DOCSLIB.ORG

Calendar of AMS Meetings and Conferences

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences This calendar lists all meetings and conferences approved prior to the date this insofar as is possible. Abstracts should be submitted on special forms which are issue went to press. The summer and annual meetings are joint meetings of the available in many departments of mathematics and from the headquarters office of Mathematical Association of America and the American Mathematical Society. The the Society. Abstracts of papers to be presented at the meeting must be received meeting dates which fall rather far in the future are subject to change; this is par­ at the headquarters of the Society in Providence, Rhode Island, on or before the ticularly true of meetings to which no numbers have been assigned. Programs of deadline given below for the meeting. The abstract deadlines listed below should the meetings will appear in the issues indicated below. First and supplementary be carefully reviewed since an abstract deadline may expire before publication of announcements of the meetings will have appeared in earlier issues. Abstracts a first announcement. Note that the deadline for abstracts for consideration for of papers presented at a meeting of the Society are published in the journal Ab­ presentation at special sessions is usually three weeks earlier than that specified stracts of papers presented to the American Mathematical Society in the issue below. For additional information, consult the meeting announcements and the list corresponding to that of the Notices which contains the program of the meeting, of special sessions. Meetings Abstract Program Meeting# Date Place Deadline Issue 876 • October 30-November 1, 1992 Dayton, Ohio Expired October 877 • November 7-8, 1992 Los Angeles,California Expired October 878 • January 13-16, 1993 San Antonio, Texas October 8 December (99th Annual Meeting) 879 • March 26-27, 1993 Knoxville, Tennessee January 5 March 880 • April9-10, 1993 Salt Lake City, Utah January 29 April 881 • April17-18, 1993 Washington, D.C. January 29 April 882 • May 21-22, 1993 DeKalb, Illinois February 26 May-June 883 • August15-19, 1993 Vancouver, British Columbia May 18 July-August (96th Summer Meeting) (Joint Meeting with the Canadian Mathematical Society) 884 • September 18-19, 1993 Syracuse, New York May 18 September 885 * October 1-3, 1993 Heidelberg, Germany (Joint Meeting with the Deutsche Mathematiker-Vereinigung e.V.) October 22-23, 1993 College Station, Texas January 12-15, 1994 Cincinnati, Ohio (1 OOth Annual Meeting) March 18-19, 1994 Lexington, Kentucky March 25-26, 1994 Manhattan, Kansas June 16-18, 1994 Eugene, Oregon October 28-29, 1994 Stillwater, Oklahoma January 25-28, 1995 Denver, Colorado (1 01 st Annual Meeting) March 24-25, 1995 Chicago, Illinois January 10-13, 1996 Orlando, Florida (1 02nd Annual Meeting) March 22-23, 1996 Iowa City, Iowa * Please refer to page 760 for listing of Special Sessions. Conferences January 11-12, 1993: AMS Short Course on Wavelets and Applications, San Antonio, Texas. Deadlines November Issue December Issue January Issue February Issue Classified Ads* October 1 , 1992 November 13, 1992 December 10, 1992 January 7, 1993 News Items September 21, 1992 October 29, 1992 December 2, 1992 December 24, 1992 Meeting Announcements** September 21, 1992 October 29, 1992 December 2, 1992 December 24, 1992 • 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 ARTICLES 683 Letters to the Editor 694 Forum 684 Deane Montgomery (1909-1992) Armand Borel 715 News and Announcements This article pays tribute to the life and career of former AMS President 724 Funding Information for the Deane Montgomery, a distinguished topologist and longtime member of the Mathematical Sciences Institute for Advanced Study. 725 Acknowledgment of Contributions 688 Sloan Foundation Joins AMS to Aid Mathematics in the former Soviet Union 745 1992 AMS Elections Biographies of Candidates, 746 The Sloan Foundation has awarded the Society a $30,000 challenge grant to support the AMS program to assist mathematics in the former 755 Meetings and Conferences of Soviet Union. Allyn Jackson describes the assistance program, and an the AMS accompanying announcement provides information on how to contribute to Dayton, OH this important effort. Ocrober3G-November1, 755 Los Angeles, CA 689 European Meetings Bring Mathematicians Together November 7-8, 758 Invited Speakers, 760 A number of historic ''firsts" took place in Europe this summer-the joint 1992 Symposium on Some AMS meeting with the London Mathematical Society in Cambridge, England; Mathematical Questions the opening of the Isaac Newton Institute in Cambridge; and the first in Biology, 764 European Congress of Mathematics, held in Paris. Allyn Jackson reports on San Antonio, TX these events. January 13-16, 765 767 Mathematical Sciences Meetings FEATURE COLUMNS and Conferences 776 New Publications Offered by the 696 Computers and Mathematics Keith Devlin AMS Andrew Granville writes an expository article based on his paper There are 781 AMS Reports and infinitely many Carmichael numbers, cowritten with Red Alford and Carl Communications Pomerance. Following Granville's piece, Barry Simon presents the results Statistics on Women, 781 of a series of benchmark tests he has run on a number of computer Officers and Committee Members, mathematics systems. 