Notices Ofof the American Mathematicalmathematical Society June/July 2019 Volume 66, Number 6
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Recent Results in Higher-Dimensional Birational Geometry
Complex Algebraic Geometry MSRI Publications Volume 28, 1995 Recent Results in Higher-Dimensional Birational Geometry ALESSIO CORTI ct. Abstra This note surveys some recent results on higher-dimensional birational geometry, summarising the views expressed at the conference held at MSRI in November 1992. The topics reviewed include semistable flips, birational theory of Mori fiber spaces, the logarithmic abundance theorem, and effective base point freeness. Contents 1. Introduction 2. Notation, Minimal Models, etc. 3. Semistable Flips 4. Birational theory of Mori fibrations 5. Log abundance 6. Effective base point freeness References 1. Introduction The purpose of this note is to survey some recent results in higher-dimensional birational geometry. A glance to the table of contents may give the reader some idea of the topics that will be treated. I have attempted to give an informal presentation of the main ideas, emphasizing the common grounds, addressing a general audience. In 3, I could not resist discussing some details that perhaps § only the expert will care about, but hopefully will also introduce the non-expert reader to a subtle subject. Perhaps the most significant trend in Mori theory today is the increasing use, more or less explicit, of the logarithmic theory. Let me take this opportunity This work at the Mathematical Sciences Research Institute was supported in part by NSF grant DMS 9022140. 35 36 ALESSIO CORTI to advertise the Utah book [Ko], which contains all the recent software on log minimal models. Our notation is taken from there. I have kept the bibliography to a minimum and made no attempt to give proper credit for many results. -
Short CV For: Alexander Lubotzky
Short CV for: Alexander Lubotzky Personal: • born 28/6/56 in Israel. • Married to Yardenna Lubotzky (+ six children) Studies: • B. Sc., Mathematics, Bar-Ilan University, 1975. • Ph.D., Mathematics, Bar-Ilan University, 1979. (Supervisor: H. Fussten- berg, Thesis: Profinite groups and the congruence subgroup problem.) Employment: • 1982 - current: Institute of Mathematics, Hebrew University of Jerusalem; Professor - Holding the Maurice and Clara Weil Chair in Mathematics • 1999-current: Adjunct Professor at Yale University • Academic Year 2005-2006: Leading a year long research program at the Institute for Advanced Study in Princeton on \Lie Groups, Repre- sentations and Discrete Mathematics." Previous Employment: • Bar-Ilan University, 1976-1982 • Israeli Defense Forces, 1977-1982 • Member of the Israeli Parliament (Knesset), 1996-1999 Visiting Positions: • Yale University (several times for semesters or years) • Stanford University (84/5) • University of Chicago (92/3) • Columbia University (Elenberg visiting Professor Fall 2000) 1 • Institute for Advanced Study, Princeton (2005/6) Main prizes and Academic Honors: • Elected as Foreign Honorary member of the American Academy of Arts and Sciences • Ferran Sunyer i Balaguer Prize twice: 1993 for the book: \Discrete Groups, Expanding Groups and Invariant Measures", Prog. in math 125, Birkhauser 1994, and in 2002 joint with Professor Dan Segal from Oxford for the book \Subgroup Growth", Prog. in Math. 212, Birkhauser 2003. • The Rothschild Prize 2002. • The Erdos Prize in 1991. Editorial work: • Israel Journal of Mathematics (1990-now) • Journal of Algebra (1990-2005) • GAFA (1990-2000) • European Journal of Combinatorics • Geometric Dedicata • Journal of the Glasgow Mathematical Scientists Books and papers: • Author of 3 books and over 90 papers. -
Caucher Birkar — from Asylum Seeker to Fields Medal Winner at Cambridge
MATHS, 1 Caucher Birkar, 41, at VERSION Cambridge University, photographed by Jude Edginton REPR O OP HEARD THE ONE ABOUT THE ASYLUM SEEKER SUBS WHO WANDERED INTO A BRITISH UNIVERSITY... A RT AND CAME OUT A MATHS SUPERSTAR? PR ODUCTION CLIENT Caucher Birkar grew up in a Kurdish peasant family in a war zone and arrived in Nottingham as a refugee – now he has received the mathematics equivalent of the Nobel prize. By Tom Whipple BLACK YELLOW MAGENTA CYAN 91TTM1940232.pgs 01.04.2019 17:39 MATHS, 2 VERSION ineteen years ago, the mathematics Caucher Birkar in Isfahan, Receiving the Fields Medal If that makes sense, congratulations: you department at the University of Iran, in 1999 in Rio de Janeiro, 2018 now have