfach Geschiift­ Freiburg im Breisgau. INFORMATION: Mathematisches For­ sstelle: Alberstrasse 24 D-7800 schungsinstitut Oberwolfach Geschiift­ Freiburg im Breisgau. sstelle: Alberstrasse 24 D-7800 November 1992 Freiburg im Breisgau. * 27-0ctober 3. Darstellungstheorie Endlicher Gruppen, Oberwolfach, Federal Republic of * 1-7. Kombinatorik, Oberwolfach, Federal * 13-19. Asymptotische Statistik, Oberwol- Germany. Republic of Germany. fach, Federal Republic of Germany. CHAIRMEN: B. Huppert, Mainz; G. Mich­ CHAIRMEN: W. Deuber, Bielefeld; D.M. CHAIRMEN: F. GOtze, Bielefeld; J. Pfan­ ler, Essen. Jackson, Waterloo; D. Jungnickel, GieBen. zagl, KOln. INFORMATION: Mathematisches For­ INFORl\IATION: Mathematisches For­ INFORMATION: Mathematisches For­ schungsinstitut Oberwolfach Geschiift­ schungsinstitut Oberwolfach Geschiift­ schungsinstitut Oberwolfach Geschiift­ sstelle: Alberstrasse 24 D-7800 sstelle: Alberstrasse 24 D-7800 sstelle: Alberstrasse 24 D-7800 Freiburg im Breisgau. Freiburg im Breisgau. Freiburg im Breisgau.

148 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

1980 Mathematics Subject Classifications: 90005; 94S99 ISBN 0-8218-0166-X, LC 90-22771, ISSN 0160-7634 COMBINATORIAL GAMES 233 pages (hardcover), February 1991 Richard K. Guy, Editor Individual member $31, List price $52, (Proceedings of Symposia in Applied Mathematics, Volume 43) Institutional member $42 To order, please specify PSAPM/43N "The subject of combinatorics is only slowly acquiring respectability and combinatorial games will clearly take longer than the rest of combinatorics. Perhaps this partly stems from the puritanical view that anything amusing can't possibly involve any MATHEMATICAL DEVELOPMENTS ARISING worthwhile mathematics."-from the Preface FROM LINEAR PROGRAMMING Based on lectures presented at the AMS Short Course on Jeffrey C. Lagarias and Michael J. Todd, Combinatorial Games, held at the Joint Mathematics Meetings in Columbus in August 1990, the ten papers in this volume will Editors provide readers with insight into this exciting new field. Because (Contemporary Mathematics, Volume 114) the book requires very little background, it will likely find a wide In recent years, there has been intense work in linear and audience that includes the amateur interested in playing games, nonlinear programming, much of it centered on understanding the undergraduate looking for a new area of study, instructors and extending the ideas underlying N. Karmarkar's interior-point seeking a refreshing area in which to give new courses at both linear programming algorithm, which was presented in 1984. the undergraduate and graduate levels, and graduate students This interdisciplinary research was the subject of an AMS looking for a variety of research topics. Summer Research Conference on Mathematical Developments In the opening paper, Guy contrasts combinatorial games, Arising from Linear Programming, held at Bowdoin College in which have complete information and no chance moves, with the summer of 1988, which brought together researchers in those of classical game theory. Conway introduces a new mathematics, computer science, and operations research. This theory of numbers, including infinitesimals and transfinite volume contains the proceedings from the conference. numbers, which has emerged as a special case of the theory of Among the topics covered in this book are: completely games. Guy describes impartial games, with the same options integrable dynamical systems arising in optimization problems, for both players, and the Sprague-Grundy theory. Conway Riemannian. geometry and interior-point linear programming discusses a variety of ways in which games can be played methods, concepts of approximate solution of linear programs, simultaneously. Berlekamp uses the theory of "hot" games to average case analysis of the simplex method, and recent results make remarkable progress in the analysis of Go Endgames. in convex polytopes. Some of the papers extend interior-point Pless demonstrates the close connection between several methods to quadratic programming, the linear complementarity impartial games and error-correcting codes. Fraenkel explains problem, convex programming, multi-criteria optimization, the way in which complexity theory is very well illustrated by and integer programming. Other papers study the continuous combinatorial games, which supply a plethora of examples of trajectories underlying interior point methods. This book will be an harder problems than most of those which have been considered excellent resource for those interested in the latest developments in the past. Nowakowski outlines the theory of three particular arising from Karmarkar's linear programming algorithm and in games-Welter's Game, Sylver Coinage, and Dots-and-Boxes. path-following methods for solving differential equations. A list of three dozen open problems and a bibliography of 400 items are appended. Contents 1. Recent progress and new directions: Carl W. Lee, Some recent Contents results on convex polytopes; Karl Heinz Borgwardt, Probabilistic analysis of the simplex method; Nimrod Megiddo, On solving the linear Richard K. Guy, What is a game?; John Horton Conway, Numbers and programming problem approximately; Narendra Karmarkar, Riemannian games; Richard K. Guy, Impartial games; John Horton Conway, More geometry underlying interior-point methods for linear programming; ways of combining games; Elwyn R. Berlekamp, Introductory overview A. M. Bloch, Steepest descent, linear programming, and Hamiltonian of mathematical go endgames; Vera Pless, Games and codes; Aviezri flows; 2. Interior-point methods for linear programming: Yinyu Ye, S. Fraenkel, Complexity of games; Richard J. Nowakowski, ... , Welter's An O(n3 L) potential reduction algorithm for linear programming; R. J. game, Sylver coinage, dots-and boxes, ... ; Richard K. Guy, Unsolved Vanderbei and J. C. Lagarias, I. I. Dikin's convergence result for the problems in combinatorial games; Aviezri S. Fraenkel, Selected affine-scaling algorithm; Irvin J. Lustig, Phase 1 search directions bibliography on combinatorial games and some related material. for a primal-dual interior point method for linear programming; Earl R.

Use the order form in the back of this issue or call 800-321-4AMS (800-321-4267) in the U.S. and Canada to use VISA or MasterCard.

FEBRUARY 1991, VOLUME 38, NUMBER 2 149 ·········-·--······"''''"'"''' ······························-·-··-······-··"""'"""""'"''''''"''"''"''''"''"''''''"""'''''"''''''''-'''''"''"'''"'______.. ,_,____ ...... _.. _...... _...... _... ,...... -...... -...... _,_,_,_,_, __ New AMS Publications

Barnes, Some results concerning convergence of the affine scaling Contents algorithm; Kurt M. Anstreicher, Dual ellipsoids and degeneracy in the Polynomial identity rings; The standard polynomial and the Amitsur­ projective algorithm for linear programming; Miroslav D. Asic, Vera v. Levitzki theorem; Central polynomials; Posner's theorem and the ring Kovacevic-Vujcic, and Mlrjana D. Radosavljevic-Nikolic, A note on of generic matrices; The center of the generic division ring; The Capelli limiting behavior of the projective and the affine rescaling algorithms; polynomial and Arlin's theorem; Representation theory of the symmetric 3. Trajectories of interior-point methods: Christoph Witzgall, Paul and genera/linear groups; The first and second fundamental theorems T. Boggs, and Paul D. Domich, On the convergence behavior of of matrix invariants; Applications of the first and second fundamental trajectories for linear programming; llan Adler and Renato D. C. theorems; The Nagata-Higman theorem and matrix invariants. Monteiro, Limiting behavior of the affine scaling continuous trajectories 1980 Mathematics Subject for linear programming problems; Renato D. C. Monteiro, Convergence Classification: 16A38 ISBN 0-8218-0730-7, LC 90-22966, ISSN 0160-7642 and boundary behavior of the projective scaling trajectories for linear 57 pages (softcover), February 1991 programming; 4. Nonlinear optimization: F. Jarre, G. Sonnevend, All individuals $13, List price $22 and J. Stoer, On the complexity of a numerical algorithm for solving To order, please specify CBMS/78N generalized convex quadratic programs by following a central path; Bah man Kalantari, Canonical problems for quadratic programming and projective methods for their solution; Sanjay Mehrotra and Jie Sun, An interior point algorithm for solving smooth convex programs based on MINIMAL SURFACES, STRATIFIED Newton's method; A. A. Goldstein, A modified Kantorovich inequality MULTIVARIFOLDS, AND THE PLATEAU for the convergence of Newton's method; 5. Integer programming and multi-objective programming: Narendra Karmarkar, An interioropoint PROBLEM approach to NP-complete problems-Part I; John E. Mitchell and Dao Trc~mg Thi and A. T. Fomenko Michael J. Todd, Solving matching problems using Karmarkar's (Translations of Mathematical Monographs, Volume 84} algorithm; S. S. Abhyankar, T. L. Morin, and T. Trafalis, Efficient faces of polytopes: Interior point algorithms, parameterization of algebraic Plateau's problem is a scientific trend in modern mathematics varieties, and multiple objective optimization. that unites several different problems connected with the study of minimal surfaces. In its simplest version, Plateau's problem 1980 Mathematics Subject Classifications: 90C, 65K, 490; 52A25, 58F07 is concerned with finding a surface of least area that spans ISBN 0-8218-5121-7, LC 90-22942, ISSN 0271-4132 a given fixed one-dimensional contour in three-dimensional 341 pages (softcover), February 1991 space-perhaps the best-known example of such surfaces is Individual member $35, List price $59, provided by soap films. From the mathematical Institutional member $47 point of view, To order, please specify CONM/114N such films are described as solutions of a second-order partial differential equation, so their behavior is quite complicated and has still not been thoroughly studied. Soap films, or, more generally, interfaces between physical media in equilibrium, arise THE POLYNOMIAL IDENTITIES AND in many applied problems in chemistry, physics, and also in INVARIANTS OF n x n MATRICES nature. In applications, one finds not only two-dimensional but Edward Formanek also multidimensional minimal surfaces that span fixed closed (CBMS Regional Conference Series, Number 78 "contours" in some multidimensional Riemannian space. An Supported by the National Science Foundation) exact mathematical statement of the problem of finding a surface The theory of polynomial identities, as a well-defined field of of least area or volume requires the formulation of definitions of study, began with a well-known 1948 article of Kaplansky. The such fundamental concepts as a surface, its boundary, minimality field has since developed along two branches: the structural, of a surface, and so on. It turns out that there are several natural which investigates the properties of rings which satisfy a definitions of these concepts, which permit the study of minimal polynomial identity; and the varietal, which investigates the set of surfaces by different, and complementary, methods. polynomials in the free ring which vanish under all specializations In the framework of this comparatively small book it would be in a given ring. almost impossible to cover all aspects of the modern problem of This book is based on lectures delivered during an Plateau, to which a vast literature has been devoted. However, NSF-CBMS Regional Conference, held at DePaul University in this book makes a uniqije contribution to this literature, for the July 1990, at which the author was the principal lecturer. The first authors' guiding principle was to present the material with a part of the book is concerned with polynomial identity rings. The maximum of clarity and a minimum of formalization. emphasis is on those parts of the theory related to n x n matrices, Chapter 1 contains historical background on Plateau's including the major structure theorems and the construction of problem, referring to the period preceding the 1930s, and a certain polynomial identities and central polynomials for n x n description of its connections with the natural sciences. This part matrices. The ring of generic matrices and its center is described. is intended for a very wide circle of readers and is accessible, The author then moves on to the invariants of n x n matrices, for example, to first-year graduate students. The next part of the beginning with the first and second fundamental theorems, which book, comprising Chapters 2-5, gives a fairly complete survey are used to describe the polynomial identities statisfied by n x n of various modern trends in Plateau's problem. This section is matrices. accessible to second- and third-year students specializing in One of the exceptional features of this book is the way it physics and mathematics. The remaining chapters present a emphasizes the connection between polynomial identities and detailed exposition of one of these trends (the homotopic version invariants of n x n matrices. Accessible to those with background of Plateau's problem in terms of stratified multivarifolds) and the at the level of a first-year graduate course in algebra, this book Plateau problem in homogeneous symplectic spaces. This last gives readers an understanding of polynomial identity rings and part is intended for specialists interested in the modern theory invariant theory, as well as an indication of current problems and of minimal surfaces and can be used for special courses; a research in these areas. command of the concepts of functional analysis is assumed.

