Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces

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