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         Algebraic Geometry:     more books (100)
  1. Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) by David Eisenbud, 1999-02-11
  2. Algebraic Geometry in East Asia: Proceedings of the Symposium
  3. Algebraic Integrability, Painlevé Geometry and Lie Algebras (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) by Mark Adler, Pierre van Moerbeke, et all 2004-10-15
  4. Geometric Modeling and Algebraic Geometry
  5. Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics) by Saugata Basu, Richard Pollack, et all 2006-08-21
  6. Selected Topics in Algebraic Geometry/2 Volumes in 1 (AMS Chelsea Publishing) by Virgil Snyder, 1970-10
  7. Algebraic Geometry by Daniel Bump, 1998-11
  8. Introduction to algebraic geometry by David Mumford, 1967
  9. ON RIEMANN'S THEORY OF ALGEBRAIC FUNCTIONS AND THEIR INTEGRALS: A Supplement to the Usual Treatises by Felix Klein, 2007-04-15
  10. A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics) by J. P. May, 1999-09-01
  11. The Arithmetic and Geometry of Algebraic Cycles (NATO SCIENCE SERIES: C Mathematical and Physical Sciences) by Stefan Muller-Stach, 2000-02-29
  12. Number Theory and Algebraic Geometry (London Mathematical Society Lecture Note Series)
  13. Algebraic Curves: An Introduction to Algebraic Geometry (Advanced Book Classics) by William Fulton, 1989-03
  14. Algebraic Geometry: A Volume in Memory of Paolo Francia

81. Special Year: Langlands Programme
Special year, Feb.2001 to Jan.2002, Tata Institute of Fundamental Research, Mumbai.
http://www.math.tifr.res.in/maths/langlands/
Special year on
Algebraic Geometry and the Langlands Programme
February 1, 2001 - January 31, 2002
Main Page Courses Visitors Conference The School of Mathematics of the Tata Institute of Fundamental Research (Mumbai), will have a special year dedicated to Algebraic Geometry and the Langlands Programme ( February 1 , 2001 to January 31 , 2002). A 3 week workshop/conference will be organized at the end of the year. Area of interest. The area of the special year will be the Langlands programme in the case of function fields, both in characteristic zero and positive characteristic, and related areas of algebraic geometry. There has been a lot of activity in this subject in recent years. There has been very significant progress by Lafforgue towards a proof of the Langlands conjecture for GL(r) over function fields, using technology based on shtukas. Besides the above, there has also been recent progress in understanding from other geometric points of view, with significant work (or work in progress) by several authors. This work involves geometric approaches to the fundamental lemma, lattice varieties, local models, stacks of vector bundles and principal bundles on curves, Higgs bundles, Hitchin Hamiltonian systems, quantization, D-modules, perverse sheaves, infinite dimensional algebras of various kinds, etc. The whole range of the above topics, and various related topics as well, are of interest for the special year. As the area is vast, more attention will be given to certain topics, and this will of course be influenced by the participants. Our attempt will be also to include detailed lecture courses on a few chosen topics, which will be designed to allow mathematicians who are newcomers to this area to learn the basics. Together with this, the programme will feature advanced technical lectures by experts on the current state of the art. We will also try to get a fair number of less technical overview talks by experts, at the beginning of each new topic.

82. Wen-Chen Chi
National Taiwan Normal University. Number theory, Arithmetic algebraic geometry.
http://math.ntnu.edu.tw/~wchi/EnglishPage.html
Wen-Chen Chi (Wenchen Chi) Professor of Mathematics National Taiwan Normal University Department of Mathematics 88, Sec.4, Ting-Chou Road, Taipei, Taiwan 116 Phone: (886)2-2931-2611 ext.315 Fax: (886)2-2933-2342 e-mail: wchi@math.ntnu.edu.tw wchi@cc.ntnu.edu.tw Brief CV Professor, 1996/8 - Present, National Taiwan Normal University Head, 1994/3 - 1996/7, Department of Mathematics, National Tsing Hua University Professor, 1991/8 - 1996/7, National Tsing Hua University Associate Professor, 1988/8 - 1991/7, National Tsing Hua University Lecturer, 1986/7 - 1988/6, University of Pennsylvania Ph.D., 1986/5, University of California, Berkeley B. Sc., 1977/7, National Taiwan Normal University Research Interests Number Theory, Arithmetical Algebraic Geometry Current Courses
Abstract Algebra (undergraduate course) Topics in Algebra (graduate course) Seminar (graduate course) Current Sponsered Project On some computation of Brauer subgroups (NSC 93-2115-M-003-004, 2004/8 ~ 2005/7) Publications Twists of Central Simple Algebras and Endomorphism Algebras of Some Abelian Varieties ", Math. Annalen, 276 (1987), 615-632.

