DOCSLIB.ORG

Research Proposal Chitrabhanu Chaudhuri [email protected]

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Research Proposal Chitrabhanu Chaudhuri Chitrabhanu@Gmail.Com Research Proposal Chitrabhanu Chaudhuri [email protected] My area of research broadly falls under Complex Algebraic Geometry. Algebraic geometry is a branch of mathematics where one studies the geometry of zero sets of a collection of polynomials over a certain field, (C in my case), using algebraic techniques. These zero sets are called algebraic varieties. More specifically my research concerns Moduli of Algebraic curves. The Moduli Space of algebraic curves has been a classical object of study within Algebraic geometry and has connections with various other fields of mathematics, including but not limited to enumerative geometry [KM94], number theory [KM85], mathematical physics [GK98] and dynamical systems [EMM15]. I am currently pursuing several projects all revolving around the central topic of Moduli of Curves: 1. Arakelov Geometry of Modular curves, 2. Enumerative Geometry of Curves, 3. Topological study of the moduli of curves. I shall describe each of them in a separate section below. 1. Arakelov Geometry of Modular Curves This is ongoing joint work with Debargha Banerjee and Diganta Borah. We are interested in finding the minimal regular model and stable arithmetic self-intersection of certain modular curves with arithmetic applications in mind. 1.1. Arakelov Goemetry. Let K=Q be a number field and Ok be its ring of integers. An arith- metic surface X over OK is a regular scheme of dimension 2 with a proper map to X! Spec OK , defined in [Liu02]. The algebraic intersection theory doesn't work very well in this situation since X is not proper. Arakelov [Ara75] introduced an intersection pairing suited to this situation for the special case K = Q. Deligne [Del87] later generalised this intersection theory to arbitrary number fields. Faltings [Fal84] studied this theory extensively, proving results like the Riemmann-Roch theorem, Hodge index theorem and Noether's formula in this situation. Faltings's motivation for studying Arakelov intersection pairing was to prove results about arithmetic surfaces (or number fields), that were known for algebraic surfaces (or function fields), in particular Mordell conjec- ture which is now known as Faltings's theorem. Although Faltings's proof of Mordell conjecture did not involve Arakelov theory, but Vojta [Voj91] gave a proof using Arakelov's pairing. Faltings [Fal91]later proved a generalisation of Mordell conjecture using his results in Arakelov theory. In this section we shall use the notation h·; ·iAr for the Arakelov intersection pairing. 1.2. Modular curves. First let us discuss certain finite index subgroups of SL(2; Z), known as congruence subgroups. Fix a positive integer N called the level and let a b Γ (N) = 2 SL(2; ) j c ≡ 0 (mod N) 0 c d Z a b Γ (N) = 2 SL(2; ) j c ≡ 0 (mod N); a; d ≡ 0 (mod N) 1 c d Z 1 0 Γ(N) = A 2 SL(2; ) j A ≡ (mod N) : Z 0 1 The modular group SL(2; Z) acts on the upper half plane H = fx + iy 2 C j y > 0g through M¨obiustransformations hence so does a subgroup Γ ⊂ SL(2; Z). The quotient Y (Γ) = ΓnH is a 1 2 non-compact Riemann surface. Y (Γ) can be compactified by adding finitely many points called cusps and the compactification is denoted by X(Γ). Being a compact Riemann surface, X(Γ) is an algebraic curve over C. In fact for congruence subgroups X(Γ) is an algebraic curve over Q. We abbreviate X0(N) = X(Γ0(N)), X1(N) = X(Γ1(N)) and X(N) = X(Γ(N)). In fact, X(Γ) are moduli spaces of generalised elliptic curves for congruence subgroups Γ and are closely connected to modular forms for the corresponding subgroups. A modern reference for modular curves and modular forms is [DS05]. 1.3. Stable Arithmetic self-intersection. Let X be a smooth projective geometrically connected curve over a number field K. A regular model of X over OK is an arithmetic surface X! Spec OK with generic fiber isomorphic to X. If genus of X is atleast 1, there is a minimal (in the sense of birational geometry) regular model X which is unique upto isomorphism, but not functorial in X. Such a model is called semi-stable if all the scheme theoretic fibers of π : X! Spec OK are reduced and have only nodal singularities. There is a distinguished line bundle on X the relative dualizing sheaf !X . This line bundle !X when restricted to any fiber of π is the canonical line bundle of that curve. If X is semi-stable, the quantity 2 h!X ;!X iAr !X = [K : Q] 0 0 is independent of K in the following sense: let K =K be a finite extension and X = X ×Spec OK Spec OK0 , then h! 0 ;! 