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Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometry, Fall 2008
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In this undergraduate level seminar series topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Kleiman, Steven
Date Added:
01/01/2008
Seminar in Geometry, Fall 2004
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Seminar for mathematics majors. Students present and discuss the subject matter, taken from current journals or books and write up exercises. Topic for spring 2003: Elementary topological properties of differentiable manifolds. Topics covered include Sard's theorem, the Thom transversality theorem, vector fields and the Poincare-Hopf theorem, and cohomolgy via differential forms. Prerequisites subject to negotiation with the instructor. Instruction and practice in oral communication provided. In this course, students take turns in giving lectures. For the most part, the lectures are based on Robert Osserman's classic book A Survey of Minimal Surfaces, Dover Phoenix Editions. New York: Dover Publications, May 1, 2002. ISBN: 0486495140.

Subject:
Education
Geometry
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Carberry, Emma
Carberry, Emma Elizabeth, 1974-
Date Added:
01/01/2004
Topics in Algebraic Geometry: Algebraic Surfaces, Spring 2008
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The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Kumar, Abhinav
Date Added:
01/01/2008
Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces, Spring 2006
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CC BY-NC-SA
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Topics vary from year to year. Fall Term: Numerical properties and vanish theorems for ample, nef, and big line bundles and vector bundles; multiplier ideals and their applications

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Coskun, Izzet
Date Added:
01/01/2006
Topics in Geometry, Fall 2006
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CC BY-NC-SA
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This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin. Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry. For this reason, the latter is intimately related to the ideas of mirror symmetry.

Subject:
Geometry
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Gualtieri, Marco
Date Added:
01/01/2006
Topics in Geometry: Mirror Symmetry, Spring 2009
Conditional Remix & Share Permitted
CC BY-NC-SA
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" This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed to formulate various mathematical versions of mirror symmetry will be introduced along the way, in variable levels of detail and rigor."

Subject:
Geometry
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Auroux, Denis
Date Added:
01/01/2009