782 783 Miscellaneous 711 Inside ~he AMS Personal Items, 793 Alice Schafer, Chair of the AMS Committee on Human Rights of Deaths, 793 Mathematicians, reports on the Committee's activities and accomplishments 794 Classified Advertising over the past two years. 809 Forms 712 Washington Outlook Lisa Thompson discusses how the government allocates resources among the various elements of the scientific enterprise. SEPTEMBER 1992, VOLUME 39, NUMBER 7 681 --------·········· ................................................................................................................................................................................... From the Executive Director ... RESOURCES FOR EXCELLENCE AMERICAN MATHEMATICAL SOCIETY There have been numerous national reports pointing out the need for the renewal of academic mathematical sciences departments. The reports call upon the departments to maintain the tradition of first class research; reform mathematics education at all levels; revise the curriculum to introduce experimental classes, varied instructional approaches, and new technologies; become involved in teacher enhancement and preparation; en­ EDITORIAL COMMITIEE gage in interdisciplinary activity and university service; increase the participation of Michael G. Crandall underrepresented minorities and women; and contribute to economic competitiveness. Amassa Fauntleroy This is only a partial list. Information is available, in varying degrees of detail and Robert M. Fossum (Chairman) clarity, as to how to go about doing all these things. Carolyn S. Gordon (Forum Editor) D. J. Lewis These reports have been useful in providing a springboard for debate, in distributing L. Ridgway Scott (Letters Editor) important information, and in outlining means for change. However, it is time to move Robert E. L. Turner beyond the reports and into action, and mathematical sciences departments are the natural institutions to take actions to bring about substantial, long-term change within MANAGING EDITOR the community. There is general agreement on what needs to be done, and there are John S. Bradley laudable examples of activities of individuals, groups, and departments that are doing ASSOCIATE EDITORS exciting things. But, is the academic mathematical sciences community positioned to Ronald L. Graham, Special Articles respond? Does this community have the resources (or the political sophistication to get Jeffrey C. Lagarias, Special Articles them) necessary to meet these challenges and opportunities? SUBSCRIPTION INFORMATION Mathematical sciences departments, on the whole, are not viewed as major players Subscription prices for Volume 39 (1992) are in acquiring academic resources. There is a history of little attention being paid to the $131 list; $105 institutional member; $79 individ­ political avenues by which mathematical sciences departments might position them­ ual member. (The subscription price for members selves more favorably. The current challenges and opportunities come at a time when is included in the annual dues.) A late charge of there is a shortage of federal research funds and there is a depressed economy that is af­ 10% of the subscription price will be imposed upon fecting academic finances. Indeed, department resources are vulnerable to serious cuts. orders received from nonmembers after January 1 Distressed departments cannot respond adequately to the new challenges confronting of the subscription year. Add for postage: Surface them. Faculty, staff (including technical assistance), appropriate space, computers and delivery outside the United States and lndia-$15; networking, libraries, instructional labs, and research and travel funds are just some of to lndia-$28; expedited delivery to destinations in for departments to respond to the recommendations that are North America-$32; elsewhere-$67. Subscrip­ the resources necessary tions and orders for AMS publications should be being made. How can we make the case
Recommended publications
  • JUNE 2017 - Vol