0 i h! ;! i X X Ar = X X Ar : [K0 : Q] [K : Q] This quantity will henceforth be called the stable arithmetic self-intersection of X. The significance of this invariant has been shown by Szpiro [Szp90], who showed that the strict positivity of this number is equivalent to Bogomolov's conjecture. 1.4. Bogomolov's conjecture. Let X be a smooth projective geometrically connected curve over a number field K with genus g > 1. Let J be the Jacobian of X. Fix an embedding φ : X ! J for some degree 1 divisor of X. Bogomolov's conjecture, now a theorem due to Ullmo [Ull98] and Zhang [Zha93] says that there is an > 0 such that fx 2 X(K) j hNT(φ(x)) < g is finite; hNT denotes the Neron-Tate height on J. This conjecture is a generalisation of the Manin- Mumford conjecture. An effective version of this conjecture is known to be true due to Zhang [Zha93], where the author demonstrates an explicit value for in terms of the stable arithmetic self-intersection of the curve X. 1.5. Survey of known results. The minimal regular models of modular curves have been com- puted in many cases. In the case of square free levels N, Deligne and Rapoport [DR73] constructed regular models of X(N);X1(N) and X0(N) as moduli spaces of generalised elliptic curves. Katz and Mazur [KM85] gave a different moduli theoretic construction for Y (N);Y1(N) and Y0(N) using Drinfeld level structures and then compactified these by adding cusps. The encyclopaedic work of Katz and Mazur is now the most comprehensive reference for this material. It turns out that when N is not square, these models are not regular. Hence for non-square free level constructing a m minimal regular model is a major task, which has been undertaken by many people, for X0(p N) see Edixhoven [Edi90], and Weinstein [Wei16] for semi-stable models for X(pmN). The stable arithmetic self-intersection has also been studied extensively in the case of modular curves. In the case of X0(N), Abbes|Ullmo have given asymptotic upper and lower bounds for !2 , when N is square-free and co-prime to 6. X0(N) 3 For the modular curves X1(N), Mayer has shown that when N is odd, square free and of the form N = N 0qr with q; r > 4 !2 = 3g log N + o(g log N); X1(N) N N where gN is the genus of X1(N). In [BC18] using results from [BBC17], we have have shown that for N = p2, 2 2 2 ! 2 = 2g 2 log p + o(g 2 log p ): X0(p ) p p Using this and results of Zhang [Zha93], we are able to give an effective version of Bogomolov's conjecture: for a sufficiently large prime p, the set 1 x 2 X (p2)( ) j h (φ(x)) < − log(p2) 0 Q NT 2 is finite whereas 2 2 x 2 X0(p )(Q) j hNT(φ(x)) ≤ (1 + ) log(p ) is infinite. 1.6. Future research. There are several future direction in this project. 3 Stable model for X0(p ) has been computed by Coleman and McMurdy in [CM06] and [CM10] along with a study of the special fiber. So using their work we would like to carry out the program 3 of [BC18] for X0(p ). More precisely: 3 Question 1. Find the stable arithmetic self-intersection of X0(p ). The stable model of Coleman|McMurdy is not regular so the first task is to compute a minimal 3 regular model for X0(p ). The geometry of the special fiber of the stable model is much more complicated in this case and it will be a much harder task to compute the algebraic (or finite) part of the self-intersection of the relative dualizing sheaf. However, computation of the analytic (or 2 infinite) part should be analogous in flavour to the case of X0(p ). n Finding stable models of X0(p ) for n > 3 is a well known open problem as well as finding regular semi-stable models. It would be a long term goal to study the geometry of regular minimal models n for X0(p ) over the ring of integers of finite extensions of Q over which the models are semi-simple. 2. Enumerative Geometry of Curves This is a joint project with Ritwik Mukherjee and Nilkantha Das. Our varieties are over C. An algebraic curve is a projective variety of dimension 1. There are two invariants associated to an algebraic curve, the geometric genus and the arithmetic genus. When the curve is smooth these are the same, but for singular curves the two numbers may be different. In this section genus will mean geometric genus. 2.1. Curve counting. A fundamental problem in enumerative algebraic geometry is: (g) 2 Question 2.
