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         Algebraic Geometry:     more books (100)
  1. Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne, 2010-11-02
  2. Elementary Algebraic Geometry (Student Mathematical Library, Vol. 20) (Student Mathematical Library, V. 20) by Klaus Hulek, 2003-02-13
  3. Basic Algebraic Geometry 1: Varieties in Projective Space by Igor R. Shafarevich, 1994-08-08
  4. Lie Algebras and Algebraic Groups (Springer Monographs in Mathematics) by Patrice Tauvel, Rupert W. T. Yu, 2010-11-30
  5. Introduction to Algebraic Geometry by Brendan Hassett, 2007-05-21
  6. Using Algebraic Geometry (Graduate Texts in Mathematics) by David A. Cox, John Little, et all 2005-03-17
  7. Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics, 6) by Qing Liu, 2002-07-18
  8. Fourier-Mukai Transforms in Algebraic Geometry (Oxford Mathematical Monographs) by Daniel Huybrechts, 2006-06-29
  9. Computational Methods in Commutative Algebra and Algebraic Geometry (Algorithms and Computation in Mathematics) by Wolmer Vasconcelos, 2004-07-12
  10. Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics) (v. 1) by Claire Voisin, 2008-02-04
  11. An Invitation to Algebraic Geometry (Universitext) by Karen E. Smith, Lauri Kahanpää, et all 2010-11-02
  12. Real Algebraic Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics) by Jacek Bochnak, Michel Coste, et all 2010-11-02
  13. Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series (Ergebnisse der Mathematik Und Ihrer Grenzgebiete) (Volume 0) by R.K. Lazarsfeld, 2004-08-24
  14. Complex Analysis and Algebraic Geometry: A Collection of Papers Dedicated to K. Kodaira

1. Algebraic Geometry - Wikipedia, The Free Encyclopedia
algebraic geometry is a branch of mathematics which, as the name suggests, combines techniques of abstract algebra, especially commutative algebra,
http://en.wikipedia.org/wiki/Algebraic_geometry
Algebraic geometry
From Wikipedia, the free encyclopedia
Jump to: navigation search Algebraic geometry is a branch of mathematics which, as the name suggests, combines techniques of abstract algebra , especially commutative algebra , with the language and the problematics of geometry . It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis topology and number theory . Initially a study of polynomial equations in many variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations, as to find some solution; this does lead into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique. The fundamental objects of study in algebraic geometry are algebraic varieties , geometric manifestations of solutions of systems of polynomial equations Plane algebraic curves , which include lines circles parabolas lemniscates , and Cassini ovals , form one of the best studied classes of algebraic varieties. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve relative position of different curves and relations between the curves given by different equations.

2. Algebraic Geometry -- From Wolfram MathWorld
algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of
http://mathworld.wolfram.com/AlgebraicGeometry.html
Algebra
Applied Mathematics

Calculus and Analysis

Discrete Mathematics
...
Less...

Algebraic Geometry Algebraic geometry is the study of geometries that come from algebra, in particular, from rings . In classical algebraic geometry , the algebra is the ring of polynomials , and the geometry is the set of zeros of polynomials, called an algebraic variety . For instance, the unit circle is the set of zeros of and is an algebraic variety , as are all of the conic sections In the twentieth century, it was discovered that the basic ideas of classical algebraic geometry can be applied to any commutative ring with a unit, such as the integers . The geometry of such a ring is determined by its algebraic structure, in particular its prime ideals . Grothendieck defined schemes as the basic geometric objects, which have the same relationship to the geometry of a ring as a manifold to a coordinate chart . The language of category theory evolved at around the same time, largely in response to the needs of the increasing abstraction in algebraic geometry. As a consequence, algebraic geometry became very useful in other areas of mathematics, most notably in

3. Algebraic Geometry
algebraic geometry. pdf (for printing on letter paper 11x8.5 in) pdf (for printing on a4 paper 29.7x21 cm) The page numbering etc. for the two files is
http://www.jmilne.org/math/CourseNotes/math631.html
Algebraic Geometry
pdf (for printing on letter paper 11x8.5 in)
pdf (for printing on a4 paper 29.7x21 cm)