    JUNE 2017 - Vol

    Knob Hill United Church, 23 Gage Avenue, Scarborough, ON, M1J 1T3 Email: [email protected] or [email protected] www.khuc.org Minister: Rev. Hannah Lee, 416.431.5054 ____________________________________________________________________________________ Dear Friends, Welcome. You have probably read this word on our church bulletin, projected on our sanctuary wall, or on a church sign next to the road. What does it mean to be a welcoming community? There was a time when the church followed a process of welcome based on “Behaving, Believing, Belonging.” Christians were told you had to behave a certain way, believe a set of doctrines, and then they were allowed to belong to the church community. According to this model, belonging is dependent on behaving and believing in line with what is deemed acceptable by the community. Is this truly welcoming in God’s eyes? Or are we distorting our understanding of God and God’s grace? Jesus calls his disciples – and us today – to welcome all. We are all agents in giving and receiving welcome. The process of welcome we at KHUC are striving to do is “Belonging, Believing, Becoming.” God welcomes us and we in turn welcome one another, especially those who are marginalized, or considered the least and the lost. This model of welcome allows people to come as they are. It allows people to be honest and vulnerable. It leaves room for grace. It acknowledges that we are not perfect, but God is. It doesn’t matter who you are, what you’ve done, how you believe – it doesn’t even matter if you are Christian.
  • On the Uniqueness of Gibbs States in the Pirogov-Sinai Theory?

    On the Uniqueness of Gibbs States in the Pirogov-Sinai Theory?

    Commun. Math. Phys. 189, 311 – 321 (1997) Communications in Mathematical Physics c Springer-Verlag 1997 On the Uniqueness of Gibbs States in the Pirogov-Sinai Theory? J.L. Lebowitz1, A.E. Mazel2 1 Department of Mathematics and Physics, Rutgers University, New Brunswick, NJ 08903, USA 2 International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow 113556, Russia Received: 4 June 1996 / Accepted: 30 October 1996 Dedicated to the memory of Roland Dobrushin Abstract: We prove that, for low-temperature systems considered in the Pirogov-Sinai theory, uniqueness in the class of translation-periodic Gibbs states implies global unique- ness, i.e. the absence of any non-periodic Gibbs state. The approach to this infinite volume state is exponentially fast. 1. Introduction The problem of uniqueness of Gibbs states was one of R.L.Dobrushin’s favorite subjects in which he obtained many classical results. In particular when two or more translati- on-periodic states coexist, it is natural to ask whether there might also exist other, non translation-periodic, Gibbs states, which approach asymptotically, in different spatial directions, the translation periodic ones. The affirmative answer to this question was given by R.L.Dobrushin with his famous construction of such states for the Ising model, using boundary conditions, in three and higher dimensions [D]. Here we consider the opposite± situation: we will prove that in the regions of the low-temperature phase diagram where there is a unique translation-periodic Gibbs state one actually has global uniqueness of the limit Gibbs state. Moreover we show that, uniformly in boundary conditions, the finite volume probability of any local event tends to its infinite volume limit value exponentially fast in the diameter of the domain.
  • The Ninety-Seventh Commencement Asbury Theological Seminary

    The Ninety-Seventh Commencement Asbury Theological Seminary

    The Ninety-Seventh Commencement asbury theological seminary Saturday, November 14, 2020 THE NINETY-SEVENTH COMMEncEMENT NOVEMBER 14, 2020 ASBURY THEOLOGIcaL SEMInaRY THE PRESIDENT’S CABINET President TIMOTHY C. TENNENT, PH.D. Provost and Vice President of Academic Affairs DOUGLAS K. MattHEWS, PH.D. Associate Provost and Vice President of Enrollment Management and Student Services KEVIN BISH, M.ED. Vice President of Advancement JAY E. MANSUR, C.F.S. Vice President of Finance and Administration and Chief Financial Officer BRYAN P. BLANKENSHIP, M.B.A. Vice President of Formation DOnna COVINGTON, M.A.C.L. Vice President of Seedbed JOHN DAVID WALT, J.D. Associate Vice President of the Florida Dunnam Campus R. STEPHEN GOBER, D.MIN. Associate Vice President of Enrollment Management and Operations of the Florida Dunnam Campus ERIC CURRIE, M.DIV. AcaDEMIC OFFICERS Associate Provost Dean of Advanced Research Programs CHRIstINE L. JOHNSON, PH.D. LALsanGKIMA PacHUAU, PH.D. Dean of the Beeson School of Practical Theology Dean of the School of Theology and Formation THOMAS F. TUMBLIN, PH.D. JAMES R. THOBABEN, PH.D. Associate Provost and Dean of the Assistant Provost of Institutional Evaluation, Orlando School of Ministry Assessment and Academic Administration BRIAN D. RUSSELL, PH.D. S. BRIAN YEICH, PH.D. Dean of the School of Biblical Interpretation Dean of Library, Information, DAVID R. BAUER, PH.D. and Technology Services PAUL A. TIPPEY, PH.D. Dean of the E. Stanley Jones School of World Mission and Evangelism GREGG A. OKESSON, PH.D. THE NINETY-SEVENTH COMMEncEMENT Saturday, The Fourteenth of November Two Thousand Twenty Eleven o’clock in the morning PRESIDENT TIMOTHY C.
  • Of 23 Case No: 19-L-0846 CIRCUIT COURT for the 20TH JUDICIAL CIRCUIT COUNTY of ST. CLAIR, STATE of ILLINOIS LISA MOORE