Load more

Recommended publications
  • The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary
    The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary i Reproduction. The work may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents. In any reproduction, the original publication by the Publisher must be credited in the following manner: “First published in The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commen- tary, c 2002 by the Mathematical Association of America,” and the copyright notice in proper form must be placed on all copies. Ravi Vakil’s photo on p. 337 is courtesy of Gabrielle Vogel. c 2002 by The Mathematical Association of America (Incorporated) Library of Congress Catalog Card Number 2002107972 ISBN 0-88385-807-X Printed in the United States of America Current Printing (last digit): 10987654321 ii The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary Kiran S. Kedlaya University of California, Berkeley Bjorn Poonen University of California, Berkeley Ravi Vakil Stanford University Published and distributed by The Mathematical Association of America iii MAA PROBLEM BOOKS SERIES Problem Books is a series of the Mathematical Association of America consisting of collections of problems and solutions from annual mathematical competitions; compilations of problems (including unsolved problems) specific to particular branches of mathematics; books on the art and practice of problem solving, etc. Committee on Publications Gerald Alexanderson, Chair Roger Nelsen Editor Irl Bivens Clayton Dodge Richard Gibbs George Gilbert Art Grainger Gerald Heuer Elgin Johnston Kiran Kedlaya Loren Larson Margaret Robinson The Inquisitive Problem Solver, Paul Vaderlind, Richard K.
    [Show full text]
  • Lecture Notes in Mathematics
    Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann Subseries: Mathematisches Institut der Universit~it und Max-Planck-lnstitut for Mathematik, Bonn - voL 5 Adviser: E Hirzebruch 1111 Arbeitstagung Bonn 1984 Proceedings of the meeting held by the Max-Planck-lnstitut fur Mathematik, Bonn June 15-22, 1984 Edited by E Hirzebruch, J. Schwermer and S. Suter I IIII Springer-Verlag Berlin Heidelberg New York Tokyo Herausgeber Friedrich Hirzebruch Joachim Schwermer Silke Suter Max-Planck-lnstitut fLir Mathematik Gottfried-Claren-Str. 26 5300 Bonn 3, Federal Republic of Germany AMS-Subject Classification (1980): 10D15, 10D21, 10F99, 12D30, 14H10, 14H40, 14K22, 17B65, 20G35, 22E47, 22E65, 32G15, 53C20, 57 N13, 58F19 ISBN 3-54045195-8 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-15195-8 Springer-Verlag New York Heidelberg Berlin Tokyo CIP-Kurztitelaufnahme der Deutschen Bibliothek. Mathematische Arbeitstagung <25. 1984. Bonn>: Arbeitstagung Bonn: 1984; proceedings of the meeting, held in Bonn, June 15-22, 1984 / [25. Math. Arbeitstagung]. Ed. by E Hirzebruch ... - Berlin; Heidelberg; NewYork; Tokyo: Springer, 1985. (Lecture notes in mathematics; Vol. 1t11: Subseries: Mathematisches I nstitut der U niversit~it und Max-Planck-lnstitut for Mathematik Bonn; VoL 5) ISBN 3-540-t5195-8 (Berlin...) ISBN 0-387q5195-8 (NewYork ...) NE: Hirzebruch, Friedrich [Hrsg.]; Lecture notes in mathematics / Subseries: Mathematischee Institut der UniversitAt und Max-Planck-lnstitut fur Mathematik Bonn; HST This work ts subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re~use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
