| 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 |