    Of 23 Case No: 19-L-0846 CIRCUIT COURT for the 20TH JUDICIAL CIRCUIT COUNTY of ST. CLAIR, STATE of ILLINOIS LISA MOORE

    Electronically Filed Kahalah A. Clay Circuit Clerk CARMEN GLENN 19L0846 St. Clair County CIRCUIT COURT FOR THE 20TH JUDICIAL CIRCUIT 6/22/2020 10:42 AM COUNTY OF ST. CLAIR, STATE OF ILLINOIS 9555049 LISA MOORE, individually and on behalf of ) all others similarly situated, ) ) Plaintiff, ) v. ) No. 19-L-0846 ) KIMBERLY-CLARK WORLDWIDE, INC., ) ) Defendant. ) MOTION FOR FINAL APPROVAL OF CLASS ACTION SETTLEMENT AND MEMORANDUM IN SUPPORT THEREOF Plaintiff Lisa Moore (“Plaintiff”), by and through Class Counsel,1 respectfully submits this memorandum in support of Plaintiff’s Motion for Final Approval of Class Action Settlement. The Settlement Agreement (hereafter, “Settlement”) and its exhibits are attached as Exhibit 1 to the concurrently filed Declaration of Scott A. Bursor In Support Of Plaintiff’s Application For Attorneys’ Fees, Costs, And Class Service Awards (“Bursor Decl.”). On April 21, 2020, this Court granted preliminary approval to the parties’ Settlement Agreement and ordered that the Settlement Administrator execute the approved Notice Plan. See Order Granting Preliminarily Approval of Class Action Settlement. The tremendous response from Class Members confirms that the Settlement is fair and reasonable and provides outstanding relief to the Class. Although the claims deadline is not until August 18, 2020, the Claims Administrator estimates that upon receipt of 228,311 Claims, the entire $7,000,000 Benefit Fund will be exhausted. See Exhibit MFA1, the June 22, 2020 Decl. of Jeanne C. 1 All capitalized terms not otherwise defined herein shall have the same definitions as set out in the Settlement Agreement. Page 1 of 23 Case No: 19-L-0846 Finegan (“Finegan Decl.”) ¶ 31.
  • The Problem of Distributed Consensus: a Survey Stephen Wolfram*

    The Problem of Distributed Consensus: a Survey Stephen Wolfram*

    The Problem of Distributed Consensus: A Survey Stephen Wolfram* A survey is given of approaches to the problem of distributed consensus, focusing particularly on methods based on cellular automata and related systems. A variety of new results are given, as well as a history of the field and an extensive bibliography. Distributed consensus is of current relevance in a new generation of blockchain-related systems. In preparation for a conference entitled “Distributed Consensus with Cellular Automata and Related Systems” that we’re organizing with NKN (= “New Kind of Network”) I decided to explore the problem of distributed consensus using methods from A New Kind of Science (yes, NKN “rhymes” with NKS) as well as from the Wolfram Physics Project. A Simple Example Consider a collection of “nodes”, each one of two possible colors. We want to determine the majority or “consensus” color of the nodes, i.e. which color is the more common among the nodes. A version of this document with immediately executable code is available at writings.stephenwolfram.com/2021/05/the-problem-of-distributed-consensus Originally published May 17, 2021 *Email: [email protected] 2 | Stephen Wolfram One obvious method to find this “majority” color is just sequentially to visit each node, and tally up all the colors. But it’s potentially much more efficient if we can use a distributed algorithm, where we’re running computations in parallel across the various nodes. One possible algorithm works as follows. First connect each node to some number of neighbors. For now, we’ll just pick the neighbors according to the spatial layout of the nodes: The algorithm works in a sequence of steps, at each step updating the color of each node to be whatever the “majority color” of its neighbors is.
  • 2021 Nba Pinnacle Award Winners - Radio