    [Show full text]
  • Mathematical Genealogy of the Wellesley College Department Of
    Nilos Kabasilas Mathematical Genealogy of the Wellesley College Department of Mathematics Elissaeus Judaeus Demetrios Kydones The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. http://www.genealogy.math.ndsu.nodak.edu/ Georgios Plethon Gemistos Manuel Chrysoloras 1380, 1393 Basilios Bessarion 1436 Mystras Johannes Argyropoulos Guarino da Verona 1444 Università di Padova 1408 Cristoforo Landino Marsilio Ficino Vittorino da Feltre 1462 Università di Firenze 1416 Università di Padova Angelo Poliziano Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo 1477 Università di Firenze 1433 Constantinople / Università di Mantova Università di Mantova Leo Outers Moses Perez Scipione Fortiguerra Demetrios Chalcocondyles Jacob ben Jehiel Loans Thomas à Kempis Rudolf Agricola Alessandro Sermoneta Gaetano da Thiene Heinrich von Langenstein 1485 Université Catholique de Louvain 1493 Università di Firenze 1452 Mystras / Accademia Romana 1478 Università degli Studi di Ferrara 1363, 1375 Université de Paris Maarten (Martinus Dorpius) van Dorp Girolamo (Hieronymus Aleander) Aleandro François Dubois Jean Tagault Janus Lascaris Matthaeus Adrianus Pelope Johann (Johannes Kapnion) Reuchlin Jan Standonck Alexander Hegius Pietro Roccabonella Nicoletto Vernia Johannes von Gmunden 1504, 1515 Université Catholique de Louvain 1499, 1508 Università di Padova 1516 Université de Paris 1472 Università di Padova 1477, 1481 Universität Basel / Université de Poitiers 1474, 1490 Collège Sainte-Barbe
    [Show full text]
  • FOCUS August/September 2005
    FOCUS August/September 2005 FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, FOCUS August/September, October, November, and Volume 25 Issue 6 December. Editor: Fernando Gouvêa, Colby College; [email protected] Inside Managing Editor: Carol Baxter, MAA 4 Saunders Mac Lane, 1909-2005 [email protected] By John MacDonald Senior Writer: Harry Waldman, MAA [email protected] 5 Encountering Saunders Mac Lane By David Eisenbud Please address advertising inquiries to: Rebecca Hall [email protected] 8George B. Dantzig 1914–2005 President: Carl C. Cowen By Don Albers First Vice-President: Barbara T. Faires, 11 Convergence: Mathematics, History, and Teaching Second Vice-President: Jean Bee Chan, An Invitation and Call for Papers Secretary: Martha J. Siegel, Associate By Victor Katz Secretary: James J. Tattersall, Treasurer: John W. Kenelly 12 What I Learned From…Project NExT By Dave Perkins Executive Director: Tina H. Straley 14 The Preparation of Mathematics Teachers: A British View Part II Associate Executive Director and Director By Peter Ruane of Publications: Donald J. Albers FOCUS Editorial Board: Rob Bradley; J. 18 So You Want to be a Teacher Kevin Colligan; Sharon Cutler Ross; Joe By Jacqueline Brennon Giles Gallian; Jackie Giles; Maeve McCarthy; Colm 19 U.S.A. Mathematical Olympiad Winners Honored Mulcahy; Peter Renz; Annie Selden; Hortensia Soto-Johnson; Ravi Vakil. 20 Math Youth Days at the Ballpark Letters to the editor should be addressed to By Gene Abrams Fernando Gouvêa, Colby College, Dept. of 22 The Fundamental Theorem of ________________ Mathematics, Waterville, ME 04901, or by email to [email protected].
