Math 252: Modular Abelian Varieties

		Almost Complete Notes in Book Form: all
DATE	n	TITLE (future lecture titles subject to change)
Monday, Sep 15	1	Overview of Course
Wednesday, Sep 17	2	SL₂(Z) is generated by S and T
Friday, Sep 19	3	Congruence subgroups
Monday, Sep 22	4	Modular curves
Wednesday, Sep 24	5	Points on modular curves
Friday, Sep 26	6	More about points and genus formulas; Modular symbols
Monday, Sep 29	7	Modular symbols I
Wednesday, October 1	8	Modular symbols II (improved version of notes from Monday)
Friday, October 3	9	Hecke Operators, Modular Symbols and L-functions
Monday, October 6	10	Complex Tori
Wednesday, October 8	11	Hermitian Forms
Friday, October 10	12	Divisors, Neron-Severi, Polarizations and the Dual Abelian Variety
Monday, October 13		(Columbus Day)
Wednesday, October 15	13	Jacobians
Friday, October 17	14	Jacobians and Néron Models
Monday, October 20	15	Néron Models II
Wednesday, October 22	16	Modular Forms of Level 1
Friday, October 24	17	Modular Forms of Level 1: Hecke operators
Monday, October 27	18	Modular Forms of Level 1: Part 3 -- Some Conjectures
Wednesday, October 29	19	Modular Forms of Higher Level: Part 1
Friday, October 31	20	Modular Forms of Higher Level: Part 2
Monday, Nov 3	21	Hecke Operators as Correspondences
Wednesday, Nov 5		Grigor Grigorov: p-adic L-functions of elliptic curves: Part 1
Friday, Nov 7		Grigor Grigorov: p-adic L-functions of elliptic curves: Part 2
Monday, Nov 10	22	Newforms and Atkin-Lehner Theory
Wednesday, Nov 12	23	Structure of the Hecke Algebra
Friday, Nov 14	24	Attaching an abelian variety A_fto a modular form (see also Brian Conrad's appendix on the Shimura construction in weight 2)
Monday, Nov 17	25	Abelian varieties attached to modular forms, part II
Wednesday, Nov 19	26	The Eichler-Shimura Relation
Friday, Nov 21		Guest lecture by Barry Mazur: The U_p operator
Monday, Nov 24	27	Modularity Theorems and Conjectures
Wednesday, Nov 26	28	L-functions attached to modular forms: Hecke's Theorem
Monday, Dec 1	29	Introduction to the Birch and Swinnerton-Dyer Conjecture
Wednesday, Dec 3	30	The Refined BSD Conjecture
Friday, Dec 5	31	Intrinsic Definition of L(A,s), Shafarevich-Tate groups and Visibility
Monday, Dec 8	32	Shafarevich-Tate groups and Visibility
Wednesday, Dec 10	33	??
Friday, Dec 12	34	??
Monday, Dec 15	35	??