    2021 Nba Pinnacle Award Winners - Radio

    2021 NBA PINNACLE AWARD WINNERS - RADIO SERVICE TO COMMUNITY Gold KFOR Lincoln Lincoln is a Great Place to Have a Heart Attack Silver KRVN Lexington SCC Ag Club Fundraising Goal Bronze KROR Grand Island Light A Hero's Home SERVICE TO CHILDREN Gold KGOR Omaha Lisa Seeman Interview Silver KFOR Lincoln All Means All - LPS Buses Homeless Children Bronze KNEB Scottsbluff 4-H Spotlight: Show Pigs SERVICE TO BUSINESS, INDUSTRY, GOVERNMENT OR EDUCATION Gold KGOR Omaha Spend Local Silver KEZO Omaha New Year, New Career Bronze KIOS Omaha "Leta of Lincoln" Goes Viral SERVICE TO AGRICULTURE Gold KRVN Lexington Keeping Agriculture Safe During COVID-19 Silver KTIC AM West Point Friday Feeders Bronze KTIC AM West Point Potential Groundwater Management Area BEST SPOT NEWS REPORTING Gold KLIN Lincoln Madsen's Saga Escalates Silver KBRY Broken Bow Accountant Accused of Stealing Thousands Bronze KHAS Hastings HPS Returns to Classroom Learning BEST IN-DEPTH OR INVESTIGATIVE STORY OR SERIES Gold KODY-KXNP-KHAQ North Platte Local Leaders Respond to Proposed Meat Packing Plant Silver Nebraska Public Media Lincoln Remote Learning in Remote Nebraska Bronze KIOS Omaha Portrait of a Pandemic BEST CONTINUING COVERAGE OF A NEWS STORY Gold KFAB Omaha James Scurlock - Don Kleine Silver KFAB Omaha 11-Worth Café: Mayor Stothert & Chief Schmaderer Bronze KNEB Scottsbluff Local Processing Act BEST USE OF MULTIMEDIA JOURNALISM Gold KUVR Holdrege Holdrege Deep Freeze and Power Outage Silver Nebraska Public Media Lincoln A Wilbur Man is Running for President…Again Bronze
  • TRINITY COLLEGE Cambridge Trinity College Cambridge College Trinity Annual Record Annual

    TRINITY COLLEGE Cambridge Trinity College Cambridge College Trinity Annual Record Annual

    2016 TRINITY COLLEGE cambridge trinity college cambridge annual record annual record 2016 Trinity College Cambridge Annual Record 2015–2016 Trinity College Cambridge CB2 1TQ Telephone: 01223 338400 e-mail: [email protected] website: www.trin.cam.ac.uk Contents 5 Editorial 11 Commemoration 12 Chapel Address 15 The Health of the College 18 The Master’s Response on Behalf of the College 25 Alumni Relations & Development 26 Alumni Relations and Associations 37 Dining Privileges 38 Annual Gatherings 39 Alumni Achievements CONTENTS 44 Donations to the College Library 47 College Activities 48 First & Third Trinity Boat Club 53 Field Clubs 71 Students’ Union and Societies 80 College Choir 83 Features 84 Hermes 86 Inside a Pirate’s Cookbook 93 “… Through a Glass Darkly…” 102 Robert Smith, John Harrison, and a College Clock 109 ‘We need to talk about Erskine’ 117 My time as advisor to the BBC’s War and Peace TRINITY ANNUAL RECORD 2016 | 3 123 Fellows, Staff, and Students 124 The Master and Fellows 139 Appointments and Distinctions 141 In Memoriam 155 A Ninetieth Birthday Speech 158 An Eightieth Birthday Speech 167 College Notes 181 The Register 182 In Memoriam 186 Addresses wanted CONTENTS TRINITY ANNUAL RECORD 2016 | 4 Editorial It is with some trepidation that I step into Boyd Hilton’s shoes and take on the editorship of this journal. He managed the transition to ‘glossy’ with flair and panache. As historian of the College and sometime holder of many of its working offices, he also brought a knowledge of its past and an understanding of its mysteries that I am unable to match.
  • Floer Homology, Gauge Theory, and Low-Dimensional Topology