    [Show full text]
  • Algebra & Number Theory
    Algebra & Number Theory Volume 4 2010 No. 2 mathematical sciences publishers Algebra & Number Theory www.jant.org EDITORS MANAGING EDITOR EDITORIAL BOARD CHAIR Bjorn Poonen David Eisenbud Massachusetts Institute of Technology University of California Cambridge, USA Berkeley, USA BOARD OF EDITORS Georgia Benkart University of Wisconsin, Madison, USA Susan Montgomery University of Southern California, USA Dave Benson University of Aberdeen, Scotland Shigefumi Mori RIMS, Kyoto University, Japan Richard E. Borcherds University of California, Berkeley, USA Andrei Okounkov Princeton University, USA John H. Coates University of Cambridge, UK Raman Parimala Emory University, USA J-L. Colliot-Thel´ ene` CNRS, Universite´ Paris-Sud, France Victor Reiner University of Minnesota, USA Brian D. Conrad University of Michigan, USA Karl Rubin University of California, Irvine, USA Hel´ ene` Esnault Universitat¨ Duisburg-Essen, Germany Peter Sarnak Princeton University, USA Hubert Flenner Ruhr-Universitat,¨ Germany Michael Singer North Carolina State University, USA Edward Frenkel University of California, Berkeley, USA Ronald Solomon Ohio State University, USA Andrew Granville Universite´ de Montreal,´ Canada Vasudevan Srinivas Tata Inst. of Fund. Research, India Joseph Gubeladze San Francisco State University, USA J. Toby Stafford University of Michigan, USA Ehud Hrushovski Hebrew University, Israel Bernd Sturmfels University of California, Berkeley, USA Craig Huneke University of Kansas, USA Richard Taylor Harvard University, USA Mikhail Kapranov Yale
    [Show full text]
  • Annales Scientifiques De L'é.Ns
    ANNALES SCIENTIFIQUES DE L’É.N.S. J.-B. BOST Potential theory and Lefschetz theorems for arithmetic surfaces Annales scientifiques de l’É.N.S. 4e série, tome 32, no 2 (1999), p. 241-312 <http://www.numdam.org/item?id=ASENS_1999_4_32_2_241_0> © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1999, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www. elsevier.com/locate/ansens) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systé- matique est constitutive d’une infraction pénale. Toute copie ou impression de ce fi- chier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Ann. sclent. EC. Norm. Sup., 4° serie, t. 32, 1999, p. 241 a 312. POTENTIAL THEORY AND LEFSCHETZ THEOREMS FOR ARITHMETIC SURFACES BY J.-B. BOST ABSTRACT. - We prove an arithmetic analogue of the so-called Lefschetz theorem which asserts that, if D is an effective divisor in a projective normal surface X which is nef and big, then the inclusion map from the support 1-D) of -D in X induces a surjection from the (algebraic) fondamental group of \D\ onto the one of X. In the arithmetic setting, X is a normal arithmetic surface, quasi-projective over Spec Z, D is an effective divisor in X, proper over Spec Z, and furthermore one is given an open neighbourhood ^ of |-D|(C) on the Riemann surface X(C) such that the inclusion map |D|(C) ^ f^ is a homotopy equivalence.
    [Show full text]
  • Correspondences in Arakelov Geometry and Applications to the Case of Hecke Operators on Modular Curves
    CORRESPONDENCES IN ARAKELOV GEOMETRY AND APPLICATIONS TO THE CASE OF HECKE OPERATORS ON MODULAR CURVES RICARDO MENARES Abstract. In the context of arithmetic surfaces, Bost defined a generalized Arithmetic 2 Chow Group (ACG) using the Sobolev space L1. We study the behavior of these groups under pull-back and push-forward and we prove a projection formula. We use these results to define an action of the Hecke operators on the ACG of modular curves and to show that they are self-adjoint with respect to the arithmetic intersection product. The decomposition of the ACG in eigencomponents which follows allows us to define new numerical invariants, which are refined versions of the self-intersection of the dualizing sheaf. Using the Gross-Zagier formula and a calculation due independently to Bost and K¨uhnwe compute these invariants in terms of special values of L series. On the other hand, we obtain a proof of the fact that Hecke correspondences acting on the Jacobian of the modular curves are self-adjoint with respect to the N´eron-Tate height pairing. Contents 1. Introduction1 2 2. Functoriality in L1 5 2 2.1. The space L1 and related spaces5 2 2.2. Pull-back and push-forward in the space L1 6 2 2.3. Pull-back and push-forward of L1-Green functions 12 3. Pull-back and push-forward in Arakelov theory 16 2 3.1. The L1-arithmetic Chow group, the admissible arithmetic Chow group and intersection theory 16 3.2. Functoriality with respect to pull-back and push-forward 18 4.
