Calendar

Lec # Topics
1 Introduction to Moduli Spaces
2 Introduction to Grassmannians
3 Enumerative Geometry using Grassmannians, Pieri and Giambelli
4 Littlewood - Richardson Rules and Mondrian Tableaux
5 Introduction to Hilbert Schemes
6 The Construction of Hilbert Schemes and First Examples
7 Enumerative Geometry using Hilbert Schemes: Conics in Projective Space
8 Local Properties of Hilbert Schemes: Mumford’s Example
9 An Introduction to G.I.T.
10 The Hilbert-Mumford Criterion and Examples of G.I.T. Quotients
11 The Construction of the Moduli Space of Curves I
12 The Construction of the Moduli Space of Curves II
13 The Cohomology of the Moduli Space of Curves: Harer’s Theorems
14 The Euler Characteristic of the Moduli Space
15 Keel’s Thesis
16 The Second Cohomology of the Moduli Space
17 The Picard Group of the Moduli Functor
18 Divisors on the Moduli Space
19 Brill-Noether Theory and Divisors of Small Slope
20 The Moduli Space of Curves is of General Type when g > 23
21 An Introduction to the Kontsevich Moduli Space
22 Enumerative Geometry and Gromov-Witten Invariants
23 The Picard Group of the Kontsevich Moduli Space
24 Vakil’s Algorithm for Counting Rational Curves in Projective Space
25 The Ample and Effective Cones of the Kontsevich Moduli Space

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Spring 2006
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