    Floer Homology, Gauge Theory, and Low-Dimensional Topology

    Floer Homology, Gauge Theory, and Low-Dimensional Topology Clay Mathematics Proceedings Volume 5 Floer Homology, Gauge Theory, and Low-Dimensional Topology Proceedings of the Clay Mathematics Institute 2004 Summer School Alfréd Rényi Institute of Mathematics Budapest, Hungary June 5–26, 2004 David A. Ellwood Peter S. Ozsváth András I. Stipsicz Zoltán Szabó Editors American Mathematical Society Clay Mathematics Institute 2000 Mathematics Subject Classification. Primary 57R17, 57R55, 57R57, 57R58, 53D05, 53D40, 57M27, 14J26. The cover illustrates a Kinoshita-Terasaka knot (a knot with trivial Alexander polyno- mial), and two Kauffman states. These states represent the two generators of the Heegaard Floer homology of the knot in its topmost filtration level. The fact that these elements are homologically non-trivial can be used to show that the Seifert genus of this knot is two, a result first proved by David Gabai. Library of Congress Cataloging-in-Publication Data Clay Mathematics Institute. Summer School (2004 : Budapest, Hungary) Floer homology, gauge theory, and low-dimensional topology : proceedings of the Clay Mathe- matics Institute 2004 Summer School, Alfr´ed R´enyi Institute of Mathematics, Budapest, Hungary, June 5–26, 2004 / David A. Ellwood ...[et al.], editors. p. cm. — (Clay mathematics proceedings, ISSN 1534-6455 ; v. 5) ISBN 0-8218-3845-8 (alk. paper) 1. Low-dimensional topology—Congresses. 2. Symplectic geometry—Congresses. 3. Homol- ogy theory—Congresses. 4. Gauge fields (Physics)—Congresses. I. Ellwood, D. (David), 1966– II. Title. III. Series. QA612.14.C55 2004 514.22—dc22 2006042815 Copying and reprinting. Material in this book may be reproduced by any means for educa- tional and scientific purposes without fee or permission with the exception of reproduction by ser- vices that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given.
  • Obituary Roland Lvovich Dobrushin, 1929 – 1995

    Obituary Roland Lvovich Dobrushin, 1929 – 1995

    Obituary Roland Lvovich Dobrushin, 1929 ± 1995 Roland Lvovich Dobrushin, an outstanding scientist in the domain of probability theory, information theory and mathematical physics, died of cancer in Moscow, on November 12, 1995, at the age of 66. Dobrushin's premature decease is a tremendous loss to Russian and world science. Dobrushin was born on July 20, 1929 in Leningrad (St.-Petersburg). In early childhood he lost his father; his mother died when he was still a schoolboy. In 1936, after his father's death, the family moved to Moscow. In 1947, on leaving school, Dobrushin entered the Mechanico-Mathematical Department of Moscow Univer- sity and after graduating from it did postgraduate studies. Then, from 1955 to 1965, he worked at the Proba- bility Theory Section of the Mechanico-Mathematical Department of Moscow University, and since 1967 until his demise was Head of the Multicomponent Random Systems Laboratory, within the Institute for Information Transmission Problems of the Russian Academy of Sciences (the Academy of Sciences of the USSR). Since 1967 Dobrushin was a Professor in the Electromagnetic Waves Section of the Moscow Physics Technologies Institute and since 1991 he was a Professor in the Probability Theory Section at Moscow University as well. In 1955 Dobrushin presented his candidate's thesis, and in 1962 he took his Doctor's degree. Even as a schoolboy Dobrushin conceived an interest in mathematics and participated in school mathemat- ical contests where he won a number of prizes. While at the University Dobrushin was an active member of E.B. Dynkin's seminar 1 . On A.N.
  • Commentary on Thurston's Work on Foliations

