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L' Addio a Un Grande Matematico
CAPITOLO 1 L' ADDIO A UN GRANDE MATEMATICO Si riportano i discorsi pronunciati il 27 ottobre 1996 nel cortile della Scuola Normale Superiore di Pisa, in occasione del commiato accademico. Nello stesso giorno, presso la Chiesa di S. Frediano (Pisa) si `e tenuto il fu- nerale, officiato dal teologo Severino Dianich; il giorno dopo presso la Basilica di S. Croce (Lecce) il funerale `e stato officiato dall' Arcivescovo di Lecce, Cosmo Francesco Ruppi. 1.1 DISCORSO DI L. MODICA Intervento di Luciano Modica, allievo di De Giorgi e Rettore dell' Universita` di Pisa. Confesso che quando Franco Bassani e Luigi Radicati mi hanno chiesto di prendere la parola oggi durante questo triste e solenne commiato acca- demico da Ennio De Giorgi, la mia prima reazione `e stata quella di tirarmi indietro, temendo che l' empito della commozione e dei ricordi dell' allie- vo sopraffacessero la partecipazione, certo commossa, ma necessariamente composta, di chi qui `e chiamato da Rettore a rappresentare l' Ateneo pisa- no e la sua comunita` di studenti e docenti. Se poi ho accettato, non `e stato perch´e, sono sicuro di superare questo timore, ma perch´e spero che tutti voi familiari, allievi, amici di Ennio, saprete comprendere e scusare l' emotivita` da cui forse non riusciro` ad evitare che sia pervaso il tono delle mie parole. Perch´e la vostra presenza in questo cortile, le cui soavi linee architettoniche tanto Ennio ha amato e che rimangono per tanti dei presenti indissolubil- mente legate alla loro giovinezza, non ha nulla del dovere accademico, se 2 L' ADDIO A UN GRANDE MATEMATICO non i suoi aspetti spirituali piu` alti, mentre invece vuole manifestare la ri- conoscenza e l' affetto tutti umani verso una persona accanto a cui abbiamo avuto il privilegio di trascorrere un periodo piu` o meno lungo, ma sempre indimenticabile, della nostra vita. -
2008 Doob Prize
2008 Doob Prize The 2008 Joseph Doob Prize was awarded at the The book also develops the extraordi- 114th Annual Meeting of the AMS in San Diego in nary work of Zhang and others on the January 2008. Bogomolov conjecture, puts forward an This prize was established by the AMS in elegant approach to Hilbert irreducibil- 2003 and endowed in 2005 by Paul and Virginia ity, and includes a detailed discussion Halmos in honor of Joseph L. Doob (1910–2004). of the Nevanlinna-Vojta theory. There Paul Halmos (1916–2006) was Doob’s first Ph.D is a lovely exposition of the important student. Doob received his Ph.D. from Harvard theory of unit equations and a most in 1932 and three years later joined the faculty brilliant discussion of the Subspace at the University of Illinois, where he remained Theorem of Schmidt and Schlickewei, until his retirement in 1978. He worked in prob- as well as the possibilities afforded by ability theory and measure theory, served as AMS the abc-conjecture and further develop- president in 1963–1964, and received the Steele ments along these lines. Enrico Bombieri Prize in 1984. The Doob Prize recognizes a single, The book is self-contained, yet sur- relatively recent, outstanding research book that prisingly accessible given the depth of makes a seminal contribution to the research lit- the material. Links between classical erature, reflects the highest standards of research Diophantine arithmetic and modern exposition, and promises to have a deep and long- arithmetic geometry are emphasized term impact in its area. The book must have been throughout the text in an appealing published within the six calendar years preceding way. -
Uva-DARE (Digital Academic Repository)
