Math 602D   Fall 2009

Topics in Geometry

Moduli Spaces

Time: MWF   13:00 - 14:00  

Place:   MATH 102  

Instructor: K. Behrend

Office hour: Tuesdays 15:00 - 16:00

Prerequisites:
The prerequisite is Math 532 (Algebraic Geometry I), or equivalent. If you have not taken Algebraic Topology before, you should take it concurrently.

Course Content:
This will be an introduction to moduli spaces. We focus on the moduli space of sheaves on a projective variety. We follow a new approach based on differential graded Lie algebras. Along the way we learn a few important techniques in algebraic geometry, for example Geometric invariant theory. Moduli spaces of sheaves lie at the foundation of Donaldson-Thomas theory, a new field, which is the focus of much recent research in algebraic geometry.

Topics covered include: Sheaves on projective varieties, Hilbert polynomials, Quivers and their representations, Differential graded Lie algebras, Geometric invariant theory, Stability, Moduli spaces, Donaldson-Thomas invariants.

Homework:

There will be occasional homework assignments. Your mark will be based on these.

Course Materials:

To be posted as warranted.

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