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 |

## Calendar

## Course Info

##### Learning Resource Types

*notes*Lecture Notes