UvA-DARE (Digital Academic Repository) Optimality properties of curves over finite fields Zaitsev, A.I. Publication date 2008 Link to publication Citation for published version (APA): Zaitsev, A. I. (2008). Optimality properties of curves over finite fields. Thomas Stieltjes Institute for Mathematics. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:27 Sep 2021 Bibliography [1] Aldo Andreotti. On a theorem of Torelli. Amer.J.Math., 80:801–828, 1958. [2] Juscelino Bezerra, Arnaldo Garcia, and Henning Stichtenoth. An explicit tower of function fields over cubic finite fields and Zink’s lower bound. J. Reine Angew. Math., 589:159–199, 2005. [3] Pierre Deligne. Vari´et´es ab´eliennes ordinaires sur un corps fini. Invent. Math., 8:238–243, 1969. -
GUIDO STAMPACCHIA Silvia Mazzone
1 GUIDO STAMPACCHIA Silvia Mazzone 1. Formazione scientifica e prima attività di ricerca alla Scuola Normale Superiore di Pisa e all’Università di Napoli. Guido Stampacchia nasce a Napoli, nel quartiere Chiaia, il 26 marzo 1922 da Emanuele e Giulia Campagnano. Giulia, di religione ebraica,1 apparteneva ad una famiglia di origini fiorentine che aveva un laboratorio di biancheria ricamata a mano; gli Stampacchia, invece, erano una famiglia di origine leccese ed osservavano la religione valdese. Il papà, Emanuele, gestiva una fabbrica di ferramenta che sarà costretto a vendere al tempo della guerra in Etiopia, come conseguenza del suo rifiuto a prendere la tessera del partito fascista. Il giovane Guido riceve una educazione essenzialmente laica anche se, da bambino, insieme alle due sorelle frequenta la chiesa valdese. Egli consegue la maturità classica a 18 anni, nel 1940, al Liceo-Ginnasio Gian Battista Vico di Napoli riportando come unico voto di eccellenza 9 in matematica e fisica. Nonostante gli studi classici, aveva chiara l'intenzione di dedicarsi alla matematica e perciò aveva approfondito per suo conto la preparazione di matematica e di fisica studiando “i capisaldi del programma di Liceo Scientifico, cercando … di intravederne il processo logico”2. Nell’autunno del 1940 è ammesso come alunno interno alla Scuola Normale Superiore di Pisa, classe di Scienze, corso di laurea in matematica pura, essendo riuscito quinto al concorso3 e, nei tre anni successivi, supera brillantemente tutti gli esami previsti dal piano di studio assolvendo agli obblighi cui sono tenuti i normalisti. In particolare all’università ha come docenti Francesco Cecioni e Salvatore Cherubino per gli insegnamenti del primo biennio mentre il terzo anno frequenta il corso di Analisi superiore di Leonida Tonelli e quello di Teoria delle funzioni di Lamberto Cesari. -
CURRICULUM VITAE Ted Chinburg Home Address
CURRICULUM VITAE Ted Chinburg Home address: Department of Mathematics 506 Rockavon Rd., Narberth, Pa. 19072 University of Pennsylvania office: 215-898-8340 Philadelphia, PA 19104-6395 home: 215-664-8031 EDUCATION B.S. Mathematics Harvey Mudd College June, 1975 M.A. Mathematics Harvard University June, 1979 Ph.D. Mathematics Harvard University November, 1980 RESEARCH AREAS Number theory, arithmetic and hyperbolic geometry Particular interests: Galois module structure, values of L- functions, hyperbolic three-manifolds, arithmetic groups, deformation theory, group actions on varieties, Arakelov theory, capacity theory, cryptography HONORS AND GRANTS SATC medium grants 2015, 2017 Simons Fellowship, 2015 U. Penn Dean's Fellowship, 2015 Kloosterman Professor, University of Leiden, 2009 NSF FRG grants, 2013-2016 and 2014-2017. Individual NSF grants 1982-1989, 1992-2014 NSA grant 1990-1992 G. de B. Robinson research Award, Canadian Mathematical Society, 2002 University of Pennsylvania research grant, 1989 University of Pennsylvania Natural Sciences grant, 1986 MSRI mid-career fellowship, 1986 Sloan fellowship, 1985 PROFESSIONAL EXPERIENCE Editor, Transactions of the A. M. S., 2012 - present Editor, Proceedings of the A. M. S., 2006 - 2010 Editor, J. Theorie de Nombres de Bordeaux, 2006 - 2017 Editor, Compositio Mathematica, 2002 - 2005 Visitor, U. C. Berkeley, Fall 2016 Visitor, University of Leiden, Spring 2016 Visitor, I.H.E.S. Fall 2015 1 ACADEMIC POSITIONS Professor, University of Pennsylvania, 1989-present Associate Professor, Columbia University, Barnard College, 1987 - 1989 Assistant Professor, University of Pennsylvania, 1982 - 1987 Acting Assistant Professor, University of Washington, 1981 - 1982 PH.D STUDENTS 1. S. Bae, Univ. of Penn. Thesis (June, 1988) \Conjectures of Lichtenbaum and Chin- burg over Function Fields." 2. -