150 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·······························-······------New AMS Publications

Contents Contents Historical survey and introduction to the classical theory of minimal A. M. Vershik, Local stationary algebras; E. B. Vinberg, The surfaces; Information about some topological facts used in the modern volume of polyhedra on a sphere and in Lobachevsky space; S. G. theory of minimal surfaces; The modern state of the theory of minimal Gindikin, Integral geometry on symmetric manifolds; E. I. Zel'manov, surfaces; The multidimensional Plateau problem in the spectral class Superalgebras and identities; B. I. Zil'ber, Algebraic geometry and of all manifolds with a fixed boundary, Multidimensional minimal combinatorics: the model-theoretic point of view; Yu. S. ll'yashenko, surfaces and harmonic maps; Multidimensional variational problems and Finiteness theorems for limit cycles; A. R. Kerner, Identities of multivarifolds. The solution of Plateau's problem in the homotopy class associative algebras; G. A. Margulis, Lie groups and ergodic theory; of a map of a multivarifold; The space of multivarifolds; Parametrizations A. L. Onishchik, Lie superalgebras of vector fields; V. L. Popov, and parametrized multivarifolds; Problems of minimizing generalized Invariant theory. integrands in classes of parametriza.tions and parametrized multivarifolds. 1980 Mathematics Subject Classification: A criterion for global minimality, Criteria for global minimality, Globally ISBN 0-8218-3700-1, ISSN 0065-9290 minimal surfaces in regular orbits of the adjoint representation of the 112 pages (hardcover). February 1991 classical Lie groups. Individual member $38, List price $63, Institutional member $50 1980 Mathematics Subject Classifications: 49F1 0, 53A 10; 58E12, 58E20 To order, please specify TRANS2/148N ISBN 0-8218-4536-5, LC 90-22932, ISSN 0065-9282 404 pages (hardcover), February 1991 Individual member $91, List price $152, The following videotapes are now available through the AMS. Institutional member $122 To order, please specify MMON0/84N

CASE STUDY OF POLITICAL OPINIONS Addition to Translations-Series 2 PASSED OFF AS SCIENCE AND MATHEMATICS In the Soviet Union, regional mathematics conferences, or Serge Lang "schools," are periodically conducted to bring researchers In this fascinating videotaped presentation, Serge Lang together for several days to focus on topics of current interest. discusses his nationally publicized battle against what he sees as Led by eminent Soviet mathematicians, the schools typically quantitative verbiage used by some people in the social sciences draw the top experts from the Soviet mathematical community in the process of passing off political opinions as science. The and produce proceedings consisting of ten to fifteen papers. central part of the lecture focuses on some works of Samuel These papers have been unavailable in English and difficult to Huntington, a well-known political scientist who was rejected by obtain outside of the USSR. the National Academy of Sciences, partly as a result of Lang's Now these papers will be available in English translation campaign against him. Quoting from original sources, Lang as part of the AMS book series, Translations - Series 2. documents how Huntington, and other authors whom Huntington The first collection of these proceedings, The First Siberian mentions uncritically, not only misused what some people call School "Algebra and Analysis", will appear this month and mathematics in the way they assigned numerical values to is described below. Proceedings of the Second Siberian various social phenomena (such as a "frustration index" for a School "Algebra and Analysis," and of the All-Union School society), but also misrepresented historical facts. Lang describes on operator theory in function spaces (held in Kuibyshev), are some reactions in the social science community and in the scheduled to appear later this year. press, as well as those of several students who have used Huntington's textbooks in their classes. Never one to shy away from controversy over causes he believes in, Lang has devoted a great deal of time and energy to what he sees as a crucial fight for standards and integrity in academia. His story raises FIRST SIBERIAN WINTER SCHOOL challenging questions about the standards that scholars set for "ALGEBRA AND ANALYSIS" themselves, their institutions, and their colleagues. The lecture A. D. Aleksandrov, 0. V. Belegradek, I. A. would be suitable for students and scholars in any academic Bokut', and Yu. L. Ershov, Editors discipline. A writeup of the talk, with references, is included. (American Mathematical Society Translations, 1980 Mathematics Subject Classification: 00 Series 2, Volume 148) ISBN 0-8218-8037-3 NTSC format on 1/2" VHS videotape; approx. one hour, This collection consists of lectures delivered at the First January 1991 Siberian Winter School, "Algebra and Analysis," held in March Price $59 1987 at a retreat near Kemerovo. The school was organized by To order, please specify VIDLANG/N Kemerovo State University and the Institute of Mathematics of the Siberian Branch of the Academy of Sciences of the USSR. The conference drew more than one hundred participants from Novosibirsk, Kemerovo, Omsk, Moscow, Leningrad, and other A CENTURY OF REPRESENTATION THEORY Soviet cities. OF FINITE GROUPS The aim of the school was to organize a system of contacts between algebraists and those working in analysis, in the broad Charles W. Curtis sense of the term. The lectures acquainted the participants with In this videotaped lecture, Charles W. Curtis presents an current research in algebra and areas at the interface of algebra overview of the historical development of the representation and analysis. theory of finite groups. Starting with the roots of the subject in

FEBRUARY 1991, VOLUME 38, NUMBER 2 151 New AMS Publications

Gauss' work, Curtis covers Frobenius' research in character theory and Burnside's work in representation theory around the turn of the century. He indicates how Burnside's research led to the landmark Fait-Thompson theorem about groups of odd order and discusses the contributions of Noether and Brauer, who were also prominent players in the development of representation theory. Curtis' clear and absorbing lecture provides an excellent balance of historical development and mathematical detail that allows for appreciation of the richness of this subject. The lecture should be accessible to undergraduates with background in algebra and group theory. Mathematical Surveys and Monographs, Volume 35 1980 Mathematics Subject Classifications: 20C15, 20C20, 20C05 ISBN 0-8218-8038-1 NTSC format on 1/2" VHS videotape; approx. one hour, This book, based on lectures presented in courses January 1991 on algebraic geometry taught by the author at Price $59 To order, please specify VIDCURTIS/N Purdue University, is intended for engineers and scientists (especially computer scientists), as well as graduate students and advanced under­ NATURAL MINIMAL SURFACES VIA THEORY graduates in mathematics. In addition to provid­ AND COMPUTATION ing a concrete or algorithmic approach to alge­ David Hoffman braic geometry, the author also attempts to Mathematicians have been interested in area-minimizing surfaces for hundreds of years, from both the geometric motivate and explain its link to more modem and analytic points of view. The same surfaces have been algebraic geometry based on abstract algebra. investigated by experimental scientists in more than one field. The book covers various topics in the theory of In recent years, computation and graphical methods have been employed in both the theoretical investigation of these algebraic curves and surfaces, such as rational mathematical objects and in the applications of this knowledge and polynomial parametrization, functions and of surfaces to the investigation of microstructure in compound materials. In this videotaped presentation, Hoffman covers differentials on a curve, branches and valu­ the basic analysis and geometry necessary to understand the ations, and resolution of singularities. The mathematical study of minimal surfaces and also discusses the emphasis is on presenting heuristic ideas and computer techniques employed in recent discoveries of families of new examples. Many beautiful computer-generated images of suggestive arguments rather than formal proofs. these examples are shown. Hoffman also presents some of the Readers will gain new insight into the subject of recent applications to the study of block copolymers. algebraic geometry in a way that should increase 1980 Mathematics Subject Classification: 53 ISBN 1-87831 0-1 0-0 appreciation of modem treatments of the sub­ NTSC format on 1/2" VHS videotape; approx. one hour, ject, as well as enhance its utility in applications January 1991 Price $59 in science and industry. To order, please specify VIDHOFFMAN/N

ERRATA: The new publication listing for Theories of 1980 Mathematics Subject Classifications: 14 Singularities and its Applications (ADVSOV/1 N), in the ISBN 0-8218-1535-0, LC 90-815, ISSN 0076-5376 October 1990 Notices, p. 1142, was listed as a softcover book 295 pages (hardcover), October 1990 when it should have been listed as a hardcover book. Individual member $52, List price $87, Institutional member $70 To order, please specify SURV/35NA

All prices subject to change. Free shipment by surface; for air delivery, please add $6.50 per title. Prepayment required. Order from American Mathematical Society, P .0. Box 1571, Annex Station, Providence, RI 0290 1-1571, or call toll free 800-321-4AMS (321-4267) in the continental U.S. and Can­ ada to charge with Visa or MasterCard.

152 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications

Recent Appointments Leo P. Comerford, Jr. and Robert M. Salah Baouendi (1992) and E. Megginson were appointed by Ex­ Carol L. Walker (1992) were reap­ Committee members' terms of of­ President William Browder as Tellers pointed to the Committee on Agenda for fice on standing committees expire for the election of 1990. the Business Meeting by Ex-President on January 31 following the year Dusa McDuff (1993) and Nancy William Browder. The other member given in parentheses following their K. Stanton (1993) were appointed by of the committee is Robert M. Fossum, names, unless otherwise specified. Ex-President William Browder to the chair. Program Committee for National Meet­ Peter W. K. Li (1993) and Haynes Peter J. Weinberger (1993) was reap­ ings. Jean E. Taylor (1991) was reap­ R. Miller (1993) were appointed by pointed and as chair to the Visiting pointed as chair. Continuing members Ex-President William Browder to the Committee on Computer Operations and of the committee are James G. Arthur Committee on Progress in Mathemat­ Facilities by then chair of the Board (1991), Spencer Bloch (1992), Robert ics. Hyman Bass (1992) was appointed of Trustees, Ronald L. Graham. Con­ M. Fossum (ex officio), and Peter Sar­ chair. Continuing members of the com­ tinuing members of the committee are nak (1991). mittee are Armand Borel (1991) and Ronald L. Graham (ex officio), Richard John M. Franks (1992) and Jang­ Alan D. Weinstein (1991). Mandelbaum (1992), and Jill P. Mesirov Mei Wu (1992) were appointed by Josefina Alvarez (1993) and Law­ (1991). Ex-President William Browder to the rence E. Morris (1993) were appointed Frederick W. Gehring (1992) was Central Section Program Committee. to the Committee on Academic Free­ reappointed by then chair of the Board Robert Griess (1991) was appointed dom, Tenure, and Employment Secu­ of Trustees, Ronald L. Graham, to the chair. Continuing members of the com­ rity by Ex-President William Browder. Committee on Investment. Continuing mittee are Carolyn S. Gordon (1991) Mary Ellen Rudin (1992) was appointed members of the committee are Steve and Andy Roy Magid (ex officio). chair. Continuing members of the com­ Armentrout (ex officio) and Franklin P. John C. Moore (1992), Lesley M. mittee are Ellis Kolchin (1992), Charles Peterson (ex officio). Sibner (1992), and Gregg J. Zuckerman E. Rickart (1991), and Gail S. Young M. Salah Baouendi (1993) was (1993) were appointed by Ex-President (1992). appointed and Frederick W. Gehring William Browder to the Eastern Sec­ Harvey B. Keynes (1992) was ap­ (1992) was reappointed and as chair to tion Program Committee. Richard N. pointed by Ex-President William Brow­ the Committee on Membership by then Lyons (1991) was appointed chair. The der to the Committee on Education. chair of the Board of Trustees, Ronald continuing member of the committee is Continuing members of the committee L. Graham. Other members of the com­ W. Wistar Comfort (ex officio). are Michael Artin (ex officio), Ramesh mittee are Carol-Ann Blackwood, con­ Ex-President William Browder ap­ A. Gangolli ( 1992), chair, Andrew M. sultant, Susan Friedlander (1992 ), and pointed Sue E. Goodman (1992) and Gleason (1992), Fern Y. Hunt (1992), Hugo Rossi (1991). Carl Pomerance (1992) to the South­ William H. Jaco (ex officio), Don J. Steve Armentrout (1993) was reap­ eastern Section Program Committee. Lewis (1992), Michael C. Reed (ex pointed by then chair of the Board Ronald F. Gariepy (1991) was ap­ officio), Richard C. Tapia (1992), and of Trustees, Ronald L. Graham, to pointed chair. Continuing members of Alan C. Tucker (1993). The Publication Program Committee. the committee are Joseph A. Cima (ex Wen-Ching Winnie Li ( 1993), Hung­ Continuing members of the committee officio) and Edward B. Saff (1991). Hsi Wu (1993), were appointed and Al­ are Robert Devaney (1992), Robert M. Janos Kollar (1992) and Ronald ice T. Schafer (1993) was reappointed Fossum (ex officio), Eric Friedlander J. Stern ( 1992) were appointed by and as chair to the Committee on Hu­ (1992), Ramesh A. Gangolli (1992), Ex-President William Browder to the man Rights of Mathematicians by Ex­ chair, William H. Jaco (ex officio), Western Section Program Committee. President William Browder. Continu­ Cathleen S. Morawetz (1991), Andrew Michael G. Crandall (1991) was ap­ ing members are Raymond G. Ayoub M. Odlyzko (1992), John C. Polking pointed chair. Continuing members of (1991), Joan S. Birman (1992), Chan­ (ex officio), and Paul J. Sally, Jr. (ex the committee are Michael Aschbacher dler Davis (1991), Cora S. Sadosky officio). (1991) and Lance W. Small (ex officio). (1992), and Steven Weintraub (1992).

FEBRUARY 1991. VOLUME 38, NUMBER 2 153 ------··-··-···-······················································-············-·-·································· AMS Reports and Communications