a very hazy understanding of Nottingham received an email algebraic geometry. This is the field that from an asylum seeker who Birkar works in. wanted to talk to someone about The problem with explaining maths is REPR algebraic geometry. not, or at least not always, the stupidity of his They replied and invited him in. listeners. It is more fundamental than that: O OP N So it was that, shortly afterwards, it is language. Mathematics is not designed Caucher Birkar, the 21-year-old to be described in words. It is designed to be son of a Kurdish peasant family, described in mathematics. This is the great stood in front of Ivan Fesenko, a professor at triumph of the subject. It was why a Kurdish Nottingham, and began speaking in broken asylum seeker with bad English could convince SUBS English. -
Introduction to Birational Geometry of Surfaces (Preliminary Version)
INTRODUCTION TO BIRATIONAL GEOMETRY OF SURFACES (PRELIMINARY VERSION) JER´ EMY´ BLANC (Very) quick introduction Let us recall some classical notions of algebraic geometry that we will need. We recommend to the reader to read the first chapter of Hartshorne [Har77] or another book of introduction to algebraic geometry, like [Rei88] or [Sha94]. We fix a ground field k. All results of the first 4 sections work over any alge- braically closed field, and a few also on non-closed fields. In the last section, the case of all perfect fields will be discussed. For our purpose, the characteristic is not important. n n 0.1. Affine varieties. The affine n-space Ak, or simply A , is the set of n-tuples n of elements of k. Any point x 2 A can be written as x = (x1; : : : ; xn), where x1; : : : ; xn 2 k are the coordinates of x. An algebraic set X ⊂ An is the locus of points satisfying a set of polynomial equations: n X = (x1; : : : ; xn) 2 A f1(x1; : : : ; xn) = ··· = fk(x1; : : : ; xn) = 0 where each fi 2 k[x1; : : : ; xn]. We denote by I(X) ⊂ k[x1; : : : ; xn] the set of polynomials vanishing along X, it is an ideal of k[x1; : : : ; xn], generated by the fi. We denote by k[X] or O(X) the set of algebraic functions X ! k, which is equal to k[x1; : : : ; xn]=I(X). An algebraic set X is said to be irreducible if any writing X = Y [ Z where Y; Z are two algebraic sets implies that Y = X or Z = X. -
BERNOULLI NEWS, Vol 24 No 1 (2017)
Vol. 24 (1), May 2017 Published twice per year by the Bernoulli Society ISSN 1360–6727 CONTENTS News from the Bernoulli Society p. 1 Awards and Prizes p. 2 New Executive Members A VIEW FROM THE PRESIDENT in the Bernoulli Society Dear Members of the Bernoulli Society, p. 3 As we all seem to agree, the role and image of statistics has changed dramatically. Still, it takes ones breath when realizing the huge challenges ahead. Articles and Letters Statistics has not always been considered as being very necessary. In 1848 the Dutch On Bayesian Measures of Ministry of Home Affairs established an ofŮice of statistics. And then, thirty years later Uncertainty in Large or InŮinite minister Kappeyne van de Coppelo abolishes the “superŮluous” ofŮice. The ofŮice was Dimensional Models p. 4 quite rightly put back in place in 1899, as “Centraal Bureau voor de Statistiek” (CBS). Statistics at the CBS has evolved from “simple” counting to an art requiring a broad range On the Probability of Co-primality of competences. Of course counting remains important. For example the CBS reports in of two Natural Numbers Chosen February 2017 that almost 1 out of 4 people entitled to vote in the Netherlands is over the at Random p. 7 age of 65. But clearly, knowing this generates questions. What is the inŮluence of this on the outcome of the elections? This calls for more data. Demographic data are combined with survey data and nowadays also with data from other sources, in part to release the “survey pressure” that Ůirms and individuals are facing. -
A Group Theoretic Characterization of Linear Groups
