581g: List of Lectures

(28 lectures)

1. The main objects of this course: torsion points, Galois representations, modular forms, and Hecke operators
2. Modularity of elliptic curves and Serre's conjecture
3. Modular forms of level 1
4. Hecke operators on modular forms of level 1
5. Duality and eigenforms of level 1
6. Integrality (level 1)
7. Modular curves (analytic definition)
8. Cusp forms, modular curves, and Eichler Shimura
9. Modular symbols (part 1)
10. Modular symbols (part 2)
11. Modular symbols (part 3)
12. Modular forms of higher level
13. Atkin-Lehner theory (part 1)
14. Atkin-Lehner theory (part 2)
15. Field of definition of modular curves (part 1)
16. Field of definition of modular curves (part 2)
17. Hecke operators as correspondences (part 1)
18. Hecke operators as correspondences (part 2)
19. The Eichler-Shimura relation
20. Abelian varieties (part 1)
21. Abelian varieties (part 2)
22. Neron models
23. Abelian varieties attached to modular forms (part 1)
24. Abelian varieties attached to modular forms (part 2)
25. L-functions attached to modular forms
26. The Birch and Swinnerton-Dyer conjecture: rank conjecture
27. The Birch and Swinnerton-Dyer conjecture: leading coefficient
28. Survey of results toward the conjecture