    Commentary on Thurston's Work on Foliations

    COMMENTARY ON FOLIATIONS* Quoting Thurston's definition of foliation [F11]. \Given a large supply of some sort of fabric, what kinds of manifolds can be made from it, in a way that the patterns match up along the seams? This is a very general question, which has been studied by diverse means in differential topology and differential geometry. ... A foliation is a manifold made out of striped fabric - with infintely thin stripes, having no space between them. The complete stripes, or leaves, of the foliation are submanifolds; if the leaves have codimension k, the foliation is called a codimension k foliation. In order that a manifold admit a codimension- k foliation, it must have a plane field of dimension (n − k)." Such a foliation is called an (n − k)-dimensional foliation. The first definitive result in the subject, the so called Frobenius integrability theorem [Fr], concerns a necessary and sufficient condition for a plane field to be the tangent field of a foliation. See [Spi] Chapter 6 for a modern treatment. As Frobenius himself notes [Sa], a first proof was given by Deahna [De]. While this work was published in 1840, it took another hundred years before a geometric/topological theory of foliations was introduced. This was pioneered by Ehresmann and Reeb in a series of Comptes Rendus papers starting with [ER] that was quickly followed by Reeb's foundational 1948 thesis [Re1]. See Haefliger [Ha4] for a detailed account of developments in this period. Reeb [Re1] himself notes that the 1-dimensional theory had already undergone considerable development through the work of Poincare [P], Bendixson [Be], Kaplan [Ka] and others.
  • Classification of 3-Manifolds with Certain Spines*1 )

    Classification of 3-Manifolds with Certain Spines*1 )

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 205, 1975 CLASSIFICATIONOF 3-MANIFOLDSWITH CERTAIN SPINES*1 ) BY RICHARD S. STEVENS ABSTRACT. Given the group presentation <p= (a, b\ambn, apbq) With m, n, p, q & 0, we construct the corresponding 2-complex Ky. We prove the following theorems. THEOREM 7. Jf isa spine of a closed orientable 3-manifold if and only if (i) \m\ = \p\ = 1 or \n\ = \q\ = 1, or (") (m, p) = (n, q) = 1. Further, if (ii) holds but (i) does not, then the manifold is unique. THEOREM 10. If M is a closed orientable 3-manifold having K^ as a spine and \ = \mq — np\ then M is a lens space L\ % where (\,fc) = 1 except when X = 0 in which case M = S2 X S1. It is well known that every connected compact orientable 3-manifold with or without boundary has a spine that is a 2-complex with a single vertex. Such 2-complexes correspond very naturally to group presentations, the 1-cells corre- sponding to generators and the 2-cells corresponding to relators. In the case of a closed orientable 3-manifold, there are equally many 1-cells and 2-cells in the spine, i.e., equally many generators and relators in the corresponding presentation. Given a group presentation one is motivated to ask the following questions: (1) Is the corresponding 2-complex a spine of a compact orientable 3-manifold? (2) If there are equally many generators and relators, is the 2-complex a spine of a closed orientable 3-manifold? (3) Can we say what manifold(s) have the 2-complex as a spine? L.
  • A View from the Bridge Natalie Paquette

    A View from the Bridge Natalie Paquette

    INFERENCE / Vol. 3, No. 4 A View from the Bridge Natalie Paquette tring theory is a quantum theory of gravity.1 Albert example, supersymmetric theories require particles to Einstein’s theory of general relativity emerges natu- come in pairs. For every bosonic particle there is a fermi- rally from its equations.2 The result is consistent in onic superpartner. Sthe sense that its calculations do not diverge to infinity. Supersymmetric field theory has a disheartening String theory may well be the only consistent quantum impediment. Suppose that a supersymmetric quantum theory of gravity. If true, this would be a considerable field theory is defined on a generic curved manifold. The virtue. Whether it is true or not, string theory is indis- Euclidean metric of Newtonian physics and the Lorentz putably the source of profound ideas in mathematics.3 metric of special relativity are replaced by the manifold’s This is distinctly odd. A line of influence has always run own metric. Supercharges correspond to conserved Killing from mathematics to physics. When Einstein struggled spinors. Solutions to the Killing spinor equations are plen- to express general relativity, he found the tools that he tiful in a flat space, but the equations become extremely needed had been created sixty years before by Bernhard restrictive on curved manifolds. They are so restrictive Riemann. The example is typical. Mathematicians discov- that they have, in general, no solutions. Promoting a flat ered group theory long before physicists began using it. In supersymmetric field theory to a generic curved mani- the case of string theory, it is often the other way around.