David W. Ballew (1993), Lynne members of the committee are Robert Past President Lida K. Barrett M. Butler (1993), and Bruce Reznick M. Thrall (1993) and Daniel H. Wagner (MAA) and Ex-President William Brow­ (1993) were appointed by Ex-President (1993). der (AMS) appointed H. Hope Daly, William Browder to the Pi Mu Epsilon Arunas Liulevicius (AMS, 1993) consultant, Robert M. Fossum (AMS), Liaison Committee. Continuing mem­ and Washek Pfeffer (AMS, 1992) were William H. Jaco (AMS), Gerald J. bers of the committee are Rhonda J. appointed to the joint AMS-ASL-IMS­ Porter (MAA), Kenneth A. Ross (MAA). Hughes (1991), Eileen Poiani (1992), SIAM Committee on Translations from and John M. Smith (MAA) to the and Carol L. Walker (1991), chair. Russian and Other Slavic Languages. joint AMS-MAA Committee on Sum­ Leonard D. Berkovitz (1993) and Continuing members of the AMS sub­ mer Meetings. Dr. Jaco and Professor Judith Roitman (1993) were appointed committee are V. I. Arnol' d, consultant, Ross will serve as co-chairs. to the Committee on Professional Ethics David G. Ebin (1991), S. G. Gindikin, Stanley Benkoski (AMS, 1993) was by Ex-President William Browder. Con­ consultant, Askol' d Georgievic Kho­ appointed to the AMS-MAA-SIAM tinuing members of the committee are vanskii, consultant, Peter Landweber Joint Committee on Employment Op­ Harold M. Edwards (1991), Everett (1991), chair, Alexander Lichtman portunities by Ex-President William Pitcher (1992), chair, and George B. (1991), N. K. Nikol'skii, consultant. Browder. Continuing members of the Seligman (1991). The ASL subcommittee members are committee are Peter E. Castro (SIAM, Ex-President William Browder ap­ Vladimir Lifschitz (1993), Elliott Men­ 1992), Ronald M. Davis (MAA, 1993), pointed James A. Donaldson (1993), delson (1992), chair, Grigori Mints James W. Maxwell (ex officio), S. Brent Rhonda J. Hughes (1993), and Frank (1993), and Benjamin F. Wells (1992). Morris (AMS, 1991), Marc A. Rieffel W. Warner III (1993) to the Com­ The IMS subcommittee members are (MAA, 1991), and Leon H. Seitelman mittee on Science Policy. Michael C. M. I. Freidlin, chair, B. Pittel, A. (SIAM, 1991), chair. Reed (1992) was reappointed chair. Rukhin, and W. J. Studden. Past President Ivar Stakgold (SIAM) Continuing members of the committee Edward A. Connors (AMS, 1993) and Ex-President William Browder are Michael Artin (ex officio), William and Donald E. McClure (AMS, 1993) (AMS), appointed James M. Hyman Browder (ex officio), Ramesh A. Gan­ were reappointed by Ex-President Wil­ (1993) and Michael Shub (1993) to the golli (ex officio), William H. Jaco (ex liam Browder to the joint AMS-MAA joint AMS-SIAM Committee on Ap­ officio), Joseph J. Kohn (1992), Joel L. Data Committee. Professor McClure plied Mathematics. Continuing mem­ Lebowitz (1992), Jerrold E. Marsden was appointed chair. Continuing mem­ bers of the committee are Andrew (1991), Cathleen S. Morawetz (1991), bers of the committee are Lincoln J. Majda (1992), Lawrence A. Shepp Oscar S. Rothaus (1991), Paul J. Sally, K. Durst, consultant, John D. Fulton (1991), Joel Spencer (1992), and Gilbert Jr. (1992), David A. Vogan, Jr. (1991), (MAA, 1991), James F. Hurley (AMS, Strang (1991), chair. and Mary F. Wheeler (1992). 1991), Charlotte Lin (AMS, 1992), Donovan H. Van Osdol (1992) Ronald G. Douglas was appointed Don 0. Loftsgaarden (MAA, 1993), was appointed as representative to the chair to the Committee to Select the David J. Lutzer (MAA, 1993), James MAA Committee on Guidelines by Ex­ Winner of the Public Service Award by W. Maxwell (ex offico), and Donald C. President William Browder. Ex-President William Browder. Other Rung (AMS, 1992). Harvey B. Keynes (1992) and Kathy members of the committee are Robert Clayton Dodge, Pao Sheng Hsu, M. O'Hara (1993) were appointed by M. Fossum (ex officio), John C. Polk­ Philip Locke, John Mairhuber, Grat­ Ex-President William Browder as rep­ ing, and David P. Roselle. tan Murphy, Charles Slavin, Donald resentatives to the MAA Committee on Sylvain E. Cappell (1993), Harry B. Small, and William Soule were ap­ Undergraduate Program in Mathemat­ Kesten (1993), and Joseph J. Kohn pointed by Past President Lida K. Bar­ ics. (1993) were appointed by Ex-President rett (MAA) and Ex-President William William Browder to the Committee Browder (AMS) to the joint AMS­ The November Meeting on the Steele Prize. Mark Mahowald MAA Arrangements Committee for the in Denton · (1992) was appointed chair. Contin­ Orono Meeting. Professor Murphy was The 866th meeting of the Society was uing members of the commitee are appointed chair. Ex officio members of held in Denton, Texas at the Univer­ Alexandre J. Chorin (1992), Charles L. the committee are Joseph A. Cima, sity of North Texas, November 2 and Fefferman (1991), William J. Haboush William H. Jaco, and Kenneth A. 3, 1990. There were 364 registrants, (1992), Jun-ichi Igusa (1991), Arthur Ross. including 289 members of the Society. M. Jaffe (1992), and George Lusztig Past President Lida K. Barrett Invited Addresses. By invitation (1992). Terms expire on June 30. (MAA) and Ex-President William Brow­ of the Central Section Program Com­ Beresford N. Parlett (1992), Fred der (AMS) appointed Peter Gilkey mittee there were four invited ad­ S. Roberts (1992), and M. Beth Ruskai (AMS), Gerald J. Porter (MAA), Jean dresses. The speakers, their affilia­ (1992) were appointed to the Commit­ E. Taylor (AMS) and Audrey A. Terras tions, and their titles were as fol­ tee on Cooperative Symposia by Ex­ (MAA) to the AMS-MAA Joint Pro­ lows: AVNER AsH, Ohio State Uni­ President William Browder. Professor gram Committee for the Orono Meeting. versity, Galois representations attached Ruskai was appointed chair. Continuing Professor Terras was appointed chair. to GL(n, Z); PETER S. CoNSTATIN,

154 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ················································--···-·····-··"·······························-·······-······························-···'"''-"''______...... ,_ .... ,_,.. ,,. .. ,_ ...... -...... AMS Reports and Communications

University of Chicago, Navier-Stokes W. Heinzer, E. Houston, J. Huckaba, R. Shivaji, J. Albert, H. Zou, W. Run­ equations: Some new results and di­ M. Roitman, S. Huckaba, K. Raghavan, dell, C. Ahlbrandt, R. Showalter, A. rections; JOHN E. LUECKE, Univer­ I. Swanson, K. Loper, T. Marley, R. Tzavaras, G. Hetzer, J. Douglas, L. sity of Texas at Austin, Combinatorics Weigand, S. Weigand, M. Zafrullah, Shampine, L. White, G. Fix, J. Can­ of intersecting surfaces in 3-manifolds; and S. Palmer. non, R. Landes, and R. Kannan. CLARENCE W. WILKERSON, Purdue Texas topology and geometry, DAN­ Algebraic geometry, PETER F. University, Classifying spaces and finite IELS. FREED and ROBERT F. WIL­ STILLER, Texas A&M University. loop spaces. LIAMS, University of Texas at Austin, Speakers were: J. Hoffman, R. Lax, M. Special Sessions. By invitation of and MICHAEL WOLF, Rice University. Lee, C. Schwartz, M. Spurr, A. Adolph­ the same committee, there were 11 Speakers were: R. Franz, D. Swearin­ son, P. Aluffi, B. Crauder, B. Gordon, Special Sessions of selected 20 minute gen, R. de la Llave, M. Ross, T. H. Grundman, S. Katz, A. Lopez, C. papers. The topics, the names and af­ Lohrenz, A. Basmajian, B. Kasper, J. Borcea, W. Hoyt, M. Kuwata, Y. Ye, B. filiations of the organizers, and ~ Rade, L. Tuckermann, A. Norton, R. Harbourne, W. McCallum, P. Stiller, D. speakers were as follows: Mauldin, S. Williams, T. Otway, D. Ulhmer, D. Jaffee, and F. Cukierman. Arithmetic groups, AVNER AsH, Silver, D. Lathrop, C. Poon, and G. Several complex variables, EMIL Ohio State University and MARK Kamberov. J. STRAUBE, Texas A&M University. REEDER, University of Oklahoma. The probability theory of patterns Speakers were: D. Barrett, Z. Slod­ Speakers were B. Gordon, M. Reeder, and runs, AN ANT P. GODBOLE, Michi­ kowski, G. Harris, J. D'Angelo, D. L. Rudolph, A. Brownstein, S. Wein­ gan Technological University. Speakers Tartakoff, J. McNeal, R. Diaz, J. Polk­ traub, R. Lee, A. Reid, D. Grenier, A. were: S. Goloumb, B. Tang, E. Schus­ ing, H. Boas, S. Chen, S. Chiappari, J. Terras, and M. McConnell. ter, M. Leung, H. Zhang, M. Agin, Fornaess, L. Lempert, E. Gavosto, and Geometric inequalities and convex · S. Khunger, M. Gornowicz, S. Papas­ M. Peloso. bodies, lLYA BAKELMAN, Texas A&M tavridis, J. Fu, W. Griffith, and A. Contributed Papers. There were University. Speakers were: Ilya Bakel­ Godbole. two sessions of contributed 10 minute man, P. Bauman, J. Iaia, R. McOwen, Low dimensional topology, JOHN papers. The session on Algebra, Ge­ J. Beem, S. Fulling, P. Goodey, H. LUECKE, University of Texas at Austin ometry and Analysis was chaired by Groemer, E. Lutwak, R. Showalter, B. and ROBERT MYERS, Oklahoma State David Appling of the University of Dekster, P. Ehrlich, M. Gage, F. Nar­ University. Speakers were: D. McCul­ North Texas; two papers were pre­ cowich, A. Triebergs, R. Vitale, X. lough, K. Jones, M. Saito, S. Brick, A. sented. The session on Geometry was Zhou, G. Liao, S. Talliaferro, T. Vogel, Miller, J. Hoste, T. Cochran, P. Gilmer, chaired by Melvin Hagen of the Uni­ H. Wente, X. Cheng, and E. Grinberg. K. Miyazaki, J. Hempel, D. Wright, B. versity of North Texas; two papers were Banach spaces-functional analysis, Winters, W. Kazez, J. Berge, S. Beiler, presented. ELIZABETH M. BATOR, RUSSELL G. J. Carter, P. Sundheim, and W. Whitten. Committee. Melvin Hagen and BILYEU, and PAUL W. LEWIS, Uni­ Representation theory ofLie groups, John Ed Allen of the University of versity of North Texas. Speakers were LISA MANTINI and ROGER ZIERAU, North Texas supervised local arrange­ D. Alspach, K. Andrews, E. Bator, T. Oklahoma State University. Speakers ments. The University, which is cel­ Schlumprecht, S. Dilworth, P. Dowling, were: D. Milicic, M. Candia, B. Bine­ ebrating its centennial year, provided P. Greim, C. Schumacher, B. Lin, E. gar, L. Casian, T. Enright, S. Salamanca­ morning and afternoon refreshments to Odell, R. Phelps, H. Rosenthal, E. Saab, Riba, T. Przebinda, S. Sahi, M. David­ the meeting participants, and arranged P. Saab, J. Whitfield, G. Stefansson, T. son, R. Stanke, H. Hecht, J. Chang, H. for the National Atomic Museum's ex­ Randolph, P. Patterson, M. Gruenwald, Prado, C. Pfeffer, B. Currey, J. Cygan, hibit "Adventures of a Mathematician," and S. Montgomery-Smith. R. Kunze, J. Gilbert, L. Barchini, J. chronicling the life of the late Stanislaw Commutative algebra, ScoTT T. Huang, W. McGovern, and B. Boe. Ulam, to be displayed at the meeting. CHAPMAN, Trinity University, and Differential equations, JOHN W. NICK H. VAUGHN, University of North NEUBERGER and HENRY A. WAR­ Texas. Speakers were: D. Lantz, S. CRALL, University of North Texas. Andy Roy Magid McAdam, J. Mott, S. Chapman, D. D. Speakers were: C. Foias, R. Kauff­ Associate Secretary Anderson, D. F. Anderson, D. Dobbs, man, B. Loe, M. Kwong, M. Lapidus, Norman, Oklahoma

FEBRUARY 1991, VOLUME 38, NUMBER 2 155 ------·························· ... ··································· ... ·············· Classified Advertisements