The page numbering etc. for the two files is identical. v2.01 (August 24, 1996). First version on the web.
v3.01 (June 13, 1998). Added 5 sections (25 pages) and an index. Minor changes to Sections 0-8. 157pp.
v4.00 (October 30, 2003). Fixed errors; many minor revisions; added exercises; added two sections; 206 pages.
v5.00 (February 20, 2005). Heavily revised; most numbering changed; 227 pages.
Contents
  • Preliminaries
  • Algebraic sets Affine algebraic varieties Algebaic varieties Local study Projective varieties Complete varieties Finite maps Dimension theory Regular maps and their fibres Algebraic spaces: geometry over an arbitrary field Divisors and intersection theory Coherent sheaves; invertible sheaves Differentials (Outline) Algebraic varieties over the complex numbers (Outline) Descent Theory Lefschetz Pencils (Outline)
  • Solutions to the Exercises
    Annotated Bibliography
    Index Errata

    4. Algebraic Geometry
    Some information about algebraic geometry and geometers.
    http://www.math.byu.edu/~jarvis/alg-geom.html
    Search BYU
    Algebraic Geometry
    Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate. David Mumford
    Sources for preprints and other electronic texts
    Lecture notes and videos
    • MSRI lectures High quality streaming video of many lectures on a wide range of mathematical topics. PDF slides and notes also available.

    5. Front: Math.AG Algebraic Geometry
    arXiv0801.2834 Relative Proportionality for subvarieties of moduli spaces of K3 and abelian surfaces. S. MüllerStach, E. Viehweg, K. Zuo. math.AG.
    http://front.math.ucdavis.edu/math.AG
    Front for the arXiv Fri, 14 Mar 2008
    Front
    math AG search register submit
    journals
    ... iFAQ math.AG Algebraic Geometry Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 14 Mar arXiv:0803.2026 Geometry of obstructed equisingular families of projective hypersurfaces. Anna Gourevitch , Dmitry Gourevitch math.AG 14 Mar arXiv:0803.1996 Rational points on homogeneous varieties and Equidistribution of Adelic periods. Alex Gorodnik , Hee Oh (with appendix by Mikhail Borovoi). math.AG math.NT 13 Mar arXiv:0803.1825 On the algebraic geometry of polynomial dynamical systems. Abdul S. Jarrah , Reinhard Laubenbacher math.AG math.AC 13 Mar arXiv:0803.1756 Equisingularity of families of hypersurfaces and applications to mappings. Kevin Houston math.AG math.CV 13 Mar arXiv:0803.1743 Poincare series of filtrations corresponding to ideals on surfaces. A. Campillo (Valladolid University, Spain), F. Delgado (Valladolid University, Spain), S. M. Gusein-Zade (Moscow State University, Russia). math.AG

    6. Algebraic Geometry Authors/titles Recent Submissions
    Subjects algebraic geometry (math.AG); Representation Theory (math.RT) AG/0509587 with a not poor exposition and no essential material added.
    http://arxiv.org/list/math.AG/recent
    arXiv.org math math.AG
    Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages
    Algebraic Geometry
    Authors and titles for recent submissions
    [ total of 28 entries:
    [ showing 25 entries per page: fewer more all
    Fri, 14 Mar 2008
    arXiv:0803.2026 ps pdf other
    Title: Geometry of obstructed equisingular families of projective hypersurfaces Authors: Anna Gourevitch Dmitry Gourevitch Comments: 26 pages Subjects: Algebraic Geometry (math.AG)
    arXiv:0803.1996 ps pdf other
    Title: Rational points on homogeneous varieties and Equidistribution of Adelic periods Authors: Alex Gorodnik Hee Oh (with appendix by Mikhail Borovoi) Comments: 58 pages, and 27 pages of appendix Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)
    arXiv:0803.1950 (cross-list from math.CV) [ ps pdf other
    Title: Capacities and weighted volumes of line bundles Authors: Robert Berman Sebastien Boucksom Comments: 57 pages, 1 figure Subjects: Complex Variables (math.CV) ; Algebraic Geometry (math.AG); Number Theory (math.NT)