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector JOURNAL OF ALGEBRA 113, 207-214 (1988) A Group Theoretic Characterization of Linear Groups ALEXANDER LUBOTZKY Institute qf Mathematics, Hebrew University, Jerusalem, Israel 91904 Communicated by Jacques Tits Received May 12, 1986 Let r be a group. When is f linear? This is an old problem. The first to study this question systematically was Malcev in 1940 [M], who essen- tially reduced the problem to finitely generated groups. (Note that a finitely generated group is linear over some field of characteristic zero if and only if it can be embedded in CL,(C) for some n.) Very little progress was made since that paper of Malcev, although, as linear groups are a quite special type of group, many necessary conditions were obtained, e.g., r should be residually finite and even virtually residually-p for almost all primes p, f should be virtually torsion free, and if not solvable by finite it has a free non-abelian subgroup, etc. (cf. [Z]). Of course, none of these properties characterizes the finitely generated linear groups over @. In this paper we give such a characterization using the congruence structure of r. First some definitions: For a group H, d(H) denotes the minimal number of generators for H. DEFINITION. Let p be a prime and c an integer. A p-congruence structure (with a bound c) for a group r is a descending chain of finite index normal subgroups of r = N, 2 N, 2 N, z . -
Annual Report
COUNCIL ON FOREIGN RELATIONS ANNUAL REPORT July 1,1996-June 30,1997 Main Office Washington Office The Harold Pratt House 1779 Massachusetts Avenue, N.W. 58 East 68th Street, New York, NY 10021 Washington, DC 20036 Tel. (212) 434-9400; Fax (212) 861-1789 Tel. (202) 518-3400; Fax (202) 986-2984 Website www. foreignrela tions. org e-mail publicaffairs@email. cfr. org OFFICERS AND DIRECTORS, 1997-98 Officers Directors Charlayne Hunter-Gault Peter G. Peterson Term Expiring 1998 Frank Savage* Chairman of the Board Peggy Dulany Laura D'Andrea Tyson Maurice R. Greenberg Robert F Erburu Leslie H. Gelb Vice Chairman Karen Elliott House ex officio Leslie H. Gelb Joshua Lederberg President Vincent A. Mai Honorary Officers Michael P Peters Garrick Utley and Directors Emeriti Senior Vice President Term Expiring 1999 Douglas Dillon and Chief Operating Officer Carla A. Hills Caryl R Haskins Alton Frye Robert D. Hormats Grayson Kirk Senior Vice President William J. McDonough Charles McC. Mathias, Jr. Paula J. Dobriansky Theodore C. Sorensen James A. Perkins Vice President, Washington Program George Soros David Rockefeller Gary C. Hufbauer Paul A. Volcker Honorary Chairman Vice President, Director of Studies Robert A. Scalapino Term Expiring 2000 David Kellogg Cyrus R. Vance Jessica R Einhorn Vice President, Communications Glenn E. Watts and Corporate Affairs Louis V Gerstner, Jr. Abraham F. Lowenthal Hanna Holborn Gray Vice President and Maurice R. Greenberg Deputy National Director George J. Mitchell Janice L. Murray Warren B. Rudman Vice President and Treasurer Term Expiring 2001 Karen M. Sughrue Lee Cullum Vice President, Programs Mario L. Baeza and Media Projects Thomas R. -
Download the Program
The first International Congress of Neuroimmunology was held in Stresa, Italy, in 1982 and wasThe organized first International by Drs. Peter Congress O. Behan of Neuroimmunology and Federico Spreafico. was held The in secondStresa, Italy,International in Congress1982 and of wasNeuroimmunology organized by Drs. was Peter held O.in Philadelphia,Behan and Federico PA, and Spreafico. was organised The second by C.S. Raine andInternational Dale E. McFarlin. Congress It was of atNeuroimmunology this meeting in Philadelphiawas held in inPhiladelphia, 1987 that itPA, was and decided was to startorganised an international by C.S. Raine society, and the Dale International E. McFarlin. Society It was ofat Neuroimmunology,this meeting in Philadelphia and an election wasin 1987held forthat a it panel was decided of officers. to start C.S. anRaine international was elected society, President, the International John Newson-Davis Society Vice President,of Neuroimmunology, Robert Lisak andTreasurer an election and Kenethwas held Johnson for a panel Secretary, of officers. together Cedric with S. an InternationalRaine was Advisoryelected President,Board. The John Society Newson-Davis was incorporated Vice President,in 1988. Subsequent Robert Lisak meetings wereTreasurer in Jerusalem and Kenneth 1991 (Oder Johnson Abramsky Secretary, and togetherHaim Ovadia), with Amsterdaman International 1994 (KeeAdvisory Lucas), Board. Montreal 1998 (Jack Antel and Trevor Owens), Edinburgh 2001 (John Greenwood,The Society Sandra was Amor,incorporated David Baker, in 1988.John -
Counting Arithmetic Lattices and Surfaces