SUGGESTED USES for classified advertising are positions available, books or lecture notes for who will actively participate in the mathematical sale, books being sought, exchange or rental of houses, and typing services. life of the Claremont Colleges. THE 1991 RATE IS $55.00 per inch on a single column (one-inch minimum), calculated from Applications are to be sent to: The Search the top of the type; $25 for each additional 'h.. inch or fraction thereof. No discounts for multiple Committee, Department of Mathematics, Po­ ads or the same ad in consecutive issues. For an additional $10 charge, announcements can be mona College, Claremont, CA 91711-6348. placed anonymously. Correspondence will be forwarded. Applications received by January 31, 1991, will Advertisements in the "Positions Available" classified section will be set with a minimum be given full consideration. Applications must one-line headline, consisting of the institution name above body copy, unless additional headline include a vita and letters of recommendation, copy is specified by the advertiser. Advertisements in other sections of the classified pages will including letters evaluating teaching, graduate be set according to the advertisement insertion. Headlines will be centered in boldface at no extra school transcripts, and a description, written for charge. Classified rates are calculated from top of type in headline to bottom of type in body copy, the non-specialist, of research accomplishments including lines and spaces within. Any fractional text will be charged at the next 1h.. inch rate. Ads and plans. Please let us know if you will be will appear in the language in which they are submitted. attending the January AMS meeting in San Prepayment is required of individuals but not of institutions. There are no member discounts Francisco. for classified ads. Dictation over the telephone will not be accepted for classified advertising. Pomona College is an Affirmative Ac­ DEADLINES are listed on the inside front cover or may be obtained from the AMS Advertising tion/Equal Opportunity Employer and encour­ Department. ages applications from minority candidates and U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, women. religion or national origin. "Positions Available" advertisements from institutions outside the U. S. cannot be published unless they are accompanied by a statement that the institution does not discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific wording may be found near the Classified Advertisements in the January and July/August issues COLORADO of the Notices. SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians UNIVERSITY OF COLORADO AT are accepted under certain conditions for free publication. Call toll-free 800-321-4AMS (321-4267) COLORADO SPRINGS in the U.S. and Canada for further information. Department of Mathematics SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence, Rhode Island 02940. AMS location for express delivery packages is 201 Charles Street, Colorado Springs, CO 80933-7150 Providence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are not Applications are invited for a tenure-track Assis­ required to do so. AMS FAX 401-455-4004. tant Professor position for Fall 1991. Preferred area of research interest: probability theory. However, consideration will also be given to POSITIONS AVAILABLE applied mathematics or mathematical physics. exceptionally strong candidates if their area Requirements include receipt of a Ph.D. by the of expertise is consistent with present re­ Fall of 1991, demonstrated record or poten­ search interests: harmonic analysis, computer vision and algebra. Current faculty expertise ALABAMA tial in research, and a strong commitment to teaching. Responsibilities include teaching 9- in probability theory includes perculation the­ ory, population genetics and theory of large THE UNIVERSITY OF 12 hours, depending on research and/or other deviations. Applicants should have significant ALABAMA AT BIRMINGHAM contributions. Send vita and three letters of recommendation to Mary Rosen, Hiring Com­ research accomplishments or exceptional re­ Department of Mathematics mittee Chair, Dept. of Mathematics, California search promise and evidence of good teaching. Ph.D. is required. The average weekly teach­ Applications are invited for one or more antic­ State University, Northridge, Northridge, CA ing load is 7 1/2 hours. Generous support for ipated tenure or tenure-track positions. Prefer­ 91330 by February 15, 1991 for full consid­ faculty development such as travel, teaching ence will be given to strong candidates whose eration. Women and minorities are especially off-loads, and summer research. Send resume research interests are compatible with those encouraged to apply. CSUN is located in a and 3 letters of reference to K. M. Rangaswamy, of our current faculty; this includes numeri­ Northwestern suburb of Los Angeles and is in Chairman. Screening will begin on Feb. 1, 1991 cal POE/Scientific computation, mathematical proximity to Cal. Tech., USC, and UCLA. An and continue until filled. physics, partial differential equations, nonlinear Equal Opportunity/Affirmative Action, litle IX, analysis, dynamical systems, including topolog­ Section 504 Employer. ical dynamics, differential topology and differ­ ential geometry. Faculty members have access to the Alabama Super Computer (using a Sun CONNECTICUT Station and a T-1 line to a Gray X-MP/24). Rank UNIVERSITY OF CONNECTICUT and salary will be subject to qualifications. Send as soon as possible a curriculum vitae, selected POMONA COLLEGE ASSISTANT PROFESSOR -MATHEMATICS reprints, and three letters of reference to Search Claremont, CA (AVERY POINT CAMPUS). The University of Committee, Department of Mathematics, Uni­ Connecticut Mathematics Department invites versity of Alabama at Birmingham, Birmingham, Pomona College seeks to hire a tenure-track applications for an anticipated full-time As­ AL 35294. UAB is an Affirmative Action/Equal Assistant Professor of Mathematics, preferably sistant Professor position at the Avery Point Opportunity Employer. with postdoctoral experience. Excellent candi­ Campus. The Avery Point Campus is located in dates from all fields of mathematics will be the Groton-New London area. A Ph.D. in math­ seriously considered, but preference will be ematics, experience in teaching at the college given to applied mathematicians. Pomona Col­ level, demonstrated talent in teaching under­ CALIFORNIA lege, a highly selective liberal arts college with graduates, and evidence of ability to contribute intellectually gifted students, is one of the Clare­ to the research mission of the Department are CALIFORNIA STATE UNIVERSITY, mont Colleges, which together provide an active required. Rank and salary will be competitive, NORTHRIDGE professional community of over 30 mathemati­ commensurate with qualifications. Screening cians, an excellent research library, weekly will begin March 1 , 1991 and continue until the Applications are invited for two tenure-track Mathematics Colloquia, research seminars, and position is filled. Please send curriculum vitae positions at the rank of Assistant Professor for clinics in applied mathematics. We are looking and have at least three letters of reference the Fall of 1991. We will consider candidates for someone who can continue Pomona's tra­ sent to: Professor Howard Roberts, Associate in the areas of algebra, analysis, topology, dition of excellent and innovative teaching and Head, Department of Mathematics, University

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of Connecticut, U-9, 196 Auditorium Rd., Storrs, a member of the State University system of five faculty. It has bachelor degree programs CT 06269-3009. AA/EOE. (Search #1 A209) Florida, with approximately 22,000 students. in Mathematics, Mathematics Education, and The department offers bachelor's and master's Computer Science. It also has master degree degrees. programs in Mathematics and Mathematics Ed­ ucation. The Department is especially interested DELAWARE in applicants with doctoral degrees in Statistics or Computer Science, but all specialties are UNIVERSITY OF DELAWARE ILLINOIS encouraged to apply. Department of Mathematical Sciences Please send a letter of application, vita, and Chairperson NORTHWESTERN UNIVERSITY have three letters of reference sent to: Department of Mathematics Chairperson The University of Delaware invites applications 2033 Sheridan Road, Department of Mathematics and for the position of Chair of the Department of Evanston, Illinois 60208-2730 Computer Science Mathematical Sciences in the College of Arts Indiana State University and Science. Applicants for the position should Applications are invited for one or more tenure­ Terre Haute, IN 47809 have an outstanding record of research and track positions starting September 1991. Al­ Interviews will begin in March 1991. Indiana scholarly activity and should have the skills though priority will be given to young, excep­ State University is an Equal Opportunity/Affir­ to chair a department with major research, tional research mathematicians (no more than mative Action Employer. teaching, and service responsibilities. several years after Ph.D.), more senior candi­ The Department has 40 regular faculty posi­ dates with very exceptional credentials may be tions and an active graduate (Ph.D.) program. considered for a tenured position. Fields of inter­ Programs include pure mathematics, applied est of the department include Algebra, Analysis, mathematics, and statistics. The Department is Dynamical Systems, Probability, Partial Differ­ unusual in its strength and commitment to ap­ ential Equations, and Topology. Northwestern plied mathematics and related areas of analysis. is an affirmative action, equal opportunity em­ IOWA The University has good computing and library ployer committed to fostering a diverse faculty, UNIVERSITY OF NORTHERN IOWA facilities, and in addition, the Department has a so women and minority candidates are espe­ number of workstations and two Sun 3/180 file cially encouraged to apply. Candidates should Department Head Search Update servers. The University of Delaware is located in arrange that at least three letters of recommen­ Mathematics & Computer Science the pleasant university town of Newark midway dation be sent to Chair, Personnel Committee, We are/have been seeking a new department between Washington, DC and New York City. Department of Mathematics, Northwestern Uni­ head. It now appears we will propose forming Applicants should submit a resume, the versity, Evanston, Illinois 60208. In order to a separate department for computer science as names and addresses of three references, and receive full consideration, applications should soon as possible. Thus, the head position will be a letter of interest to (or contact) be received by February 15, 1991. Hiring is filled with the expectation that the Department Prof. B.F. Caviness contingent upon eligibility to work in the United will soon contain only mathematics and mathe­ Chair: Search Committee for States. matics education. Screening will begin March 1 , Mathematics 1991 . Interested persons should contact Philip Department of Computer and East, Mathematics and Computer Science, Uni­ Information Sciences versity of Northern Iowa, Cedar Falls, lA 50614 103 Smith Hall NORTHWESTERN UNIVERSITY (319-273-2631, [email protected]). University of Delaware Mathematics Department UNI is an affirmative action, equal opportu­ Newark, DE 19716 2033 Sheridan Road, nity educator and employer. Phone: 302/451-8234 Evanston, Illinois 60208-2730 email: [email protected] The position will be available beginning Septem­ The Mathematics Department will sponsor an ber 1, 1991. The deadline for the receipt of Emphasis Year in algebraic topology, cohomol­ applications is March 1, 1991. ogy of groups, and related topics. This program The University of Delaware is an equal op­ will include 2-year Assistant Professorship po­ portunity employer and invites and encourages sitions starting September 1991 and possible KANSAS applications from women and minorities. visiting positions for more senior mathemati­ cians for part or all of the academic year. UNIVERSITYOF KANSAS Applications should be sent to Prof. Mark Department of Mathematics E. Mahowald at the department address and FLORIDA include a curriculum vitae and three letters Applications are invited for a visiting assis­ of recommendation. In order to ensure full tant professor position commencing August 16, FLORIDA INTERNATIONAL UNIVERSITY consideration, an application must be received 1991 or as negotiated. (The availability of this by February 15, 1991. position is contingent upon final administrative The Department of Mathematics announces Northwestern University is an Affirmative approval.) Preference will be given to can­ tenure-track positions beginning August 1991. Action/Equal Opportun~y employer. Hiring is didates whose research interests mesh well These positions are usually at the beginning contingent upon eligibility to work in the United with those of present mathematics department Assistant Professor level. Candidates must States. faculty. Require Ph.D. or Ph.D. dissertation have a Ph.D. in Mathematics and a commitment accepted with only formalities to be completed. to research and quality teaching. Qualified Application, detailed resume with description candidates in all areas of Mathematics will be of research, and three recommendation letters condisered. INDIANA should be sent to C.J. Himmelberg, Chairman, Teaching load consists of no more than Department of Mathematics, 405 Snow, Univer­ five 3-credit courses per academic year. Send INDIANA STATE UNIVERSITY sity of Kansas, Lawrence, KS 66045--2142. resume and arrange for 3 letters of recommen­ Department of Mathematics Deadlines: February 1, 1991 for first consid­ dation to be sent to: Recruitment Committee, and Computer Science eration, then monthly until August 1, 1991. Department of Mathematics, Florida Interna­ The University of Kansas is an AA/EOE. tional University, Miami, FL 33199. Applications are invited for one or more tenure­ Florida International University is an Equal track positions starting in the fall semester of Opportun~y/Affirmative Action Employer. It is 1991-92. The Department currently has twenty-

FEBRUARY 1991, VOLUME 38, NUMBER 2 157 Classified Advertisements

nity/Affirmative Action Employer. Women and LOUISIANNA minorities are encouraged to apply. MASSACHUSETTS LOUISIANA STATE UNIVERSITY AMHERST COLLEGE Department of Mathematics Baton Rouge, LA 70803; (504)388-1534 Applications are invited for a one-year visiting position in Mathematics, preferrably at the The department anticipates openings for the LOYOLA UNIVERSITY Assistant Professor level, beginning in August 1991. 91-92 academic year primarily at the Assis­ New Orleans, Louisiana tant Professor level, but invites applications for Amherst College is a private, undergraduate positions at all professorial-rank levels includ­ The Department of Mathematical Sciences at college which emphasizes both research and ing visiting and tenure-track positions. Essen­ Loyola University invites applications for an an­ teaching. We attract bright students, possess a tial qualifications include competitive research, ticipated tenure-track position in Mathematics lively faculty, and have an administration com­ good teaching and a Ph.D. or equivalent by at the Assistant or Associate Professor level. mitted to a vigorous program in mathematics. August 1991. Preferred fields include areas of The position will begin in August 1991, pending The Department of Mathematics and Com­ combinatorics and graph theory and algebraic availability of funds. Candidates are expected puter Science consists of seven mathematicians number theory. Strong candidates in other areas to have a Ph.D. degree in Mathematics and and three computer scientists. We are located are encouraged to apply. Application deadline is a strong commitment to teaching at an under­ in the Seeley G. Mudd building, which also March 1, 1991. To apply, specify your interests, graduate Liberal Arts institution. An established houses classrooms, seminar rooms, a library enclose a full resume, and arrange for at least record of scholarly research is necessary for for mathematics and computer science, and the three persons to send letters of evaluation to Dr. appointment at the rank of Associate Professor. academic computer center. Research facilities Jimmie Lawson, Chairman (address above). Preference will be given to candidates in anal­ include computers in most faculty offices and a LSU IS AN EQUAL OPPORTUNITY UNI­ ysis or geometry; however, strong candidates network of Sun workstations. VERSITY. in all areas of pure or applied mathematics are Amherst College is part of a five college invited to apply. Salary is competitive. consortium that also includes the University of Candidates should send (1) official tran­ Massachusetts and Hampshire, Mount Holyoke and Smith Colleges. There are numerous faculty LOUISIANA STATE UNIVERSITY scripts of college work, (2) a curriculum vita, and (3) three letters of recommendation to: seminars held at Amherst and the University, Department of Mathematics Dr. Duane Randall, Chair and Boston is less than two hours away. Baton Rouge, LA 70803; (504)388-1534 Department of Mathematical Sciences If some anticipated leaves take place and MS-2 if we receive authorization from the administra­ We anticipate openings for full and part-time P.O. Box 104, Loyola University tion, the position may be extended to a second Instructors and Teaching Associates starting (and possibly third) year given satisfactory per­ in August 1991, to teach freshman/sophomore 6363 St. Charles Avenue New Orleans, Louisiana 70118 formance in the first year. courses, including developmental mathematics. Applicants should hold a Ph.D. in mathemat­ The teaching load averages 12 hours of class Applications must be received by March 22, 1991. Loyola University is an Equal Opportu­ ics. Please submit a vita, three references, and per week. Applicants should have completed at transcripts from both your graduate and under­ least 18 graduate credit hours in mathematics nity/Affirmative Action Employer. Women and minorities are encouraged to apply. graduate institutions. All applications received and hold a master's degree (in mathematics by February 15 are assured of consideration. for Instructor positions). Application deadline is Amherst College is an Affirmative Ac­ April 1, 1991. To apply, specify your interest, tion/Equal Opportunity Employer and encour­ enclose a full resume, and arrange for at least ages applications from minorities and women. three persons to send letters of evaluation to Dr. Reply to: Jimmie Lawson, Chairi"Tian (address above). Professor David A. Cox, Chair LOYOLA UNIVERSITY LSU IS AN EQUAL OPPORTUNITY UNI­ Department of Mathematics and VERSITY. New Orleans, Louisiana Computer Science The Department of Mathematical Sciences at Amherst College Amherst, MA 01 002 Loyola University invites applications for an or send electronic mail to: [email protected] LOYOLA UNIVERSITY anticipated tenure-track position in Mathematics New Orleans, Louisiana at the Assistant Professor level. The position or [email protected] will begin in August 1991, pending availability The Department of Mathematical Sciences at of funds. Candidates are expected to have Loyola University invites applications for an a Ph.D. degree in Mathematics and a strong anticipated tenure-track position in Mathematics commitment to teachng at an undergraduate MICHIGAN at the Assistant Professor level. The position Liberal Arts institution. Candidates with strong will begin in August 1991 , pending availabHity research potential in all areas of pure or applied MICHIGAN TECHNOLOGICAL UNIVERSITY of funds. Candidates are expected to have mathematics are invited to apply. Salary is Department of Mathematical Sciences a Ph.D. degree in Mathematics and a strong competitive. commitment to teachng at an undergraduate Candidates should send (1) official tran­ Applications are invited for the following posi­ Liberal Arts institution. Candidates with strong scripts of all college work, (2) a curriculum vita, tions, starting Sep. 3, 1991. (1) At least two research potential in all areas of pure or applied and (3) three letters of recommendation to: tenure-track positions at the AssistanVAssociate mathematics are invited to apply. Salary is Chair of Search Committee, MS-3 level in Applied Mathematics. Areas of special competitive. Department of Mathematical Sciences interest include fluid mechanics, mathematical Candidates should send (1) official tran­ P.O. Box 104, Loyola University modelling, computational mathematics and par­ scripts of all college work, (2) a curriculum vita, 6363 St. Charles Avenue tial differential equations. (2) One tenure-track and (3) three letters of recommendation to: New Orleans, Louisiana 70118 position in Combinatorics. Areas of special in­ Chair of Search Committee. MS-1 Applications must be received by March 22, terest include pure and applied combinatorics, Department of Mathematical Sciences 1991. Loyola University is an Equal Opportu­ combinatorial optimization, coding theory, cryp­ P. 0. Box 104, Loyola University nity/Affirmative Action Employer. Women and tography and combinatorial designs. Appoint­ 6363 St. Charles Avenue minorities are encouraged to apply. ments at the non-entry level require substantial New Orleans, Louisiana 70118 record of published research. Requirements Application must be received by March 22, include a Ph.D. in Mathematics, excellence in 1991. Loyola University is an Equal Opportu- research or potential for such, as well as a