Handbook of Moduli
Moduli of abelian varieties in mixed and in positive characteristic Frans Oort Abstract. We start with a discussion of CM abelian varieties in character- istic zero, and in positive characteristic. An abelian variety over a finite field is a CM abelian variety, as Tate proved. Can it be CM lifted to characteristic zero? Here are other questions. Does there exist an abelian variety, say over a Q , or over Fp, of dimension g > 3 not isogenous with the Jacobian of an algebraic curve? Can we construct algebraic curves, say over C, where the Ja- cobian is a CM abelian variety? We give (partial) answers to these questions and discuss stratifications and foliations of moduli spaces of abelian varieties in positive characteristic. Contents Introduction 2 1 Notation/Preliminaries. 6 Moduli of CM abelian varieties 7 2 Complex multiplication on abelian varieties 7 3 The isogeny class of a CM abelian variety is defined over a finite extension of the prime field 9 4 CM liftings 12 5 Abelian varieties isogenous to a Jacobian 14 Stratifications and foliations of moduli spaces of abelian varieties in positive characteristic 22 6 Supersingular abelian varieties 22 7 NP strata 28 8 A conjecture by Grothendieck 31 9 Purity 33 10EO strata 34 11Foliations 42 12Minimal p-divisible groups 48 13Hecke orbits 50 2000 Mathematics Subject Classification. Primary ; Secondary: Key words and phrases. Curves and their Jacobians, complex multiplication, abelian varieties, CM liftings, stratifications, foliations. 2 Moduli of abelian varieties in mixed and in positive characteristic 14Complete subvarieties of Ag 51 Introduction 0.1. In 1857, discussing what we now call Riemann surfaces of genus p, Riemann wrote: “.. -
A Bibliography of Collected Works and Correspondence of Mathematicians Steven W
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by eCommons@Cornell A Bibliography of Collected Works and Correspondence of Mathematicians Steven W. Rockey Mathematics Librarian Cornell University [email protected] December 14, 2017 This bibliography was developed over many years of work as the Mathemat- ics Librarian at Cornell University. In the early 1970’s I became interested in enhancing our library’s holdings of collected works and endeavored to comprehensively acquire all the collected works of mathematicians that I could identify. To do this I built up a file of all the titles we held and another file for desiderata, many of which were out of print. In 1991 the merged files became a printed bibliography that was distributed for free. The scope of the bibliography includes the collected works and correspon- dence of mathematicians that were published as monographs and made available for sale. It does not include binder’s collections, reprint collec- tions or manuscript collections that were put together by individuals, de- partments or libraries. In the beginning I tried to include all editions, but the distinction between editions, printings, reprints, translations and now e-books was never easy or clear. In this latest version I have supplied the OCLC identification number, which is used by libraries around the world, since OCLC does a better job connecting the user with the various ver- sion than I possibly could. In some cases I have included a title that has an author’s mathematical works but have not included another title that may have their complete works. -
Newton Polygons and Formal Groups: Conjectures by Manin And