    [Show full text]
  • THE WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION 1985–2000 Problems, Solutions, and Commentary
    AMS / MAA PROBLEM BOOKS VOL 33 THE WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION 1985–2000 Problems, Solutions, and Commentary Kiran S. Kedlaya Bjorn Poonen Ravi Vakil 10.1090/prb/033 The William Lowell Putnam Mathematical Competition 1985-2000 Originally published by The Mathematical Association of America, 2002. ISBN: 978-1-4704-5124-0 LCCN: 2002107972 Copyright © 2002, held by the American Mathematical Society Printed in the United States of America. Reprinted by the American Mathematical Society, 2019 The American Mathematical Society retains all rights except those granted to the United States Government. ⃝1 The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at https://www.ams.org/ 10 9 8 7 6 5 4 3 2 24 23 22 21 20 19 AMS/MAA PROBLEM BOOKS VOL 33 The William Lowell Putnam Mathematical Competition 1985-2000 Problems, Solutions, and Commentary Kiran S. Kedlaya Bjorn Poonen Ravi Vakil MAA PROBLEM BOOKS SERIES Problem Books is a series of the Mathematical Association of America consisting of collections of problems and solutions from annual mathematical competitions; compilations of problems (including unsolved problems) specific to particular branches of mathematics; books on the art and practice of problem solving, etc. Committee on Publications Gerald Alexanderson, Chair Problem Books Series Editorial Board Roger Nelsen Editor Irl Bivens Clayton Dodge Richard Gibbs George Gilbert Art Grainger Gerald Heuer Elgin Johnston Kiran Kedlaya Loren Larson Margaret Robinson The Contest Problem Book VII: American Mathematics Competitions, 1995-2000 Contests, compiled and augmented by Harold B.
    [Show full text]
  • Volume Function Over a Trivially Valued Field
    Volume function over a trivially valued field Tomoya Ohnishi∗ May 15, 2019 Abstract We introduce an adelic Cartier divisor over a trivially valued field and discuss the bigness of it. For bigness, we give the integral representation of the arithmetic volume and prove the existence of limit of it. Moreover, we show that the arithmetic volume is continuous and log concave. Contents 1 Introduction 1 2 Preliminary 3 2.1 Q- and R-divisors . .3 2.2 Big divisors . .5 2.3 Normed vector space . .6 2.4 Berkovich space . .8 3 Adelic R-Cartier divisors over a trivially valued field 9 3.1 Green functions . 10 3.2 Continuous metrics on an invertible OX -module . 11 3.3 Adelic R-Cartier divisors . 12 3.4 Associated R-Weil divisors . 13 3.5 Canonical Green function . 14 3.6 Height function . 15 3.7 Scaling action for Green functions . 16 4 Arithmetic volume 16 4.1 Big adelic R-Cartier divisors . 16 4.2 Existence of limit of the arithmetic volume . 17 4.3 Continuity of F(D;g)(t)........................................ 20 arXiv:1905.05447v1 [math.AG] 14 May 2019 4.4 Continuity of the arithmetic volume . 21 4.5 Log concavity of the arithmetic volume . 23 1 Introduction Arakelov geometry is a kind of arithmetic geometry. Beyond scheme theory, it has been developed to treat a system of equations with integer coefficients such by adding infinite points. In some sense, it is an extension of Diophantine geometry. It is started by Arakelov [1], who tried to define the intersection theory on an arithmetic surface.
    [Show full text]
  • MAA Awards Given in Baltimore
    MAA Awards Given in Baltimore At the Joint Mathematics Meetings in Baltimore, concluded that “highly integrated content-methods Maryland, in January 2014, the Mathematical As- instruction provided no measurable advantage sociation of America awarded several prizes. for students but that coordination of separate courses in content and methods served to improve Gung and Hu Award for Distinguished students’ performance in both.” Another step was Service the early placement testing for high school juniors, The Yueh-Gin Gung and Dr. Charles Y. Hu Award followed by an appropriate twelfth-grade course for Distinguished Service to Mathematics is the to prepare for college mathematics. One problem most prestigious award made by the MAA. It revealed by early placement testing was that many honors distinguished contributions to mathemat- high school juniors had very limited algebra skills ics and mathematical education in one particular and no appropriate course for them to take in aspect or many, whether in a short period or over their senior year. With funding from the Battelle a career. Foundation, Leitzel and Demana undertook the The 2014 Gung and Hu Award was presented to project A Numerical Problem-Solving Course for Joan Leitzel for her farsighted work of creating Underprepared College-Intending Seniors. The programs to decrease the need for remediation course they developed took a highly numerical in colleges and for her leadership on the national approach to algebra and geometry and very suc- level. Her distinguished career began at Ohio State cessfully brought students up to competency at the University, where she led visionary projects that level of intermediate algebra.