158 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

commitment to teaching at the undergraduate Department of Mathematics, University of Mis­ employs only United States citizens and aliens and graduate level. (3) In addition, the depart­ sissippi, University, MS 38677. lawfully authorized to work in the United States. ment expects to fill several Visiting Assistant The University of Mississippi is an Equal Professorship positions. Please send a letter Opportunity/Affirmative Action Employer. . of application, resume and three letters of rec­ ommendation to: Recruitment Committee, De­ NEW HAMPSHIRE partment of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, DARTMOUTH COLLEGE Houghton, Ml 49931-1295. Applications will be MISSOURI Department of Mathematics accepted until February 15, 1991. MTU is an and Computer Science equal opportunity educational institutiorl'equal SOUTHWEST MISSOURI opportunity employer. STATE UNIVERSITY The Department of Mathematics and Computer Science has an openng for a tenure-track Southwest Missouri State University Depart­ Assistant Professor in Mathematics, with initial ment of Mathematics. One or more tenure­ appointment in the 1991-1992 academic year. MISSISSIPPI track and/or visiting positions in Mathematics A candidate for the position must be committed and Statistics, beginning Fall 1991. Rank and to outstanding teaching at all levels of the MISSISSIPPI STATE UNIVERSITY salary will be commensurate with qualifications. undergraduate and graduate curriculum and Department of Mathematics and Statistics Applicants must have a Ph.D. in Mathematics must give evidence of a well-regarded research or Statistics, evidence of excellence in teach­ program that shows real promise for the future. Applications are invited for two or more an­ ing, and a commitment to continued research. Candidates with several years of experience ticipated tenure-track or visiting positions for For all positions preference given to applicants should in addition be ready to direct Ph.D. 1991-92. At least one of the positions will be in with research interests compatible with those theses. statistics and probably at least at the associate of the current faculty. Duties include teaching, To create an atmosphere supportive of re­ professor level. Candidates should possess a research, and service. Applications will be re­ search, Dartmouth offers new faculty members doctoral degree, demonstrate a strong poten­ viewed as received and will be accepted until grants for research-related expenses, a quarter tial for research, and have a commitment to the positions are filled or until February 15, of sabbatical leave for each three academic effective teaching. All areas are welcomed but 1991-the final deadline for all application ma­ years in residence and flexible scheduling of preference will be given to the following: for the terials. Send vita and graduate transcripts, and teaching responsibilities. The teaching responsi­ mathematics position(s), applied mathematics, have three letters of reference sent to: Clayton bility in mathematics is two courses per quarter computational mathematics, particularly compu­ Sherman, Acting Head, Department of Math­ for two ten-week quarters or one course for tational geometry, and partial differential equa­ ematics, Southwest Missouri State University, two quarters and two courses for one quarter. tions; for the statistics positon(s), multivariate Springfield, MO 65804-0094. AA/EOE. The department encourages good teaching with analysis, nonparametric and robust inference, a combination of committed colleagues and categorical analysis, and linear and non-linear bright, responsive students. models. Applications are welcome in all fields of The Department offers graduate programs mathematics, including statistics. To apply for leading to the Master of Arts degree (M.A.) and NEVADA the position, send a letter of application, cur­ the Master of Science degree (M.S.) in both riculum vitae, and a brief statement of research mathematics and statistics and the Doctor of UNIVERSITY OF NEVADA, RENO results and interests. Also arrange for four let­ Philosophy degree (Ph.D.) in mathematical sci­ Department of Mathematics ters of reference to be sent, at least one of ences. Facilities exist for applicants with interest which addresses teaching, and, ifthe applicant's in interdisciplinary research efforts. Applicants For the 1991-92 academic year applications are native language is not English, the applicant's with an interest in the computational aspects invited for (a) one and possibly two one-year ability to use English in a classroom. All appli­ of the mathematical sciences may have the Visiting Assistant Professorships, and (b) one cation material should be addressed to Phyllis opportunity to participate in research efforts one-year Lectureship. In each case a candidate Bellmore, Recruiting Secretary, Department of with the National Science Foundation Engineer­ should have a Ph.D. in the mathematical sci­ Mathematics and Computer Science, Dartmouth ing Research Center for Computational Field ences, a demonstrated research potential, and College, Hanover, New Hampshire 03755. Ap­ Simulation at Mississippi State University. a strong commitment to excellence in teaching. plications completed by February 1 will receive Applicants should send a curriculum vitae In (a) salary for each position is $32,500, in first consideration. Dartmouth is committed to and arrange for three letters of recommendation (b) salary for the position is $31 ,000, with the Affirmative Action and encourages applications to be sent to: C. Wayne Mastin, Chairman, university contributing to TIAA retirement in both from African Americans, Asian Americans, His­ Search Committee, Department of Mathematics cases. Job responsibilities include the teaching panics, Native Americans and women. Specific and Statistics, P. 0. Drawer MA, Mississippi during the academic year of six courses (in(a), questions on the selection process can be State, MS 39762. The committee will begin to 18-19 semester credits, in (b), 21-24 semester directed to Richard E. Williamson, Recruiting review applications on March 1, 1991 , and con­ credits) and the presentation of colloquia on the Chair. tinue until positions are filled. Mississippi State candidate's research. University is an equal opportunity/affirmative To be assured of consideration, applications action employer. must be received by March 18, 1991. Starting date is August 19, 1991. NEW JERSEY Each applicant should send a resume and THE UNIVERSITY OF MISSISSIPPI arrange to have three letters of reference INSTITUTE FOR ADVANCED STUDY Department of Mathematics sent to: Professor R. N. Tompson, Chair­ Princeton, New Jersey 08540 man, Department of Mathematics, University School of Mathematics The Department invites applications for a tenure of Nevada, Reno, Reno, NV 89557. [(702) track position at the Assistant or Associate 784-6775; email address: [email protected]; The Institute for Advanced Study invites ap­ Professor level beginning August 19, 1991. FAX:702-784-1300]. plications for a professorship in the School Applicants should hold the Ph.D. degree, and The University of Nevada, Reno is an of Mathematics. Candidates must have distin­ should be committed to excellence in teaching Equal Opportunity, Affirmative Action employer guished records of achievement in mathemat­ and a productive ongoing program of research. and does not discriminate on the basis of ical research. The professors in the Institute's To ensure consideration, submit a letter of race, creed, color, sex, age, national origin, School of Mathematics are collectively responsi­ application, vita, and three letters or recommen­ veteran status or handicap in any program ble for maintaining a strong program of research dation by March 1, 1991, to: Search Committee, or activity it operates. University of Nevada through their own work and also by selecting

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a number of visiting members every year. Ap­ publications, and have three letters of reference OBERLIN COLLEGE plications, including curriculum vitae and list sent to: Daniel Waterman, Chair. Department of Mathematics of publications, should be addressed to the Syracuse University is an Equal Opportu­ Oberlin, OH 44074 School Administrative Officer, School of Mathe­ nity/Affirmative Action Employer. matics, Institute for Advanced Study, Princeton, Four-year, full-time, continuing position at the New Jersey 08540. An equal opportunity em­ level of Instructor, Assistant Professor, or higher, ployer: women and minority group members are starting 1991-92. Ph.D. in hand or expected encouraged to apply. by September 1991. Background in modern ap­ plied analysis essential. All specialties consid­ ered but preference given to chaotic dynamical CASE WESTERN RESERVE UNIVERSITY systems, numerical analysis, and approximation Statistics Positions RUTGERS UNIVERSITY, CAMDEN theory. Excellence in teaching and productive scholarship required. Five courses per year, Tenure track positions, possibly senior, in Ap­ The Mathematical Sciences Department seeks including at least one advanced course in mod­ Summer highly qualified applicants for a research ori­ plied Statistics will be available in the ern applied analysis. Salary commensurate with of 1991. Outstanding research record or proven ented assistant professorship. This is a tenure qualifications and experience. Vita, transcripts, potential and teaching excellence is track position at a competitive salary with a research and three letters of reference to be received be in the De­ teaching load of one course for the first two required. Initial appointments will by November 9, 1990. Send to Michael Henle, of Mathematics and Statistics. Since years. At least one year beyond the Ph.D. and partment Department of Mathematics, Oberlin College,· University has made the reestablishment of one significant publication are necessary to be the Oberlin, Ohio 44074. Affirmative Action Equal Statistics a priority for future development it is considered. Send C.V., a minimum of three let­ Opportunity Employer. Applications will continue expected that these positions will eventually be ters of recommendation, and reprints/preprints to be accepted until the position is filled. as soon as possible to: in an independent Statistics Department. Western Reserve University provides Search Committee Case scope to interact with researchers in Mathematical Sciences Department a wide Rutgers University other Schools (Medicine, Engineering, Manage­ OBERLIN COLLEGE ment, Nursing, Dentistry, Law and the Applied Camden, NJ 08102 Department of Mathematics Social Sciences). There is ample opportunity AAIEOE Oberlin, OH 44074 for cooperative ventures with members of the Faculties of Mathematics and Natural Sciences, Two-year, full-time, continuing position at the the Humanities and the Social Sciences. The level of Assistant Professor starting 1991-92. University also has several established re­ Ph.D. in hand or expected by September 1991. NEW YORK search Centers, including th CWRU Center The encumbent will teach 5 courses in the for Stochastic and Chaotic Processes in Sci­ general area of mathematics and/or computer MANHATTAN COLLEGE ence and Technology, whose efforts waul be science. Excellence in teaching and productive Department of Mathematics enhanced by cooperation with applied statisti­ scholarship required. In addition the ability to and Computer Science cians. teach computer science and/or statistics is Women and minority groups candidates are highly desirable. Salary commensurate with The Department announces the opening of one especially encouraged to apply. CWRU is an quualifications and experience. Vita, transcripts, or more full-time tenure-track positions to begin affirmative action and an equal opportunity and three letters of reference to be received in the fall semester 1991, at a rank appropriate employer. Send vita plus three letters of recom­ by February 1, 1991. Send to Michael Henle, to the candidate's qualifications and experience. mendation to Department of Mathematics, Oberlin College, The candidate should possess the doctorate Dr. C. A. Cullis, Dean Oberlin, Ohio 44074. Affirmative Action/Equal in mathematics or computer science, or be Faculty of Mathematics and Natural Opportunity Employer. Applications will continue completing the dissertation. Sciences to be accepted until the position is filled. The responsibilities of the position include Crawford Hall, teaching a full-time schedule of courses in Case Western University the undergraduate session, at both the intro­ Cleveland, OH 441 06 ductory and advanced levels. Current hardware --"'-oKL:AH"~ includes a VAX 11/780, IBM RTworkstations, an AT&T 3B2/400, and numerous microcomputer THE UNIVERSITY OF OKLAHOMA networks. OBERLIN COLLEGE Department of Mathematics Please send curriculum vitae to Dr. John Department of Mathematics 601 Elm Avenue, Room 423 McCabe, Department of Mathematics and Com­ Norman, Oklahoma 73019-0315 puter Science, Manhattan College, Riverdale, Oberlin, OH 44074 New York 10471. Closing date is February 16, Four-year, full-time, continuing position at the Applications are invited for two anticipated 1991. level of Instructor, Assistant Professor, or higher, tenured or tenure-track positiions in Mathemat­ ANEOE/M/F. Women and minorities are starting 1991-92. Ph.D. in hand or expected by ics beginning Fall 1991. One position at the encouraged to apply. September 1991. Background in Operations associate professor level, with preference given Research and interest in applied mathematics to applicants with research interests in the areas essential. Excellence in teaching and produc­ of Geometry, Topology, or Analysis. One Assis­ tive scholarship required. Five courses per year, tant Professor position at the entry level with SYRACUSE UNIVERSITY including a two-course OR sequence. Salary preference given to research interests compati­ Department of Mathematics commensurate with qualifications and expe­ ble with those of our current faculty. Candidates Box 1, Syracuse, NY 13244-1150 rience. Vita, transcripts, and three letters of must have a Ph.D. degree, demonstrated excel­ reference to be received by November 9, 1990. lence in research, and a strong commitment to There may possibly be positions available at Send to Michael Henle, Department of Mathe­ high-quality teaching. Duties include research, the junior level beginning Fall1991. Candidates matics, Oberlin College, Oberlin, Ohio 444074. normally teaching six credit hours per semester, should have outstanding research ability and Affirmative Action Equal Opportunity Employer. and Departmental and University service appro­ evidence of excellence in teaching. Applications Applications will continue to be accepted until priate to rank. Salary will be commensurate with are invited in any area of mathematics and the position is filled. qualifications and experience. There may also in mathematics education and statistics. Send be visiting positions. Applicants should send a letter of application and vita with a list of their vita and have at least three letters of