83. Topological Aspects Of Real Algebraic Geometry
Research semester, MSRI , Berkeley, CA, USA; 2 January 14 May 2004.
http://zeta.msri.org/calendar/programs/ProgramInfo/120/show_program

84. Special Year: Conference
Meeting to conclude the special year at Tata Institute of Fundamental Research, Mumbai (Bombay), India; 725 January 2002.
http://www.math.tifr.res.in/maths/langlands/conference.html
Conference
Main Page Courses Visitors Conference The special year will end with the three week workshop/conference from 7 January 2002 to 25 January 2002. The first two weeks will mainly feature short lecture courses (about 5 lectures each) by experts, aimed at mathematicians who do not necessarily work in the area. The last week will feature conference style lectures on recent work.
Preliminary list of short lecture courses:
  • Ben-Zvi: 3-4 lectures on vertex algebras and curves, from 7 Jan to 10 Jan
  • Gaitsgory: 5 lectures.
  • Lafforgue: 3 survey lectures on his proof for GL(n), and 3 lectures on ongoing work.
  • Frenkel: 3 lectures on local Langlands correspondence for affine algebras at the critical level (joint work with Gaitsgory) during week 3
  • Varshavsky: lectures on Lafforgue's compactification of moduli space of F-sheaves, during week 3.
    List of expected participants:
  • Anandavardhanan
  • D. Ben-Zvi
  • T.E.V. Balaji
  • V. Balaji
  • R. Bezrukavnikov
  • P. Boyer
  • Fiebig
  • E. Frenkel
  • 85. EAGER - European Algebraic Geometry Research Training Network
    European algebraic geometry research training network.
    http://euclid.mathematik.uni-kl.de/
    Your browser does not support frames! Click here for the EAGER welcome page.
    Click here for the EAGER menu.

    86. Dr T.A. Fisher
    University of Cambridge. Arithmetical algebraic geometry, specifically descent calculations for elliptic curves. Papers, slides, notes.
    http://www.dpmms.cam.ac.uk/site2002/People/fisher_ta.html
    Department of Pure Mathematics
    and Mathematical Statistics DPMMS People Dr T.A. Fisher
    Dr T.A. Fisher
    Title: University Lecturer
    College: Trinity College
    Room: E1.09
    Tel: +44 1223 764275
    Personal Home Page
    Research Interests: My research interests are in arithmetical algebraic geometry, specifically descent calculations for elliptic curves. This means that I am interested in making practical the computation of Selmer groups for elliptic curves over number fields, and in using geometric methods to investigate the Tate-Shafarevich group.
    Information provided by

    87. Harvard/MIT Algebraic Geometry Seminar
    seminar the webpage for the Seattle 05 Summer Institute in algebraic geometry. The Harvard/MIT algebraic geometry Seminar will alternate between MIT
    http://www-math.mit.edu/~jstarr/05ssem/
    Harvard/MIT Algebraic Geometry Seminar
    Spring 2005: Tuesdays 3:00-4:00
    NEW WEBPAGE
    This is an old seminar webpage. The current seminar webpage is here Rahul Pandharipande would like to point out to the participants of the seminar the webpage for the Seattle '05 Summer Institute in Algebraic Geometry. The Harvard/MIT Algebraic Geometry Seminar will alternate between MIT (Room 4-163, unless specified otherwise) and Harvard (Room 507) on Tuesdays. For directions to MIT Room 4-163, click here . You can see last semester's seminars here
    Schedule of upcoming talks:
    Click on the title of a talk for the abstract (if available). February 1 Magdalena Anca Mustata (UBC) MIT The Chow ring of stable map spaces February 8 Damiano Testa (MIT) Harvard The Severi problem for rational curves on del Pezzo surfaces February 15 Allen Knutson (UC Berkeley) MIT Torified simplicial complexes from Samuel-Rees degenerations February 22 Edward Lee (Harvard) Harvard A modular non-rigid Calabi-Yau threefold March 1 Carel Faber (Johns Hopkins) MIT On the cohomology of moduli spaces of pointed curves of low genus March 8 Sebastian Casalaina-Martin (SUNYSB) Harvard Cubic threefolds and abelian varieties of dimension five March 15 Rahul Pandharipande (Princeton) MIT A topological view of Gromov-Witten theory March 22 Harvard What kind of manifolds admit nowhere vanishing holomorphic one-forms?

    88. EIMI: Algebraic Geometry And Number Theory Conference
    Euler International Mathematical Institute, St Petersburg, Russia; 1723 June 2005.
    http://www.pdmi.ras.ru/EIMI/2005/AG/
    International conference
    ALGEBRAIC GEOMETRY AND NUMBER THEORY
    June 17-21, 2005
    St Petersburg, RUSSIA
    SCIENTIFIC COMMITEE Yu.Manin ( Moscow/Bonn )
    A.Parshin
    ( Moscow )
    J.Porras
    ( Salamanca )
    S.Vostokov
    ( St. Petersburg )
    I. Zhukov
    ( St. Petersburg )
    M.Bondarko ( St. Petersburg )
    I. Fesenko ( Nottingham )
    KEY SPEAKERS
    • Grzegorz Banaszak (Poznan)
    • Pilar Bayer (Barcelona)
    • Michael Bondarko (St. Petersburg)
    • David Burns (London)
    • Ivan Fesenko (Nottingham)
    • Cornelius Greither (Muenchen)
    • Henry H. Kim (Toronto)
    • Bernhard Koeck (Southampton)
    • Jose Maria Munoz-Porras (Salamanca)
    • Alexei Parshin (Moscow)
    • Fernando Pablos Romo (Salamanca)
    • Ivan Panin (St Petersburg)
    • Christophe Soule (Paris)
    • Michael Spiess (Bielefeld)
    • Jakob Stix (Bonn)
    • Lin Weng (Kyushu)
    • Yuri Zarhin (Pennstate)
    • Igor Zhukov (St Petersburg)
    Registration Form Registration Fee Visa Information Hotel Information ... Further information
    Previous Meetings:
    First conference on Arithmetic Geometry
    Second conference on Arithmetic Geometry

  • Back to the EIMI home-page
  • Back to the Petersburg Department of Steklov Institute of Mathematics
  • 89. M.I.T. Algebraic Geometry Seminar - Spring 1999
    Welcome to MIT s algebraic geometry Seminar s HomePage. MIT algebraic geometry Seminar. Friday, 400pm530pm Room 2-255
    http://www-math.mit.edu/alg_geom_sem.html

    90. Homepage For Frans Oort
    University of Utrecht. algebraic geometry and number theory. Publications, links.
    http://www.math.ruu.nl/people/oort/
    Department of Mathematics
    Frans Oort
    Department of Mathematics
    University of Utrecht
    P.O.Box 80.010
    3508 TA Utrecht
    The Netherlands
    tel: +31-30-2531514 / ... 1425 / ... 1430/ ... 1420
    fax: +31-30-2518394
    email address

    email: oort at math dot uu dot nl Mathematical Institute
    Budapestlaan 6
    3584 CD Utrecht ps file of "List of publications of Frans Oort". ps file of "Some questions in algebraic geometry". ps file of "Open problems in algebraic geometry". ps file of "Newton polygons and p-divisible groups: a conjecture by Grothendieck". ... ps file of F. Oort: Hecke orbits in moduli spaces. Seattle: 2005 AMS Summer Institute on Algebraic Geometry. Sheets, 22 pp. August 2005. Here are some links to other people in Algebraic Geometry and/or Number Theory: Ahmed Abbes Université de Paris 13 Dan Abramovich at Boston University Francesco Baldassarri at Padua University Pierre Berthelot at the University of Rennes 1 Frits Beukers at the University of Utrecht Ching-Li Chai at the University of Pennsylvania, Philadelphia PA, USA Robert Coleman at the University of California, Berkeley

    91. Number Theory And Algebraic Geometry Research Group
    Number Theory and algebraic geometry Research Group. Members, research interest, seminars.
    http://www.math.bgu.ac.il/~efrat/resgroup.html
    BEN GURION UNIVERSITY OF THE NEGEV
    DEPARTMENT OF MATHEMATICS
    P.O. Box 653, Be'er-Sheva 84105, ISRAEL
    Number Theory and Algebraic Geometry Research Group
    Eitan Bachmat
    PhD: MIT 1994
    Main Research Interests: Arakelov theory, Hilbert modular varieties
    E-mail: ebachmat@cs.bgu.ac.il Daniel Berend
    PhD: The Hebrew University of Jerusalem 1982
    Main Research Interests (in Number Theory): distribution modulo 1 (especially density modulo 1), Diophantine approximations, some classes of Diophantine equations
    E-mail: berend@black.bgu.ac.il Amnon Besser
    PhD: Tel Aviv University 1993
    Main Research Interests: number theory, arithmetic geometry, p-adic integration, p-adic cohomology, Shimura varieties, automorphic forms, algebraic cycles, algebraic K-theory.
    E-mail: bessera@math.bgu.ac.il Ido Efrat
    PhD: Tel-Aviv University 1990 Main Research Interests: Galois theory, field arithmetic, structure of canonical Galois groups, valuation theory E-mail: efrat@math.bgu.ac.il Nadya Gurevich PhD: Weizman Institute 2000 Main Research Interests: automorphic forms, representation theory E-mail: ngur@math.bgu.ac.il

    92. Nagaraj, D.S.
    Institute of Mathematical Sciences, C.I.T., Chennai. Algebraic number theory, algebraic geometry.
    http://www.imsc.res.in/~dsn/
    I am interested in the following areas of Mathematics: Algebraic Geometry and Algebraic Number theory.
    Hello.
    List of publications
    • On the moduli of curves with theta-characteristics
      Compositio Mathematica, Vol 75, P. 287-297, 1990.
    • The stucture of Iwasawa module associated with a $Z^r_p$-extension of a p-adic local field of characteristic
      Journal of Number theory,Vol 38,No 1, P. 52-57, May 1991.
    • (with A.R.Aithal) Splitting types of holomorphic bundles associateted to some hormonic maps.
      Comm. In Algebra Vol 21 (10), P. 3727-3731, 1993.
    • (with S.Ramanan) Polarisation of type (1,2, ... ,2) on Abelian varieties
      Duke Journal of Mathematics, (Pages, 157 - 194), Vol.80, No.1, Oct.1995.
    • (with C.S.Seshadri) Degenerations of the moduli spaces of vector bundles on curves I
      Proc.Indian Acad. Sci (Math. Sci.), Vol. 107, No. 2, pp 101-137, May 1997.
    • (with Indranil Biswas) Parabolic ample bundles, II: Connectivity of zero locus of a class of sections
      Topology, Vol. 37, No. 4, pp. 781-789, 1998.
    • (with Laytimi Fatima) On the Maximal Degeneracy Loci and the secant vector bundle
      Jour. of Math. Sci.(Newyork) 94 (1999), No.1, 1068-1072.

    93. University Of British Columbia Algebraic Geometry Seminar
    of Schubert varieties in the flag manifold involves interesting interplay between algebraic geometry, representation theory and combinatorics.
    http://www.math.ubc.ca/~shapiro/alg-geom.html
    Algebraic Geometry Seminar
    Winter 2004
    Wednesdays 10:30-11:30 am in PIMS, WMAX 110
    Schedule of talks:
    TIME SPEAKER TITLE January 25
    Tues, 10:00 am Tom Coates
    (Harvard) Floer homology, quantization and Gromov-Witten theory. January 26
    Wed, 10:30 am Tom Coates
    (Harvard) Floer homology, quantization and Gromov-Witten theory II. January 27
    Thurs, 10:00 am Tom Coates
    (Harvard) Floer homology, quantization and Gromov-Witten theory III. January 28
    Fri, 10:30 am Tom Coates
    (Harvard) Floer homology, quantization and Gromov-Witten theory IV. February 2
    Wed, 10:30 am Mitja Mastnak (UBC) About Hopf algebra extensions and cohomologies. February 9 Wed, 10:30 am Angelo Vistoli (U. of Bologna) Chow rings of classifying spaces for classical groups. February 10 Thurs, 10:00 am Megumi Harada (Toronto) Computation of generalized equivariant cohomologies of Kac-Moody flag varieties. February 16 Wed, 10:30 am No seminar (winter break) February 23 Wed, 10:30 am Julianna Tymoczko (Michigan) Generalizing group exponents using the topology of subvarieties of the flag variety. March 2 Wed, 10:30 am

    94. Nicholas M. Katz's Home Page
    Princeton University. Number theory and algebraic geometry. Publications, photographs.
    http://www.math.princeton.edu/~nmk/
    Check out monodromy.com Bibliography of Nicholas M. Katz pdf file (83 KB) C.V. of Nicholas M. Katz pdf file (22 KB) Photo from 60'th Birthday Conference jpg file (807 KB) Photo from 60'th Birthday Conference (high resolution version) TIF file (123 MB) V-Strom DL650 suspension adjustment
    Nicholas M. Katz PDF and DVI files available for download
    G_2 and hypergeometric sheaves dvi file (192 KB) pdf file (4169 KB) On a question of Lillian Pierce dvi file (44 KB) pdf file (982 KB) Hooley parameters for families of exponential sums over finite fields pdf file Notes on G_2, determinants, and equidistribution (typo's corrected Dec. 9, 2003) pdf file online version (joint with Esnault) Cohomological divisibility and point count divisibility (corrected version of nov. 10, 2003) dvi file (41 KB) pdf file (187 KB) Corrected version of Chapter 5 of "Twisted L-Functions and Monodromy" pdf file Moments, Monodromy, and Perversity: a Diophantine Perspective Corrections to "Space filling curves over finite fields" dvi file (12 KB) pdf file (88 KB) (joint with Pandharipande) Inequalities related to Lefschetz pencils and integrals of Chern classes pdf file (80 KB) Estimates for "nonsingular" multiplicative character sums dvi file (60 KB) pdf file (206 KB) A semicontinuity result for monodromy under degeneration dvi file (36 KB) pdf file (163 KB) Sato-Tate Equidistribution of Kurlberg-Rudnick Sums pdf file (94 KB) AWS2000 Lectures: L -functions and monodromy: four lectures on Weil II pdf file (184 KB) Larsen's Alternative, Moments, and the Monodromy of Lefschetz Pencils

    95. University Of British Columbia Algebraic Geometry Seminar
    (UBC), Differential Graded algebraic geometry. January 22 Th, 330pm, Anca Mustata On Deformation Quantization in algebraic geometry
    http://www.math.ubc.ca/~dmustata/alg-geom.html

    96. The Math Forum - Math Library - Algebraic Geom.
    Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating to algebraic geometry.
    http://mathforum.org/library/topics/algebraic_g/
    Browse and Search the Library
    Home
    Math Topics Geometry : Algebraic Geom.

    Library Home
    Search Full Table of Contents Suggest a Link ... Library Help
    Selected Sites (see also All Sites in this category
  • Algebraic Geometry - Dave Rusin; The Mathematical Atlas
    A short article designed to provide an introduction to algebraic geometry, which combines the algebraic with the geometric for the benefit of both. Thus the recent proof of "Fermat's Last Theorem" - ostensibly a statement in number theory - was proved with geometric tools. Conversely, the geometry of sets defined by equations is studied using quite sophisticated algebraic machinery. This is an enticing area but the important topics are quite deep. This area includes elliptic curves. Applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>>
  • The Algebraic Geometry Notebooks - Aksel Sogstad
    For non-experts. Contents: What is algebraic geometry?; What can algebraic geometry be used for?; Classification of curves in the Weierstrass familiy; Bezout's Theorem; Varieties, orbits and orbit-spaces; Automatic theorem proving using Singular. more>>
    All Sites - 98 items found, showing 1 to 50
  • 97. Ellenberg, Jordan
    Assistant Professor of Mathematics, Department of Mathematics, Princeton University. Subjects arithmetic algebraic geometry, number theory.
    http://www.math.princeton.edu/~ellenber
    Jordan S. Ellenberg
    Assistant Professor of Mathematics 808 Fine Hall
    Department of Mathematics
    Washington Road
    Princeton, NJ 08544 e-mail:
    ellenber@math.princeton.edu I have moved to the University of Wisconsin: please visit my new web page here . This page will no longer be updated. My field is arithmetic algebraic geometry: my specific interests include rational points on varieties, enumeration of number fields and other arithmetic objects, Galois representations attached to varieties and their fundamental groups, non-abelian Iwasawa theory, automorphic forms, Hilbert-Blumenthal abelian varieties, Q -curves, curves of low genus, Serre's conjecture, the ABC conjecture, and Diophantine problems related to all of the above. In Fall 2004, I taught Math 214, "Numbers, Equations, and Proofs." This course uses classical number theory as a vehicle for teaching the concepts and techniques of higher mathematics; it is suitable for both prospective math majors and interested amateurs. I wrote a novel called The Grasshopper King , which came out in 2003 from Coffee House Press Papers and Preprints My CV ( .dvi version or .pdf version Personal Page Teaching Barry Mazur's Mathematical Genealogy ...
    Send me e-mail
    Jordan Ellenberg * ellenber@math.princeton.edu * revised 8 Mar 2005

    98. Magma Workshop On Group Theory And Algebraic Geometry
    Themes. Group theory; Representation theory; Lie theory; algebraic geometry; Arithmetic geometry. Invited Speakers. The following have agreed to speak at
    http://www.maths.warwick.ac.uk/~dfh/magma05.html
    Magma Workshop on Group Theory and Algebraic Geometry
    22-26 August 2005
    A workshop on the Computer Algebra system Magma and its use in group theory and algebraic geometry was held on 22 - 26 August 2005 at the Mathematics Institute University of Warwick , Coventry, UK. This meeting was organized by
    Derek Holt ( dfh@maths.warwick.ac.uk ), Gavin Brown ( gavinb@maths.warwick.ac.uk and John Cannon ( john@maths.usyd.edu.au
    Slides of talks
    Click here to see the slides of some of the talks that took place at the meeting, or here if to see the timetable of talks.
    Description
    Themes
  • Group theory
  • Representation theory
  • Lie theory
  • Algebraic geometry
  • Arithmetic geometry
    Abstracts of talks
    Click on the name for title and abstract of the talk given at the meeting.
  • Jon Carlson (Athens, GA),
  • John Coates (Cambridge),
  • (Queen Mary),
  • John Bray (Queen Mary),
  • Peter Brooksbank (Ohio),
  • Gavin Brown (Warwick/Kent),
  • Nils Bruin (Simon Fraser),
  • John Cremona (Nottingham),
  • Tim Dokchitser (Edinburgh),
  • Bettina Eick (Braunschweig),
  • Tom Fisher (Cambridge),
  • Peter Fleischmann (Canterbury)
  • 99. Shou-Wu Zhang's HomePage
    Columbia University. Arithmetic algebraic geometry.
    http://www.math.columbia.edu/~szhang/
    Shou-Wu Zhang
    Professor of Mathematics
    Department of Mathematics Columbia University 2990 Broadway New York NY USA email: szhang@math.columbia.edu Office: 608 Mathematics Phone: (212)854-6362 Fax: (212)854-8962
    Teaching (Fall, 2005)
    Topics in Arithmetic Algebraic Geom e try Tuesday and Thursday 10:35-11:50 am, Math 507 Ordinary Differential Equations Tuesday and Thursday 1:10-2:25 pm, Math 203 Office hours Tuesday 2:30-3:30 pm and Thursday 3:30-4:30 pm, Math 608
    Seminars (Fall, 2005)
    Joint Number Theory Seminar Thursday, 5-7 pm, Columbia-CUNY-NYU
    Preprints and Publications

    100. Noriko Yui
    Queen's University at Kingston, Ontario, Canada. Arithmetic algebraic geometry.
    http://www.mast.queensu.ca/~yui/
    Noriko Yui
    Ph.D., Rutgers Research group: Algebra and Number Theory E-mail address: yui@ny.mast.queensu.ca
    Research interests
    Arithmetic algebraic geometry

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