Annals of Mathematics, 152 (2000), 183–206 Newton polygons and formal groups: Conjectures by Manin and Grothendieck By Frans Oort Introduction We consider p-divisible groups (also called Barsotti-Tate groups) in char- acteristic p, their deformations, and we draw some conclusions. For such a group we can define its Newton polygon (abbreviated NP). This is invariant under isogeny. For an abelian variety (in characteristic p) the Newton polygon of its p-divisible group is “symmetric”. In 1963 Manin conjectured that conversely any symmetric Newton poly- gon is “algebroid”; i.e., it is the Newton polygon of an abelian variety. This conjecture was shown to be true and was proved with the help of the “Honda- Serre-Tate theory”. We give another proof in Section 5. Grothendieck showed that Newton polygons “go up” under specialization: no point of the Newton polygon of a closed fiber in a family is below the Newton polygon of the generic fiber. In 1970 Grothendieck conjectured the converse: any pair of comparable Newton polygons appear for the generic and special fiber of a family. This was extended by Koblitz in 1975 to a conjecture about a sequence of comparable Newton polygons. In Section 6 we show these conjectures to be true. These results are obtained by deforming the most special abelian varieties or p-divisible groups we can think of. In describing deformations we use the theory of displays; this was proposed by Mumford, and has been developed in arXiv:math/0007201v1 [math.AG] 1 Jul 2000 [17], [18], and recently elaborated in [32] and [33]; also see [11], [31]. -
List of Publications
List of publications Frans Oort Updated 28 - VII - 2011 [1] — Reducible and multiple algebraic curves. PhD-Thesis, Leiden, 1961. [2] — Sur le sch´ema de Picard. Bull. Soc. Math. France 90 (1962), 1 - 14. [3] — A construction of generalized Jacobians by group extensions. Math. Ann. 147 (1962), 277 - 286. [4] — A note on rationality of divisor classes on algebraic schemata (separable case). Math. Ann. 149 (1963), 67 - 70. [5] — Hochschild extensions of algebraic rings. Proceed. Kon. Nederl. Acad. Wetensch. 66 (1963), 76 - 84. [6] — A note on natural maps of higher extension functors. Proceed. Cambridge Phil. Soc. 59 (1963), 283 - 286. [7] — Natural maps of extension functors. Proceed. Kon. Nederl. Acad. Wetensch. 66 (1963), 559 - 566. [8] — Yoneda extensions in abelian categories. Math. Ann. 153 (1964), 227 - 235. [9] — Commutative group schemes. Lect. Notes Math. 15, Springer - Verlag 1966. [10] — Algebraic group schemes in characteristic zero are reduced. Invent. Math. 2 (1966), 79 - 80. 1 [11] — On the definition of an abelian category. Proceed. Kon. Acad. Wetensch. 70 (1967), 83 - 92. [12] F. Oort & J. R. Strooker - The category of finite bialgebras over a field. Proceed. Kon. Acad. Wetensch. 70 (1967), 163 - 169. [13] H. Matsumura & F. Oort - Representability of group functors and automorphisms of algebraic schemes. Invent. Mat. 4 (1967), 1 - 25. [14] F. Oort & T. Oda - Higher extensions of abelian varieties. Nagoya Math. Journal 31 (1968), 81 - 88. [15] — Embeddings of finite group schemes into abelian schemes. Mimeogr. notes, AMS Summer School in Algebraic Geometry, Bowdoin College, 1967. [16] F. Oort & D. Mumford - Deformations and liftings of finite, commutative group schemes. -
Noriko YUI • Affiliation
CURRICULUM VITAE (JULY 2017) Personal Data • Name : Noriko YUI • Affiliation: Department of Mathematics and Statistics Queen’s University Kingston, Ontario Canada K7L 3N6 Tel (613) 533-2421; Fax (613) 533-2964 email [email protected] • Home Addresses: 2350 Dundas Street West #2814 Toronto, Ontario M6P 4B1 Tel (416) 536–8642 and 82 Ontario Street Apt #606 Kingston, Ontario K7L 5M2 Tel (613) 547–5209 • Date of Birth and Place: September 28, 1943, Yamanashi Prefecture, Japan • Citizenship: Japanese, Landed Immigrant of Canada and Denmark • Family: Married to George A. Elliott Higher Education • Ph.D. in Mathematics, Rutgers University, October 1974 Graduate Work in Mathematics, Rutgers