160 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

reference sent to Dr. Ruediger Landes, Search maximum of three years. A Master's Degree position. Submit a letter of application and Committee Chair, Department of Mathemat­ in Mathematics is required for this position vita, and have three reference letters sent by ics, University of Oklahoma, 601 Elm Avenue, and the successful applicant must have a February 28, 1991 to: L. Pakula, Search Com­ Room 423, Norman, Oklahoma 73019-0315. strong commitment to undergraduate mathe­ mittee Chair, Assistant Professor, Mathematics Initial screening begins December 15, 1990 matics teaching, at least one year of college (021 09BT) Position, The University of Rhode and every two weeks thereafter. Applications level teaching experience or three years of pre­ Island, P. 0. Box G, Kingston, Rl 02881. An will be accepted until the positions are filled. college teaching experience and an excellent Affirmative Action/Equal Opportunity Employer. The University of Oklahoma is an Equal Op­ teaching record. The position will remain open portunity/Affirmative Action Employer. OU has until filled but applications wil be considered a policy of being responsive to the needs of starting on March 1,1991. Interested persons --~s.o.u...,T•H•C•A•R•O•L•IN....,.A~,- dual-career couples. should contact Dr. John Whitesitt, Chair, Depart­ ment of Mathematics, Southern Oregon State COLLEGE OF CHARLESTON College, Ashland, OR 97520. SOSC is an Department of Mathematics Affirmative Action/Equal Opportunity Employer. THE UNIVERSITY OF TULSA Applications are invited for at least 2 tenure­ Dean track positions at the Assistant Professor level College of Engineering beginning August 1991. Candidates must have a Ph.D. in one of the mathematical sciences, and Applied Sciences PENNSYLVANIA a commitment to undergraduate teaching, and The University of Tulsa is accepting applications LAFAYETTE COLLEGE potential for continuing research. The normal and encouraging nominations for the position Department of Mathematics teaching load is 9 hrs/wk, with possibilities for reductions through internal grants. The of Dean of the College of Engineering and Easton, PA 18042 Applied Sciences. The University is an indepen­ salary is competitive. Applicants should send a dent comprehensive, doctoral-degree-granting Tenure-track position at the rank of Assistant vita and have three letters of recommendation research institution with approximately 3,200 Professor beginning in late August1991. Prefer­ sent to William L. Golightly, Chairman, Depart­ undergraduate, and 1,400 graduate and pro­ ence for a candidate able to help with teaching ment of Mathematics, College of Charleston, fessional students. The College of Engineering statistics at all undergraduate levels. Women Charleston, SC 29424. The process of evaluat­ and Applied Sciences consists of eight depart­ and minorities are especially encouraged to ing applications will begin on January 21, 1991, ments: Chemical Engineering, Chemistry, Elec­ apply. but applications will be considered until the po­ trical Engineering, Geosciences, Mathematical Teach undergraduate mathematics, help to sitions are filled. The College of Charleston is an and Computer Sciences, Mechanical Engineer­ develop our undergraduate mathematics pro­ Affirmative Action/Equal Opportunity Employer. ing, Petroleum Engineering, and Physics. gram, pursue scholarly development Lafayette The Dean of the College reports to the offers liberal arts and engineering in a small (2000) highly selective private college close to Provost, and should be a recognized scholar THE CITADEL with an earned doctorate in engineering, the ap­ Philadelphia and New York City. plied sciences, or physical sciences, and should Send resume, 3 reference letters and tele­ Applications are invited for a tenure track be familiar with current research trends in these phone numbers (office and home) to Chair, position at the assistant or associate level. areas. The successful candidate must have Mathematics Search Committee. Review of ap­ Qualifications include a Ph.D. in a mathematical appropriate credentials to qualify at the rank plications will begin after January 20, 1991, and science or computer science, a firm commitment of full professor with continuing appointment will continue until the position is filled. to undergraduate teaching, and a continuing (tenure) in a department of the College. The Lafayette is an Equal Opportunity Employer. program of research. Preference will be given candidate should possess leadership qualities to individuals with qualifications in the areas that will foster constructive relationships with of statistics, computing, or information science. other colleges, the community, and industry. Salary is competitive. Academic and significant administrative experi­ RHODE ISLAND The Citadel is a state-supported liberal arts, ence is required. Additional information on job military college offering undergraduate degrees responsibilities and qualifications will be sent on PROVIDENCE COLLEGE in the Arts, Sciences, Engineering, Education, request. Assistant Professor of Mathematics and Business Administration. The department The position will be available June 1, 1991. offers bachelor's degrees in mathematics and A tenure-track position will be available in The Search Committee will give full considera­ computer science. Generous support for fac­ August 1991 . Duties include teaching the full tion to applications received by March 15, 1991 ; ulty research is available. Send a resume and range of undergraduate Mathematics. Ph.D. in however, applications will be accepted until the three letters of reference to: Stephen D. Comer, Mathematics required. Send letter of application position is filled. Applications, nominations, and Search Committee, Department of Mathemat­ and resume to Mr. Frank Ford, Chair, at Math/CS correspondance should be addressed to: ics/Computer Science, The Citadel, Charleston, Department, Providence College, Providence, Dale Teeters, Chair SC 29409. Email: [email protected]. R.I. 02918 by Mar. 1st and have transcripts and EAS Dean Search Committee Review of applications will begin March 1. three letters of recommendation sent directly to Office of the Provost Women and minorities are encouraged to apply. the same address. At least one of the letters of The University of Tulsa The Citadel is an equal opportunity/affirmative recommendation must address teaching ability. 600 South College Avenue action employer. Tulsa, Oklahoma 74104-3189 Providence College is a Roman Catholic four­ The University of Tulsa is a Equal Opportu­ year liberal arts college conducted under the nity/Affirmative Action Institution. auspices of the Dominican Friars and is an Equal Opportunity Affirmative Action Employer.

AUGUSTANA COLLEGE OREGON THE UNIVERSITY OF RHODE ISLAND Sioux Falls, South Dakota Assistant Professor, Mathematics SOUTHERN OREGON STATE COLLEGE Augustana College invites applications for a Department of Mathematics Ph.D. in Mathematics required, preference given tenure-eligible position in the Department of to applicants in differential equations, combina­ Mathematics at the rank of Assistant Professor The Department anticipates one non-tenure torics, control theory, classical analysis, func­ beginning September 1991. Responsibilities in­ track instructor position starting Fall1991-1992. tional analysis. Must be able to teach and clude teaching lower and upper division courses This is a one year position renewable to a conduct research. Tenure track academic year and involvement in student research projects.

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Ph.D. in mathematics is required. Candidates in extramural research funding and in the top must demonstrate excellence in teaching, po­ five universities in the number of national merit VIRGINIA tential for excellence in research, and a com­ finalists currently enrolled. mitment to the mission of Augustana as a To apply, please send a curriculum vitae and church-related liberal arts college is expected. have at least three (3) letters of recommendation VIRGINIA POLYTECHNIC INSTITUTE Priority given to applications received prior to sent to Prof. H. E. Lacey, Head, Department AND STATE UNIVERSITY March 1, 1991. Send letter of application, vita, of Mathematics, Texas A&M University, College Department of Mathematics three current letters of reference, graduate tran­ Station, TX 77843-3368. scripts (direct from Registrar's offfice), and a Texas A&M University is an Equal Oppor­ Applications are invited for a tenure-track ap­ statement of personal and professional goals to: tunity/Affirmative Action Employer. Women and pointment, subject to budgetary approval, at the Jeanne Kruse, Administrative Assistant, Office minorities are encouraged to apply. level of Assistant Professor beginning with the of Academic Affairs, Augustana College, 29th & 1991--92 academic year. A Ph.D. and strong Summit, Sioux Falls, SD 57197. EOE/AA. research potential are required. Preference will be given to candidates with postdoctoral experi­ TEXAS A&M UNIVERSITY ence. Primary areas of interest are algebraic and Department of Mathematics differential geometry, discrete mathematics, dy­ TEXAS The Department of Mathematics at Texas A&M namical systems, and computationally oriented University hopes to fill several tenure-track mathematics. Applications will be accepted until LAMAR UNIVERSITY and visiting positions which begin in the fall March 15, 1991 or until position is filled. Appli­ Beaumont, Texas semester 1991. All areas will be considered. To cants should send a vita and arrange to have three letters of reference submitted to Chair, apply, please send a curriculum vitae and have The Department of Mathematics seeks appli­ Search Committee, Department of Mathemat­ cations for a tenure-track AssistanVAssociate at least three (3) letters of recommendation sent to Prof. H. E. Lacey, Head, Department ics, Virginia Tech, Blacksburg, VA 24061-0123. Professor position beginning Fall 1991. Ap­ Women and minorities are encouraged to apply. plicants must hold an earned Ph.D., should of Mathematics, Texas A&M University, College Station, TX 77843-3368. Virginia Tech is Equal Opportunity/Affirmative be active researchers in Applied Mathematics Action Employer. and/or Numerical Analysis/Scientific Comput­ Texas A&M University is an Equal Oppor­ ing, and have a strong commitment to teaching. tunity/Affirmative Action Employer. Women and Lamar is a state supported educational and minorities are encouraged to apply. research institution of approximately 12,000 students. The Department, which is located within the College of Engineering, offers the THE UNIVERSITY OF TEXAS B.A., B.S., and M.S. degrees in Mathematics AT SAN ANTONIO and has 16 full-time faculty. WASHINGTON For the approximately 250,000 people in The Division of Mathematics, Computer Sci­ the Beaumont area, there are eight muse­ ence, and Statistics will have three tenure-track ums, a symphony orchestra, ballet, opera, and positions at the assistant professor level in Math­ other theatrical productions. Other facilities and ematics and Statistics, beginning August 1991. UNIVERSITY OF WASHINGTON events are found in Houston 85 miles west. Although applicants in all areas of mathematics Nearby outdoor recreational opportunities in­ an statistics will be considered, preference will Tutoring Center Director clude two of the largest freshwater lakes in be given in one assistant professor position The Mathematics Department of the University Texas, the Big Thicket National Preserve, four to those candidates whose research areas are of Washington is establishing a Mathematics national forests, the Gulf of Mexico, and a large in applied or applicable mathematical analy­ Tutoring Center to provide individual assis­ inland saltwater lake. sis, one to combinatorics and graph theory, tance to students in its elementary classes. Salary and rank are commensurate with and one to mathematical physics. Applicants It seeks a director for this Tutoring Center. gualifications and experience. Send a resume should have the Ph.D. degree in Mathematics The position will be that of Senior Lecturer and three letters of recommendation to: Dr. John or a related area by August 1991, and should in Mathematics with an initial appointment for R. Canon, Chair; Department of Mathematics; demonstrate strong potential for excellence in three years. Salary will be commensurate with Lamar University; P.O. Box 10047; Beaumont, research and teaching. Responsibilities include the professional qualifications of the successful TX 7771 0. Full consideration will be given to research, teaching, direction of graduate stu­ candidate. The Ph.D. in mathematics is required completed applications received before March dents, and contributing in program developent. as is experience teaching elementary university 15, 1991. Lamar is an EEO/AA employer. San Antonio, Texas is a scenic, dynamic mathematics. Some administrative experience and fast growing city of rich cultural diversity. would also be desirable as would be previ­ UTSA is the only public university in the city ous experience with a tutoring center. Further of San Antonio, and serves a metropolitan TEXAS A&M UNIVERSITY information can be obtained from Professor population of approximately one million people. Department of Mathematics James Morrow, Department of Mathematics, The univeristy is viewed by the community as an University of Washington, Seattle, Washington, The Department of Mathematics invites appli­ important asset in the economic development 98195. (206)543-1161. Those wishing to apply cations for one or more positions in the fields of of the area. should send a letter stating their interest in the algebra and topology. The department expects Applicants should submit a resume and position and a copy of their curriculum vitae. to make several appointments in these fields arrange to have at least three letters of recom­ In addition they need to arrange for three let­ during the next 3 to 5 years in order to expand mendation sent to ters of recommendation on their behalf to be our algebra and topology group. Currently, we Professor Shair Ahmad, Director sent. Preference will be given to candida1es have active researchers in algebraic geometry, Division of Mathematics, Computer whose applications are received not later than combinatorics, algebraic K-theory and cyclic Science, and Statistics April 1,1991. The University of Washington homology, noncommutative ring theory, knot The University of Texas at San Antonio is building a multicultural faculty and strongly theory, and general topology. We are particu­ San Antonio, Texas 78285-0664 encourages applications from female and mi­ larly interested in modern algebraists who can E-mail: [email protected] nority candida1es. Preference will be given to interact with the people presently at Texas A&M The closing date for receipt of applications for applicants who can serve well an increasingly and in algebraic topologists. these positions is February 15, 1991. UTSA is an diverse University community. AA/EOE. Texas A&M University is a major research Equal Opportunky/Affirmative Action Employer. institution with a total enrollment of 42,000. It We encourage women and minorities to apply. ranks in the top seven universities nationally