    7. Algebraic Geometry
    For doing calculations in algebraic geometry and commutative algebra, Grayson and Stillman s Macaulay2 program is more powerful than Maple or Mathematica.
    http://www.math.purdue.edu/~dvb/algeom.html
    Introduction to Algebraic Geometry
    Math 665, spring 06 Donu Arapura Blow up
  • Examples
  • Geometry of 2x2 nilpotent matrices
  • Blowing up a cusp ...
  • Books
    Examples
    In order to get a feeling for what algebraic geometry is, let's to go through some simple examples.
    Geometry of 2x2 nilpotent matrices
    Consider the space of 2x2 matrices over a field k with trace 0. These can be parameterized by 3-tuples (x,y,z) where x, y and z appear in the 11, 12, and 21 positions; therefore this can be identified with three dimensional affine space A . In these coordinates the determinant det(x,y,z) = -x -yz. The determinant is an regular map A A . The fibers X t =det are algebraic subsets of A . These are in fact varieties since the polynomials -x -yz-t are irreducible for each t in k. Let's study the geometry of these sets. Suppose k= C , then I claim that X t is isomorphic to X whenever t is nonzero. To see this, choose a such that a isomorphism between X and X t ; this can be checked by comparing coordinate rings. ( This works even if C is replaced by an algebraically closed field. But it fails in general. For example when k =
  • 8. PlanetMath: Algebraic Geometry
    algebraic geometry is the study of algebraic objects using geometrical tools. By algebraic objects, we mean objects such as the collection of solutions to a
    http://planetmath.org/encyclopedia/AlgebraicGeometry.html
    (more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia
    Papers

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    talkback Polls
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    Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About algebraic geometry (Topic)
    Introduction
    Algebraic geometry is the study of algebraic objects using geometrical tools. By algebraic objects, we mean objects such as the collection of solutions to a list of polynomial equations in some ring . Of course, if the ring is the complex numbers , we can apply the highly succesful theories of complex analysis and complex manifolds to address the problems; many powerful tools are available; de Rham cohomology singular homology Hodge theory spectral sequences and many others. We also have at our disposal all the tools of real differential geometry partitions of unity curvature ... tangent spaces , as well as all the tools of point-set topology . However, if one wishes to use a different ring, perhaps the

    9. Mathematical Sciences Research Institute - Algebraic Geometry
    algebraic geometry has long been a central subject, with deep and substantial connections to almost every aspect of modern mathematics.
    http://www.msri.org/calendar/programs/ProgramInfo/251/show_program
    SITE MAP SEARCH SHORTCUT:
    Choose a Destination... Calendar Programs Workshops Summer Grad Workshops Seminars Events/Announcements Application Materials Visa Information Propose a Program Propose a Workshop Policy on Diversity MSRI Alumni Archimedes Society Why Give to MSRI Ways to Give to MSRI Donate to MSRI Planned Gifts FAQ Staff Member Directory Contact Us Directions For Visitors Pictures Library Computing SGP Streaming Video / VMath MSRI in the Media Emissary Newsletter Outlook Newsletter Subscribe to Newsletters Books, Preprints, etc. Federal Support Corporate Affiliates Sponsoring Publishers Foundation Support Academic Sponsors
    HOME
    ACTIVITIES CORP AFFILIATES ABOUT COMMUNICATIONS Calendar ... Events/Announcements
    Algebraic Geometry
    January 12, 2009 to May 22, 2009 Mathematical Sciences Research Institute, Berkeley, CA. Organized By: William Fulton, Joe Harris, Brendan Hassett, János Kollár, Sándor Kovács, Robert Lazarsfeld, Ravi Vakil Algebraic geometry has long been a central subject, with deep and substantial connections to almost every aspect of modern mathematics. There are numerous different approaches to the field, utilizing widely varying technical tools: Commutative algebra, complex analysis, sheaf theory, cohomological methods, and combinatorial techniques all play important roles.
    This multiplicity of techniques and interconnections creates a conundrum for the student of algebraic geometry: How can I learn all the specific tools of the trade, while at the same time developing an overall sense for what guides the subject? Even established researchers can feel powerful centrifugal forces pulling at the field, as it spawns new specialties with astonishing regularity.