ANNALS OF MATHEMATICS Counting arithmetic lattices and surfaces By Mikhail Belolipetsky, Tsachik Gelander, Alexander Lubotzky, and Aner Shalev SECOND SERIES, VOL. 172, NO. 3 November, 2010 anmaah Annals of Mathematics, 172 (2010), 2197–2221 Counting arithmetic lattices and surfaces By MIKHAIL BELOLIPETSKY, TSACHIK GELANDER, ALEXANDER LUBOTZKY, and ANER SHALEV Abstract We give estimates on the number ALH .x/ of conjugacy classes of arithmetic lattices of covolume at most x in a simple Lie group H . In particular, we obtain a first concrete estimate on the number of arithmetic 3-manifolds of volume at most x. Our main result is for the classical case H PSL.2; R/ where we show D that log AL .x/ 1 lim H : x x log x D 2 !1 The proofs use several different techniques: geometric (bounding the number of generators of as a function of its covolume), number theoretic (bounding the number of maximal such ) and sharp estimates on the character values of the symmetric groups (to bound the subgroup growth of ). 1. Introduction Let H be a noncompact simple Lie group with a fixed Haar measure .A discrete subgroup of H is called a lattice if . H / < . A classical theorem of n 1 Wang[Wan72] asserts that if H is not locally isomorphic to PSL2.R/ or PSL2.C/, then for every 0 < x R the number LH .x/ of conjugacy classes of lattices in H of 2 covolume at most x is finite. This result was greatly extended by Borel and Prasad [BP89]. In recent years there has been an attempt to quantify Wang’s theorem and to give some estimates on LH .x/ (see[BGLM02],[Gel04],[GLNP04],[Bel07] and[BL]). -
A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members. -
The National Archives Finding
NATIONAL ARCHIVES, LONDON (KEW) Record Finding Aid CONTENTS LIST FOREIGN OFFICE (FO) FO 115 - Foreign Office: Embassy and Consulates, United States of America: Page 4 General Correspondence 1791-1967 FO115/4285 Page 4 FO 118 - Foreign Office: Embassy and Consulates, Argentine Republic (formerly Page 4 United Provinces of the Rio de la Plata): General Correspondence 1820-1965 FO 118/717 Page 4 FO118/759 Page 5 FO 128 - Foreign Office: Embassy and Consulates, Brazil: General Page 5 Correspondence 1821-1956 FO 128/395 Page 5 FO 128/463 Page 6 FO 370 - Foreign Office: Library and the Research Department: General Page 6 Correspondence from 1906 FO 370/1315 Page 6 FO 371 - Political Departments: General Correspondence 1906-1966 Page 7 FO 371/24526 Page 7 FO 371/25710 Page 7 FO 371/32223 Page 7 FO 371/36422 Page 7 FO 371/40995 Page 7 FO 371/40996 Page 8 FO 371/40997 Page 9 FO 371/40998 Page 10 FO 371/40999 Page 10 FO 371/41000 Page 10 FO 371/41001 Page 11 FO 371/45750 Page 11 FO 371/45751 Page 12 FO 371/45769 Page 13 FO 371/45770 Page 14 FO 371/45771 Page 15 FO 371/45812 Page 15 FO 371/45813 Page 16 FO 371/45814 Page 16 FO 371/45815 Page 16 FO 371/45822 Page 16 [1] FO 371/46881 Page 16 FO 371/53104 Page 16 FO 371/53105 Page 17 FO 371/65055 Page 17 FO 371/66590 Page 18 FO 371/70972 Page 18 FO 837 – Ministry of Economic Warfare (MEW) and successors: Records Page 18 1931-1951 FO 837/293 Page 18 FO 837/1154 Page 18 FO 837/1157 Page 20 FO 837/1166 Page 21 FO 837/1167 Page 21 FO 837/1168 Page 21 FO 837/1170 & 1171 Page 21 FO 837/1282 Page 22 FO 837/1283 -
Spring 2014 Fine Letters
Spring 2014 Issue 3 Department of Mathematics Department of Mathematics Princeton University Fine Hall, Washington Rd. Princeton, NJ 08544 Department Chair’s letter The department is continuing its period of Assistant to the Chair and to the Depart- transition and renewal. Although long- ment Manager, and Will Crow as Faculty The Wolf time faculty members John Conway and Assistant. The uniform opinion of the Ed Nelson became emeriti last July, we faculty and staff is that we made great Prize for look forward to many years of Ed being choices. Peter amongst us and for John continuing to hold Among major faculty honors Alice Chang Sarnak court in his “office” in the nook across from became a member of the Academia Sinica, Professor Peter Sarnak will be awarded this the common room. We are extremely Elliott Lieb became a Foreign Member of year’s Wolf Prize in Mathematics. delighted that Fernando Coda Marques and the Royal Society, John Mather won the The prize is awarded annually by the Wolf Assaf Naor (last Fall’s Minerva Lecturer) Brouwer Prize, Sophie Morel won the in- Foundation in the fields of agriculture, will be joining us as full professors in augural AWM-Microsoft Research prize in chemistry, mathematics, medicine, physics, Alumni , faculty, students, friends, connect with us, write to us at September. Algebra and Number Theory, Peter Sarnak and the arts. The award will be presented Our finishing graduate students did very won the Wolf Prize, and Yasha Sinai the by Israeli President Shimon Peres on June [email protected] well on the job market with four win- Abel Prize.