162 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY --·------·~------···------·----·-······------·-··-·-·-·----··------··--·-·-- Classified Advertisements

WYOMING UNIVERSITY OF BRITISH COLUMBIA and graduate courses and to be committed to Vancouver, B. C., Canada, V6T 1Y4 research. Mathematics Department Appointments are normally made for a three­ THE UNIVERSITY OF WYOMING Room 121, 1984 Mathematics Road year period. AUB is an EO/AA employer. Interested persons may send their curricula Department of Mathematics The Mathematics Department is seeking an out­ vitae and three letters of recommendation be­ Junior Position in Pure Mathematics standing candidate for a tenure track Assistant fore March 1, 1991 to the Dean of Arts and The Department of Mathematics invites appli­ Professorship to begin 1 July 1991. Our highest Sciences, c/o New York Office of the American University of Beirut, 850 Third Avenue, New cations for a tenure-track assistant professor priority is for a candidate in one of the following position ih pure mathematics. Areas of inter­ fields: Real or Complex Analysis, Operator Al­ York, New York 10022, USA. est include Functional Analysis, Matrix The­ gebras, Functional Analysis, Partial Differential U.S. passports are presently invalid for travel ory, Group Theory and Algebraic/Computational Equations. In very exceptional circumstances, to, in or through Lebanon, and for residence in Combinatorics. The department has a strong this position may be upgraded. Applicants Lebanon, by order of the Department of State, Applied Mathematics group with collateral inter­ should have a proven research record of high and therefore applications from individuals who ests in scientific computation. Research areas quality and have demonstrated interest and would travel to or reside in Lebanon on a U.S. overlapping these interests are particularly eo­ ability in teaching. Preference will be given to passport cannot at this time be considered. couraged. Excellence in teaching as well as candidates who have one or more years of productive scholarship is required. Minorities postdoctoral experience. This position is subject and women are especially solicited. to final budgetary approval. The salary will be Salary is competitive and includes a startup commensurate with experience and research THE NETHERLANDS travel/equipment package. Applicants should record. Applicants should send a C. V. including send a curriculum vitae, a description of re­ list of publications, statement of research and UNIVERSITY OF AMSTERDAM search interests, and have three letters of teaching interests and arrange for three letters Department of Mathematics reference sent to: of recommendation to be sent directly to: W. G. Bridges, Head The Head, Department of Mathematics, Invites applications for the following three posi­ Department of Mathematics University of British Columbia, Vancouver, B. C. tions: Box 3036, University Station Canada V6T 1Y 4. Applications must be received 1. Chair of Analysis Laramie, WY 82071 before March 1, 1991. In accordance with 2. Chair of Mathematical Physics Email inqumes should be sent to Canadian immigration requirements, priority will 3. Chair of Geometry [email protected]. Applications completed be given to Canadian citizens and permanent Requirements for all positions include a dis­ by January 15, 1991 will receive first con­ residents of Canada UBC encourages qualified tinguished research record, evidence of good sideration. The University of Wyoming is an women and minority applicants. teaching ability and potential for leadership. Affirmative Action/Equal Opportunity Employer. Applicants for all chairs should have a broad knowledge of the field. Applicants for the Anal­ ysis Chair should have a research record in a central area of analysis and preferably an GERMANY interest in applied analysis; applicants for the Mathematical Physics Chair should have a CANADA UNIVERSITY OF BIELEFELD research record in a field of interaction of math­ Department of Mathematics ematics and physics and preferably an interest in applied analysis; applicants for the Geometry BROCK UNIVERSITY Starting October 1st, 1990, a college for post­ Chair should have a research record in a cen­ Department of Mathematics graduate and postdoctoral studies in mathemat­ tral field of geometry. Foreign candidates are ics will be instituted at Universitat Bielefeld. required to have a good command of the Dutch The Department of Mathematics at Brock Uni­ The main areas of research are: finite, language within two years. versity invites applications for a tenure-track discrete and Lie groups, potential theory, rep­ Candidates should send a letter of applica­ position at the Assistant Professor level, be­ resentation theory, topology, K-theory, combi­ tion, a vita, a list of publications and letters of ginning July 1,1991. Appointment to a higher natorics, numerical analysis, information theory reference to Dr. R. T. Jongerius, Department rank will be considered under exceptional cir­ and statistics. of Mathematics, University of Amsterdam, Plan­ cumstances. Applicants must have a Ph.D., Further information and application forms tage Muidergracht 24, 1018 TV Amsterdam, together with a strong research record, or at may be obtained from: Prof. Dr. Andreas Dress, The Netherlands. Closing date in two weeks, least demonstrated research potential. Duties Fakultat fur Mathematik, Universitat Bielefeld, but late applications may be considered. will include teaching both major courses and Postfach 8640, 4800 Bielefeld 1, West-Germany service courses. Strong candidates from all (Telefax: (0521) 106-4743). areas of mathematics will be considered; how­ ever the Department has a specific need for expertise in Statistics. PUBLICATION FOR SALE I In accordance with Canadian immigration requirements, this advertisement is directed CALCULUS BY GILBERT STRANG to Canadian citizens and permanent residents. LEBANON A direct and friendly textbook, written for stu­ Applications including a curriculum vitae and the AMERICAN UNIVERSITY OF BEIRUT dents to read. The mathematics is alive, the names of three referees should be sent to Dr. explanations are clear, the length is reduced. H. E. Bell, Department of Mathematics, Brock TEACHING OVERSEAS: This book fully supports calculus courses at all University, St. Catherines, Ontario, Canada L2S The Department of Mathematics at the institutions. 3A 1, for receipt by March 22, 1991 . Brock American University of Beirut, in Beirut, Lebanon Your students will enjoy working with this University is committed to a positive action (AUB) invites applications for faculty positions at textbook-it looks forward. Please ask to see policy aimed at reducing gender imbalance the level of Assistant Professor or above, avail­ Strang's Calculus: in faculty; qualified women candidates are able October 1, 1991. Candidates are sought WELLESLEY-CAMBRIDGE PRESS especially encouraged to apply. Smoking at in the fields of Analysis, Probability Theory, and Box 82-279 Wellesley MA 02181 Brock University is strictly controlled. Topology. Applicants in other disciplines will also (617) 431-8488 Text: 16 chapters, 615 be considered. pages Applications should hold the Ph.D. degree and would be expected to teach undergraduate

FEBRUARY 1991, VOLUME 38, NUMBER 2 163 Classified Advertisements

The novel 'THE YUKIAD' (ISBN 0-86332- robotics. Thirty publications. Fourteen years of immediately, C. Vora, 1178 Milford St., Rear, 478-9), by well-known mathematician VICTOR academic and industrial research experience in Johnstown, PA 15905. SNAITH, is a black comedy with mathematical the Academy of Science, USSR. References touches. Available via bookstores or directly available upon request. Available immediately. from the publisher: The Book Guild Ltd., Tem­ Contact: Dr. V. Zak, c/o Prof. L. Charny, Boston ple House, 25 High St., Lewes, E. Sussex University, 44 Cummington Street, Boston, MA BN7 2LU, England (FAX 011-44-273-476472). 02215 Phone: (617) 353-5442. PUBLICATIONS WANTED Price £12.95 or $25. Wanted: Mathematical books, journals, reprints, R. Dennis, Math. Dept., Seeking full professorship with (1) tenure, (2) ephemera. Contact K. U., Ithaca, NY 14853-7901. adjustments, (3) seniority since 1/1/76 at Ph.D. White Hall, Cornell POSITION WANTED FAX: 607-255-7149. email: granting institutions with teaching load of 0 Tel: 607-255-4027, dennis@mssun?.msi.cornell.edu to 6 cr. hrs. per term. Age 45. Specialty Research Mathematician, Ph.D. 1983. Spe­ Algebraic Topology (Lefschetz Type Fixed Point cialization: control theory, differential game~, Theorems.) M. experience '67 to '83. Available

Now in Paperback

INTRODUCTION TO ALGEBRAIC CURVES TRANSLATIONS OF MATHEMATICAL MONOGRAPHS, VOLUME 76 Phillip A. Griffiths

Algebraic curves and compact Riemann surfaces comprise the most developed and arguably the most beautiful portion of algebraic geometry. However, the majority of books written on the subject discuss algebraic curves and compact Riemann surfaces separately, as parts of distinct general theories. Most texts and university courses on curve theory generally conclude with the Riemann-Roch theorem, despite the fact that this theorem is the gateway to some of the most fascinating results in the theory of algebraic curves. This book is based on a six-week series oflectures presented by the author to third- and fourth-year undergraduates and graduate students at Beijing University in 1982. The lectures began with minimal technical requirements (a working knowledge of elementary complex function theory and algebra together with some exposure to topology of compact surfaces) and proceeded directly to the Riemann-Roch and Abel theorems. This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader can grasp the basic results of the subject. Although such modem techniques of sheaf theory, cohomology, and commutative algebra are not covered here, the book provides a solid foundation to proceed to more advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves. Containing numerous exercises and two exams, this book would make an excellent introductory text. 1980 Mathematics Subject Classification: 14: ISBN 0-8218-4530-6, LC 89-7000, ISSN 0065-9282; (Hardcover) 500 pages, July 1989: Individual member $59, All prices subject to change. Free shipment by surface; for air delivery, List price $99, Institutional member $79 please add $6.50 per title. Prepayment required. Order from American To order, please specify MMON0/76NA Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI ISBN 0-8218-4537-3, December 1990 02901-1571, or call toll free 800-321-4AMS (321-4267) in the (Softcover) 500 pages, Individual member $34. List price $56 continental U.S. and Canada to charge with VISA or MasterCard. To order, please specify MMONOS/76NA

164 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Applications and recommendations are invited for a one- or two-year half-time appointment as an Associate Editor of Mathemati~al Reviews (MR), to commence during the summer of 1991. Applications will be welcome from persons taking leave from other positions and in particular from tenured faculty members who can take leave to come to MR for one or two years.

The MR office of the American Mathematical Society is located in Ann Arbor, Michigan, not far from the campus ofthe University of Michigan. The editors, although employees of the AMS, enjoy many privileges at the University. At present, MR employs fifteen mathematical editors, about six consultants and over sixty nonmathematicians. It produces Mathematical Revietvs, Current Mathematical Publications, various in­ dexes, the on-line service MathSci and MathSci Disc. The responsibilities of an Associate Editor fall primarily in the day-to-day operations of selecting articles and books suitable for review, classifying these items, assigning them to reviewers, editing the reviews when they are returned and correcting the galley proof. An individual with considerable breadth in pure or applied mathematics is sought and preference will be given to those applicants with expertise in mathematical physics, statistics, theoretical computer science and/or geometry. The ability to write good English is essential and the ability to read mathematics in major foreign languages is important. (The ability to read mathematical articles in Russian or Chinese is especially desirable.)

Persons interested in combining a sabbatical or other leave with this half-time appointment as an Associate Editor are encouraged to write (or telephone) for further information. The twelve-month salary is negotiable and will be commensurate with the experience the applicant brings to the position.

Applications (including curriculum vitae, bibliography and names and addresses of at least three references) should be sent to

Dr. G. J. Janusz, Executive Editor Mathematical Reviews P. 0. Box 8604 Ann Arbor, MI 48107-8604 Telephone: 313-996-5255 FAX: 313-996-2916 INTERNET: [email protected]

Interested applicants are urged to inquire without delay.

The American Mathematical Society is an equal opportunity employer. Wadsworth & Brooks/Cole Advanced Books &Software

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A Course in Ring Theory Introduction to Holomorphic Functions of DONALD S. PASSMAN Several Variables, Volumes 1·111 This textbook for a graduate pourse in ring ROBERT C. GUNNING theory offers a module theoretic stroll through a These volumes provide an extensive introduc­ mixture of commutative and non-commutative tion to the Oka-Cartan theory of holomorphic ring theory, with emphasis on the latter. Projec­ functions of several variables and holomorphic tive and injective modules supply the framework varieties. Each volume covers a different aspect tor a coherent choice of material. 1991. 320 and can be read independently. Volume 1: Func­ pages. Casebound. ISBN: 0-534-13776-8. tion Theory. 1990. 206 pages. Casebound. ISBN: 0-534-13308-8. Volume II: Local Theory. New for 1991 1990. 300 pages. Casebound. ISBN: 0-534- 13309-6. Volume Ill: Homological Theory. 1990. 225 pages. Casebound. ISBN: 0-534-13310-X. The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Harmonic Analysis Functions HENRY HELSON BRUCE E. SAGAN This reprint of the 1983 edition is appropriate for Graduate text or reference book. This book graduate students who are familiar with the brings together for the first time many of the im­ Lebesgue integral, complex function theory, and portant results in this field. The only prerequi­ Banach spaces. 1991. 192 pages. Paperbound. sites are a familiarity with elementary group ISBN: 0-534-15570-7. theory and linear algebra. All other results about representations, combinatorics and symmetric representations are developed as they are needed. 1991. 216 pages. Casebound. ISBN: 0-534-15540-5. To order a personal copy of software or books, use our toll-tree number (800) 354-9706, or write New for 1991 to us at the address below. To request com­ plimentary copies for review, or to receive a copy of our 1991 Advanced Books & Software Probability: Theory and Examples Catalog, please write: RICHARD DURRETT Wadsworth & Brooks/Cole Advanced Books & Software This text for a one-year graduate course in prob­ AMS11 ability emphasizes results that can be used to 511 Forest Lodge Road solve problems. Unusual topics include large Pacific Grove, CA 93950 deviations, local limit theorems, renewal theory, (408) 373-0728 Markov chains on general state space, subaddi­ tive ergodic theory, and central limit theorems tor stationary sequences and martingales. 1991. 464 pages. Casebound. ISBN: 0-534-13206-5. • RUSSIAN MATHEMATICAL SURVEYS

Russian Mathematical Surveys is a cover-to-cover translation of the Soviet journal Uspekhi Matematicheskikh Nauk which is one of the foremost mathematical journals in the USSR and enjoys a high reputation world-wide.

It consists mainly of long articles, each of which is a survey of recent progress in a particular branch of mathematics; it also includes the short communications of the Moscow Mathematical Society, and the proceedings of the joint meetings of the Moscow Mathematical Society and the Petrovskii Seminar on differential equations and mathematical problems of physics. Biographi­ cal articles on prominent Soviet mathematicians also appear.

Russian Mathematical Surveys (ISSN 0036-0279) is translated and published jointly by The London Mathematical Society and The British Library; its Scientific Editor is E. J. F. Primrose (Leicester University) and Deputy Editor D. L. Johnson (Nottingham University). The English translation is published six times per year, some 6 to 8 months after the Russian original.

A selection of recently published and forthcoming articles

The Symplectic Topology of Completely Theory of n-Shapes Integrable Hamiltonian Systems A. Ch. Chigogidze A. T. Fomenko Hydrodynamics of Weakly Deformed Soliton Geometric Aspects ofAveraging Lattices S.M. Kozlov B. A. Dubrovin and S. P. Novikov

Topological Classification of Cascades on Some Unsolved Problems in the Theory of Closed Two-Dimensional Manifolds Differential Equations and Mathematical S. Kh. Aranson and V. Z. Grines Physics V.I. Arnol'd et al. The Riemann-Hilbert Problem A. A. Bolibrukh Orders and Specimen Copy requests should be sent to:

Turpin Transactions Ltd. The Distribution Centre Blackhorse Road Letchworth, Herts SG6 lHN United Kingdom

The 1991 subscription price, for Volume 46, is £276 (sterling); back numbers are also available NATIONAL UNIVERSITY OF SINGAPORE

DEPARTMENT OF MATHEMATICS

Applications are invited for teaching appointments at the Lecturer or Senior Lecturer level from candidates who are able to teach in one or more of the following areas:

Pure Mathematics Applied Mathematics Operational Research Statistics

Candidates should possess a PhD degree in Mathematics and have a strong commitment to teaching and research.

Gross annual emoluments range as follows:

Lecturer S$50,390 - 64,200 Senior Lecturer S$58,680 - 100,310 (US$1.00 = S$1. 70 approximately)

The commencing salary will depend on the candidate's qualifications, experience and the level of appointment offered.

Leave and medical benefits will be provided. Depending on the type of contract offered, other benefits may include: provident fund benefits or an end-of-contract gratuity, a settling-in allowanc~ of S$1 ,000 or S$2,000, subsidised housing at nominal rentals ranging from S$100 to S$216 p.m., education allowance for up to three children subject to a maximum of S$10,000 per annum per child, passage assistance and baggage allowance for the transportation of personal effects to Singapore. Staff members may undertake consultation work, subject to the approval of the University, and retain consultation fees up to a maximum of 60% of their gross annual emoluments in a calendar year.

The Department of Mathematics is a department in the Faculty of Science. There are 8 faculties in the National University of Singapore with a current student enrollment of some 14,000. All departments are well-equiped with a wide range of facilities for teaching and research.

All academic staff have access to the following computer and telecommunication resources: an individual microcomputer (an IBM AT­ compatible or Apple Macintosh); an IBM mainframe computer with 16 MIPS of computing power; an NEC SX supercomputer with 650 MFLOPS of computing power; departmental laser printers; a wide spectrum of mainframe and microcomputer software; voice-mail; BITNET to access academic institutions world-wide. The campus-wide network, which is based on the high speed optical fibre based FDDI technology, links up all the academic staff and student microcomputers, and provides access to the mainframe computer, the supercomputer and the on-line library catalogue.

Application forms and further information on terms and conditions of service may be obtained from:

The Director The Director Personnel Department North America Office National University of Singapore National University of Singapore 10 Kent Ridge Crescent 55 East 59th Street Singapore 0511 New York, NY 10022, USA Tel: (212) 751-0331

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FINITE GEOMETRIES UNIVERSITE DE LAUSANNE AND COMBINATORIAL DESIGNS Earl S. Kramer L'institut de rnathernatiques de notre Faculte des and Spyros S. Magliveras, Editors

sciences cherche Contemporary Mathematics, Volume 111 More than eighty participants from all over the world attended an PROFESSEUR ORDINAIRE D'ANALYSE AMS Special Session on Finite Geometries and Combinatorial De­ Plein temps signs held in Lincoln, Nebraska in the fall of 1987. This volume charge de la formation de base en analyse contains the proceedings of that Special Session, in addition to several invited papers. Employing state-of-the-art combinatorial and geomet­ fonctionnelle des etudiants en rnathernatiques et ric methods, the papers show significant advances in this area. Topics d'un cours d'analyse superieure; recherches orientees range over finite geometry, combinatorial designs, .their automorphism vers les algebres d'operateurs, les operateurs groups, and related structures. Requiring graduate-level background, this book is intended primar­ differentiels et I' analyse harrnonique. ily for researchers in finite geometries and combinatorial designs. However, the interested nonspecialist will find that the book provides Entree en fonction: ler septembre 1991. an excellent overview of current activity in these areas.

Renseignernents: prof. 0. Burlet, tel.: 011 41 21/ 1980 Mathematics Subject All prices subject to change. Free 692'20'49. Classifications: 05, 51 shipment by surface; for air delivery, ISBN 0-8218-5118-7, LC 90-45302. please add $6.50 per title. Prepay­ ISSN 0065-9266 ment required. Order from Les candidatures avec c.v. et liste des publications 312 pages (softcover), October 1990 American Mathematical Society, Individual member $32, P.O. Box 1571, Annex Station., sont aadresser au Doyen de la Faculte des Sciences, List price $53, Providence, RI 02901-1571, or call College propedeutique CH -1015 Lausanne (Suisse) Institutional member $42 toll free 800-321-4AMS (321-4267) To order, please specify in the continental U.S. and Canada to jusqu'au 28 fevrier 1991. CONM/111NA charge with Visa or MasterCard. Application for Membership 1991 AMERICAN MATHEMATICAL SOCIETY (January-December) Date ...... 19 ......

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Fold here Discrete Mathematics Editor-in-Chief: NEW JOURNALS P.L. Hammer The aim of Discrete Mathematics is to bring Call tor papers The Annals of Pure research papers in various areas of discrete papers and short Tloth,•m·ot;,,~ Contributions can be research papers, interest in pure communications, survey articles, and Computational Geometry mathematics and fields covered by OM include: graph science and other hv•,<>rnr~•nh theory, network theory, coding Theory and Applications designs, lattice theory. the theory of mathematical logic. It Editors-in-Chief: ordered sets, combinatorial geometries, publication of papers J.-R. Sack extremal set theory, logic and promptly by other · J. Urrutia polyhedra, and discrete separate book. Honorary Editors: F.P. Preparata P. Erdos Computational Geometry publishes fundamental research in all areas of the subject. as well as Asymptotic ...... v ...... disseminating information on the applications, techniques. and use of computational geometry. It Editor-in-Chief: also contains a special section containing open L.S.Frank problems and concise reports on implementations of computational geometry tools. 1991: Volume 1 (6 issues) Price: US $157.25/Dfl. 280.00 Differential Geometry and its Applications Pure and Applied Algebra that of algebra likely to be of Editor -in-Chief: algebraic results with D. Krupka development of This journal publishes original research papers and general relevance to survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate Discrete Applied Mo,~ho•~not geometrical structures. The following main areas are covered: differential equations on manifolds, global Combinatorial Operations R .....,,~rr'h analysis, Lie groups, local and global differential Computer Science geometry, the calculus of variations on manifolds, topology of manifolds, mathematical physics. Editor-in-Chief: P.L. Hammer 1991: Volume 1 (4 issues) Price: US $163.00/Dfl. 290.00 The goal of Discrete Applied M~•m••m••• publish research in different areas of combinatorics and to demonstrate All prices include postage/handling. For further mathematical tools in a variety of details (and Guide for Authors) write to Elsevier to research in discrete 1 m:,th"""' of Topology and its Science Publishers. attn. Marijcke Haccou. PO Box Among areas its applications. algebraic, general, 103, 1000 AC Amsterdam. The Netherlands. Telex network theory, optimization, facets of topology as 18582 espa nl. Fax 020-5862616 theory, utility theory and automata between topology and structures, mathematical biology, m:,th""'" ASK FOR YOUR FREE INSPECTION COPY e.g. topological sociology, mathematical chemistry, game i functional analysis, In the USA/Canada: theory. scheduling lar intervals the journal Elsevier Science Publishers 1991: Volumes 30-34 (15 issues) "Open Problems in Journal Information Center Price: US $786.50/Dfl. 1400.00 Mill and G.M. Reed. This 655 Avenue of the Americas ISSN 0166-218X nro,hi<>I'YIO liSted in the New York, NY 10010, USA by North-Holland Reed. In all other countries: Elsevier Science Publishers attn.: Marijcke Haccou PO Box 103, 1000 AC Amsterdam The Netherlands

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A. Borel, Institute for Advanced Study, Princeton, NJ A.I. Kostrikin and I.R. Shafarevich, Steklov Linear Algebraic Groups Mathematical Institute, USSR (Eds.) Second Revised and Enlarged Edition Algebra II Presents foundational material on algebraic groups, Lie al­ Noncommutative Rings. Identities. gebras, transformation spaces, and quotient spaces. It then Translated by E.J. Behr, Illinois State University, turns to solvable groups, general properties of linear alge­ Normal, IL (Ed.) braic groups and Chevally's structure theory of reductive Here is a two-part survey on the subjec1 of non-commuta­ groups over algebraically closed groundfields. The remain­ tive rings and algebras, with the second part focused on the der of the book is devoted to rationality questions over non­ theory of identities of these and other algebraic systems. It algebraically closed fields. The last part of the first edition provides a broad overview of the most modem trends en­ has been expanded by the addition of five new sections, countered in non-commutative algebra, presenting at the centering on the structure of the group of rational points of same time historical background of these trends, as well as an isotropic reductive group and on central isogenies. Some the numerous connections between algebraic theories and more results on solvable groups have also been included. other areas of mathematics. 1991/app. 304 pp./Hardcover/$49.00 1991/app. 244 pp., 13 illus./Hardcover/$59.00 ISBN 0-387-97370-2 ISBN 0-387-18177-6 Graduate Texts in Mathematics, Volume 126 The Encyclopaedia of Mathematical Sciences, Volume 18 (First edition published by W.A. Benjamin in 1969) J.H. Conway, Princeton University, Princeton, NJ; and G. Hammerlin, Ludwig Maximilians Universitat, N.J. A. Sloane, AT & T Bell Laboratories, Murray Hill, NJ Munich, FRG and K.-H. Hoffmann, Universitat Augsburg, Augsburg, FRG Sphere Packings, Lattices Numerical Mathematics and Groups Translated by L. Schumaker, Vanderbilt University, From the reviews: Nashville, TN "This book will be an essential reference for anyone Covers the classical topics of numerical analysis and in­ whose work involves lattices for the foreseeable future. cludes an up-to-date treatment of both splines and linear There is nothing else like it, and as an intellectual ac­ optimization methods. The text is designed to be used in a complishment it is breathtaking." first course in numerical analysis at the upper undergrad­ - IEEE Transactions on Information Theory uate and beginning graduate levels. A careful balance be­ "Every page crackles with evidence of the intellectual ex­ tween mathematical rigor and numerical insight is featured. citement latent in good,fresh mathematics . .. An extraor­ Each section concludes with an extensive set of exercises dinary monograph, a treasure." which instructors should find useful in helping students to - SciTech Book News master the material. Moreover, the authors have also pro­ "The authors must be congratulated on their bibliog­ vided carefully researched historical notes which will be of raphical research , which has produced more than fifteen particular interest to experts as well as to students. hundred references!" 1991/422 pp., 72 illus./Softcover/$39.95 -American Mathematical Monthly ISBN 0-387-97494-6 1988/663 pp., 112 illus./Hardcover/$89.90 Undergraduate Texts in Mathematics ISBN 0-387-96617-X Readings in Mathematics Grundlehren der mathematischen Wissenschaften, Volume290 G. Faltings, Princeton University, Princeton, NJ; and C.-L. Chai, University of Pennsylvania, Philadelphia, PA

Degeneration of Abelian Varieties Order Today! Discussed in this volume are semiabelian degenerations of • Call: Toll-Free 1-800-SPRINGE(R): 1-800-777-4643. abelian varieties and arithmetic compactifications of the In NJ call 201-348-4033 (8:30AM-4:30PM EST). Siegel moduli-space. A classification of semiabelian Your reference number is S744. schemes, construction of the toroidal and the minimal com­ • Write: Send payment plus $2.50 for postage and pactification over the integers, heights for abelian varieties handling to: Springer-Verlag New York, Inc., over number fields, and Eichler-integrals in several vari­ Order Fulfillment-S744, P .O . Box 2485, ables is included. New results that have never appeared in Secaucus, NJ 07096-2491. print before are also presented. • Visit: Your local technical bookstore. 1991/316 pp./Hardcover/$39.80/ISBN 0-387-52015-5 Instructors: Call or Write for information on textbook Ergebnisse der Mathematik und ihrer Grenzgebiete, examination copies! 3. Folge, Volume 22 ~ Springer-Verlag New York • Berlin Heidelberg Vienna London Paris Tokyo Hong Kong Barcelona