    10. 14: Algebraic Geometry
    algebraic geometry combines the algebraic with the geometric for the benefit of both. Thus the recent proof of Fermat s Last Theorem ostensibly a
    http://www.math.niu.edu/~rusin/known-math/index/14-XX.html
    Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields
    POINTERS: Texts Software Web links Selected topics here
    14: Algebraic geometry
    Introduction
    Algebraic geometry 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.
    History
    Applications and related fields
    • geometry (in particular for conics and curves),
    • algebra (since algebraic geometry is commutative ring theory...)
    • number theory (especially for Diophantine analysis).
    Subfields
    • Foundations
    • Local theory, see also 32SXX
    • Cycles and subschemes
    • Families, fibrations
    • Birational geometry [Mappings and correspondences]
    • (Co)homology theory, see also 13DXX
    • Arithmetic problems. Diophantine geometry, see also 11DXX, 11GXX
    • 14H: Curves
    • 14J: Surfaces and higher-dimensional varieties . For analytic theory, see 32JXX

    11. ALGEBRAIC GEOMETRY
    This is a graduatelevel text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all
    http://www.worldscibooks.com/mathematics/3873.html
    Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Bookshop New Titles Editor's Choice Bestsellers Book Series ... Join Our Mailing List ALGEBRAIC GEOMETRY
    by Daniel Bump (Stanford University)
    This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used. A taste of the deeper theory is given: some topics, such as local algebra and ramification theory, are treated in depth. The book culminates with a selection of topics from the theory of algebraic curves, including the Riemann–Roch theorem, elliptic curves, the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.
    Contents:
    • Affine Algebraic Sets and Varieties
    • The Extension Theorem
    • Maps of Affine Varieties
    • Dimensions and Products
    • Local Algebra
    • Properties of Affine Varieties
    • Varieties
    • Complete Nonsingular Curves
    • Ramification
    • Completions
    • Differentials and Residues
    • The Riemann–Roch Theorem
    • Elliptic Curves and Abelian Varieties
    • The Zeta Function of a Curve

    Readership: Graduate students in mathematics.

    12. The Math Forum - Math Library - Algebraic Geom.
    A short article designed to provide an introduction to algebraic geometry, which combines the algebraic with the geometric for the benefit of both.
    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 - 100 items found, showing 1 to 50
  • 13. Mathematical Sciences Research Institute - Algebraic Geometry
    In Spring 2009, MSRI will hold a special jumbo halfyear program on algebraic geometry. Jumbo in this context means that this algebraic geometry program
    http://www.math.washington.edu/~msri2009/
    MSRI PROGRAM in ALGEBRAIC GEOMETRY in 2009
    In Spring 2009, MSRI will hold a special jumbo half-year program on Algebraic Geometry. "Jumbo" in this context means that this Algebraic Geometry program will be the only program at MSRI during that time as opposed to the usual sharing between two different programs. It will be twice the size of usual programs. The application deadlines have passed. Research Memberships and Postdoctoral Fellowships are being announced by MSRI.
    Current Workshop Schedule
    Connections: Algebraic Geometry and Related Fields January 22, 2009 to January 24, 2009 Organized By: Angela Gibney (U. Pennsylvania), Brendan Hassett (Rice U.), Sándor Kovács (U. Washington), Diane Maclagan (Warwick U.), Jessica Sidman (Mt. Holyoke), and Ravi Vakil (Stanford U.) Classical Algebraic Geometry January 26, 2009 to January 30, 2009 Modern Moduli Theory February 23, 2009 to February 27, 2009 Organized By: Izzet Coskun (U. Illinois - Chicago), Sheldon Katz (U. Illinois), Alina Marian (U. Illinois - Chicago), Rahul Pandharipande (Princeton U.), Richard Thomas (Imperial College), Hsian-Hua Tseng (U. Wisconsin), Ravi Vakil (Stanford U.) Combinatorial, Enumerative and Toric Geometry

    14. Journal Of Algebraic Geometry Online
    Tables of contents, abstracts and references from vol.11 (2002). Full text to subscribers (TeX, DVI, PDF, PS).
    http://www.ams.org/jag/
    • Journals Home
    • Search
    • Author Info
    • Subscribe ... All issues Authors Author Packages Initial Submissions Where to send files for accepted papers Manuscript tracking About Editorial Board Subscription
      Information Subscribe from the AMS Bookstore License agreement The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles posted individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website. Subscriptions: Subscriptions to this journal can be obtained through the AMS Bookstore . Subscriptions and orders can also be addressed to the American Mathematical Society, P.O. Box 845904, Boston, MA 02284-5904. All orders must be accompanied by payment. A signed license agreement is required prior to electronic access activation.

    15. Introduction To Algebraic Geometry
    The description in the course guide Introduces the basic notions and techniques of modern algebraic geometry. Algebraic sets, Hilbert s Nullstellensatz
    http://math.stanford.edu/~vakil/725/course.html
    18.725: Introduction to Algebraic Geometry
    The description in the course guide: "Introduces the basic notions and techniques of modern algebraic geometry. Algebraic sets, Hilbert's Nullstellensatz and varieties over algebraically closed fields. We relate varieties over the complex numbers to complex analytic manifolds. For varieties of dimension one (i.e. curves) we discuss the genus, divisors, linear series, line bundles and the Riemann-Roch theorem." Johan de Jong will be teaching the follow-up course in the spring. The class is in Here are various notes in dvi, ps, and pdf formats. (If you would like tar archives, just let me know; due to limited diskspace, I had to remove them from this page.) I've added all the corrections I've found (or been told about) on Dec. 30, 1999, so they are in as final form as they'll ever be.
    • On the first day (Sept. 9), I gave out two handouts, one with information about the course ( dvi ps , or pdf ), and one with fun problems in algebraic geometry to pique your interest ( dvi ps , or pdf
      Here's a rather detailed summary of the first lecture ( dvi ps , or pdf
    • On the second day (Sept. 14), I gave out the first problem set (

    16. Algebraic Geometry
    algebraic geometry is a subject with historical roots in analytic geometry. At its most naive level it is concerned with the geometry of the solutions of a
    http://www.math.tamu.edu/~Peter.Stiller/agpage.html
    Algebraic Geometry
    What is Algebraic Geometry?
    Research Interests:
    For a list of related publications, click here Return to TAMU Math
    Return to Dr. Stiller's home page

    17. Seattle'05
    Three oneweek sessions Interactions with physics; Classical geometry; Arithmetic geometry. University of Washington, Seattle, WA, USA; 25 July 12
    http://www.math.princeton.edu/~rahulp/seattle05.html
    Summer Institute in Algebraic Geometry
    July 25 - August 12, 2005

  • Program: Plenary / Full AMS information brochure Participant list Graduate student workshop

  • The American Mathematical Society, the Clay Mathematics Institute, and the National Science Foundation will sponsor a three week Summer Institute in Algebraic Geometry at the University of Washington, Seattle from July 25 to August 12, 2005. The goals of the Institute are to review the major achievements of the past decade and to look forward to future developments. The focus will be structured by week:
    Interactions with physics Classical geometry Arithmetic geometry

    Plenary lecture series aimed at broad audiences will be scheduled in the morning. More specialized seminar sessions will take place in the afternoon.
    Financial support, as always, will be limited. Participants are encouraged to seek travel funds from their home institutions or funding agencies.
    The organizing committee

    18. IMA Thematic Year On Applications Of Algebraic Geometry, September 2006 - June 2
    algebraic geometry has a long and distinguished presence in the history of mathematics that produced both powerful and elegant theorems.
    http://www.ima.umn.edu/2006-2007/
    IMA home Contact IMA What's inside
    IMA Participating Orgs
    IMA Thematic Year on
    Applications of Algebraic Geometry
    September 2006 - June 2007 Poster Request Form JPEG low resolution medium resolution high resolution PDF full resolution (128 MB) 2006-2007 Annual Report: pdf Questions? Contact us at domain='ima.umn.edu'; document.write('staff@'); document.write('ima.umn.edu'); staff(at)ima.umn.edu Long Term Visitors Events Participants 2006-2007 Postdoctoral Fellows Algebraic Geometry and Applications Seminar ... Weekly Tutorial: Real Algebraic Geometry Quick Links to Events Tutorial: Algebraic geometric methods in engineering Workshop: Algorithms in algebraic geometry "Hot topics" workshop: Negative index materials Workshop: Software for algebraic geometry Public lecture: Margaret H. Wright How hard can it be? Special workshop: Blackwell-Tapia conference Math is Cool! and Who Wants to Be a Mathematician? "Hot topics" workshop: The evolution of mathematical communication in the age of digital libraries Tutorial: Algebraic algorithms in optimization Workshop: Optimization and control Public Lecture: Christopher J. Budd

    19. School Of Mathematics - New Connections Of Representation Theory To Algebraic Ge
    During the 200708 academic year, Roman Bezrukavnikov of MIT will lead a special program on algebraic geometry and physics in representation theory.
    http://www.math.ias.edu/pages/activities/special-programs/new-connections-of-rep
    • Home Activities
      • Special Programs
        New Connections of Representation Theory to Algebraic Geometry and Physics
        (2007-2008 Academic Year)
        During the 2007-08 academic year, Roman Bezrukavnikov of MIT will lead a special program on algebraic geometry and physics in representation theory. The focus of the year will be on related recent developments in representation theory, algebraic geometry and physics.
        The first conference, "Gauge Theory and Representation Theory", will be held during the week of November 26-30, 2007.
        The second conference, "Algebro-Geometric Derived Categories and Applications", will be held during term II from March 10-14, 2008.
        "For both conferences there will be financial support available for the participation of students, minorities, women and postdoctoral scholars.  Closer to the date of the conference, please refer to the conference website for information about how to apply for financial support."
        In the first term the emphasis will be on mathematics connected to quantum field theory, in particular the new differential geometric approach to the geometric Langlands program. A part of the second term will be devoted to absorbing the emerging new homotopy foundations of algebraic geometry, with a view towards applications.
        One common feature of recent trends is “categorification”, often synonymous with “geometrization”. Categorification stands for the passage from a traditional mathematical object to its higher categorical analogue, and, more loosely, for the emphasis on categories instead of particular objects. The categories involved are typically of geometric nature (categories of sheaves of certain kind) and are constructed in a homological framework, i.e., they are triangulated categories, or refinements of these. Examples in representation theory include geometric Langlands duality (a categorification of the theory of automorphic forms); character sheaves (a categorification of representation theory of finite Chevalley groups); localization techniques for modular representations; Nakajima’s geometric construction of Kac-Moody Lie algebra representations etc. However, there are many examples in other fields which are relevant for representation theory: categories of

    20. MIT OpenCourseWare | Mathematics | 18.725 Algebraic Geometry, Fall 2003 | Lectur
    Back to algebraic geometry. 6, Review of things not covered enough (Topics Fibers, Morphisms of Sheaves) (PDF) Back to Work Morphisms Varieties
    http://ocw.mit.edu/OcwWeb/Mathematics/18-725Fall2003/LectureNotes/
    • Home Courses Donate About OCW ... Mathematics Algebraic Geometry
      Lecture Notes
      The lecture notes are courtesy Moses Liskov, a student in the class. Used with permission.
      LEC # TOPICS Introduction ( PDF
      First Goal Recap of Last Time ( PDF
      Irreducible Components
      Projective Space Projective Space (cont.) ( PDF Projective Space (cont.) ( PDF
      Topological Diversion
      Sheaves Presheaves ( PDF
      Back to Algebraic Geometry Review of things not covered enough (Topics: Fibers, Morphisms of Sheaves) ( PDF
      Back to Work
      Morphisms
      Varieties Homework Review ( PDF Back to Varieties Projective Varieties ( PDF A Review on Projective Varieties ( PDF Product of Varieties Applications ( PDF Recap on the Applications ( PDF Next Definition of Variety Dimension Homework 5 Problem ( PDF Dimension Future Applications Back to Dimension ( PDF Krull Dimension Fibers of Morphisms ( PDF Fiber Products ( PDF Back to the Theorem Complete Varities Completeness ( PDF Complex Topology Chow's Lemma ( PDF Analytic Spaces Curves ( PDF What is Next? (

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