University, 1969–1974 Took summer courses at SUNY Buffalo, 1970, 1971 Took a course at The Institute for Advanced Study, 1972 Spring Took parts in research seminars at University of Copenhagen, 1972–1974 Graduate Work in Mathematics, Tsuda College, 1966–1969 • B.Sc. in Mathematics, Tsuda College, March 1966 Undergraduate Work in Mathematics, Tsuda College, 1962–1966 • Ph.D. Thesis: Elliptic Curves and Formal Groups (105 pages) • Principal Ph.D. Thesis supervisor: Richard T. Bumby (Rutgers University) (Frans Oort (University of Utrecht) was the most influential mathematician for my thesis, though he was not an official supervisor) Typeset by AMS-TEX 1 2 CURRICULUM VITAE (JULY 2017) Academic and Professional Appointments • Professor, Queen’s University, 1990–Present • Associate Professor, Queen’s University, 1987–1990 • Associate Professor, University of Toronto, -
Descargar Nro 12. Año 2020
HOMOTECIA Nº 12 – Año 18 Martes, 1º de Diciembre de 2020 1 Diciembre 2020. Haremos un alto en relación a los temas que hemos tratado en los más recientes editoriales. Hoy nos toca despedir el año. Presentar esta edición significa haber publicado durante 18 años continuos a nuestra Revista HOMOTECIA. Cuando nos iniciemos en el 2021, esperamos seguir realizando esta tarea que siempre nos ha agradado realizar. Diciembre de por sí es un mes especial, no es simplemente el final del año, es el mes del cual no dudamos en afirmar que es el más esperado por niños, jóvenes y adultos en el país, sea cuales sean las situaciones que estemos viviendo. Con él, llega la Navidad, época fundamental en el mantenimiento de nuestra fe, no solamente celebramos el nacimiento de Jesús sino que sentimos renacer en nuestros corazones el legado de su prédica. Es una celebración que comienza recordando a los seres queridos que ya se han marchado de este mundo y que siempre nos acompañaban en estas fechas. También sentimos la añoranza por la ausencia de nuestros seres queridos que por circunsta ncias lamentables en el país, han tenido que ir más allá de las fronteras buscando un mejor vivir. Aun así, nos entusiasmamos por el reencuentro familiar de los que hemos quedado, obsequiar regalos afectuosos a nuestros familiares y a nuestros niños, a los mejores amigos como muestra de hacerles ver nuestros deseos de seguir manteniendo una amistad que linda en lo fraterno. Arreglamos nuestros hogares con motivos navideños, abundantes luces de colores destellan por doquier, en se colabora entre todos en la elaboración de los platos tradicionales como las hallacas y los postres; detalles que son importantes en la vida de la mayoría de nosotros. -
Complex Multiplication and Lifting Problems
Mathematical Surveys and Monographs Volume 195 Complex Multiplication and Lifting Problems Ching-Li Chai "RIAN#ONRAD Frans Oort American Mathematical Society http://dx.doi.org/10.1090/surv/195 Complex Multiplication and Lifting Problems http://dx.doi.org/10.1090/surv/195 Mathematical Surveys and Monographs Volume 195 Complex Multiplication and Lifting Problems Ching-Li Chai Brian Conrad Frans Oort American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE Ralph L. Cohen, Chair Benjamin Sudakov Robert Guralnick MichaelI.Weinstein MichaelA.Singer 2010 Mathematics Subject Classification. Primary 11G15, 14K02, 14L05, 14K15, 14D15. For additional information and updates on this book, visit www.ams.org/bookpages/surv-195 Library of Congress Cataloging-in-Publication Data Chai, Ching-Li, author. Complex multiplication and lifting problems / Ching-Li Chai, Brian Conrad, Frans Oort. pages cm — (Mathematical surveys and monographs ; volume 195) Includes bibliographical references and index. ISBN 978-1-4704-1014-8 (alk. paper) 1. Multiplication, Complex. 2. Abelian varieties. I. Conrad, Brian, 1970– author. II. Oort, Frans, 1935– author. III. Title. QA564.C44 2014 516.353—dc23 2013036892 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA.