# 581g: List of Lectures

(28 lectures)

- The main objects of this course: torsion points, Galois representations, modular forms, and Hecke operators
- Modularity of elliptic curves and Serre's conjecture
- Modular forms of level 1
- Hecke operators on modular forms of level 1
- Duality and eigenforms of level 1
- Integrality (level 1)
- Modular curves (analytic definition)
- Cusp forms, modular curves, and Eichler Shimura
- Modular symbols (part 1)
- Modular symbols (part 2)
- Modular symbols (part 3)
- Modular forms of higher level
- Atkin-Lehner theory (part 1)
- Atkin-Lehner theory (part 2)
- Field of definition of modular curves (part 1)
- Field of definition of modular curves (part 2)
- Hecke operators as correspondences (part 1)
- Hecke operators as correspondences (part 2)
- The Eichler-Shimura relation
- Abelian varieties (part 1)
- Abelian varieties (part 2)
- Neron models
- Abelian varieties attached to modular forms (part 1)
- Abelian varieties attached to modular forms (part 2)
- L-functions attached to modular forms
- The Birch and Swinnerton-Dyer conjecture: rank conjecture
- The Birch and Swinnerton-Dyer conjecture: leading coefficient
- Survey of results toward the conjecture