    [Show full text]
  • 2004 Notices Index
    The 2004 Notices Index Index Section Page Number Index Section Page Number The AMS 1413 Memorial Articles 1424 Announcements 1414 New Publications Offered by the AMS 1425 Authors of Articles 1416 Officers and Committee Members 1425 Deaths of Members of the Society 1417 Opinion 1425 Education 1418 Opportunities 1425 Feature Articles 1418 Prizes and Awards 1426 Letters to the Editor 1419 The Profession 1428 Mathematicians 1420 Reference and Book List 1428 Mathematics Articles 1423 Reviews 1428 Mathematics History 1424 Surveys 1428 Meetings Information 1424 Tables of Contents 1428 About the Cover AMS-AAAS Mass Media Summer Fellowships, 1075 8, 207, 319, 411, 495, 619, 815, 883, 1023, 1194, 1347 AMS-AAAS Media Fellow Named, 808 AMS Associate Executive Editor Positions—Applications Invited, 602 AMS Book Prize, 450, 568 AMS Committee on Meetings and Conferences, 1249 AMS Committee on Science Policy, 1246 AMS Email Support for Frequently Asked Questions, 1365 AMS Menger Awards at the 2004 ISEF, 1235 AMS Menger Prizes at the 2004 ISEF, 913 The AMS AMS Mentoring Workshop, 1304 2000 Mathematics Subject Classification, 60, 275, 454, AMS Officers and Committee Members, 1082 572, 992, 1290 AMS Participates in Capitol Hill Exhibition, 1076 2003 AMS Election Results, 269 AMS Participates in Celebration of von Neumann’s Birth, 2003 AMS Policy Committee Reports, 264 52 2003 Annual Survey of the Mathematical Sciences (First AMS Scholarships for “Math in Moscow”, 805 Report), 218 AMS Short Course, 1161 2003 Annual Survey of the Mathematical Sciences (Second
    [Show full text]
  • The 1999 Notices Index, Volume 46, Number 11
    index.qxp 10/15/99 11:17 AM Page 1480 The 1999 Notices Index Index Section Page Number The AMS 1480 Meetings Information 1489 Announcements 1481 Memorial Articles 1490 Authors of Articles 1482 New Publications Offered by the AMS 1490 Reference and Book List 1420 Officers and Committee Members 1490 Deaths of Members of the Society 1483 Opinion 1490 Education 1484 Opportunities 1490 Feature Articles 1484 Prizes and Awards 1491 Forum 1485 Articles on the Profession 1492 Letters to the Editor 1486 Reviews 1492 Mathematicians 1487 Surveys 1493 Mathematics Articles 1489 Tables of Contents 1493 Mathematics History 1489 About the Cover, 26, 245, 318, 420, 534, 658, 781, 918, AMS Meeting in August 2000, 355 1073, 1208, 1367 AMS Menger Awards at the 1999 Intel-International Science and Engineering Fair, 912 Acknowledgment of Contributions, 947 AMS Officers and Committee Members, 1271 AMS Participates in Capitol Hill Exhibition, 918 The AMS AMS Participates in Faculty Preparation Program, 1072 1998 Election Results, 266 AMS Short Courses, 1171 1998 Report of the Committee on Meetings and Confer- AMS Standard Cover Sheet, 60, 270, 366, 698, 972, 1102, ences, 810 1282, 1428 1999 AMS Centennial Fellowships Awarded, 684 (The) Birth of an AMS Meeting, 1029 1999 AMS Election, 58, 267 Bylaws of the American Mathematical Society, 1252 1999 AMS-MAA-SIAM Morgan Prize, 469 Call for Proposals for 2001 Conferences, 1177, 1331 1999 Arnold Ross Lectures, 692 Conference Announced (Summer Mathematics Experience: 1999 Bôcher Prize, 463 A Working Conference on Summer
    [Show full text]