Week 1

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Monday, March 30

Elliptic curve factorization method

Wednesday, April 1

Victor Miller: The Weil Pairing I

Friday, April 3

Victor Miller: The Weil Pairing II

Week 2

Monday, April 6

Bill Hart: Toom-7

Wednesday, April 8

Bill Hart: Toom-7, part 2

Friday, April 10

Quadratic Sieve (Bill Hart): 20090410.sws, 20090410.pdf

Week 3

Monday, April 13

Quadratic Sieve Lecture 2 (Bill Hart): 20090413.sws

Wednesday, April 15

Quadratic Sieve Lecture 3 (Bill Hart): 20090415.sws

Friday, April 17

Quadratic Sieve Lecture 4; start of Number Field Sieve (Bill Hart): 20090417.sws

Week 4

Monday, April 20

Number Field Sieve Lecture 1 (Bill Hart) 20090420.sws

Wednesday, April 22

Number Field Sieve Lecture 2(Bill Hart) 20090422.sws

Friday, April 24

Computing Isogenies Between Elliptic Curve (Francois Morain)

Week 5

Monday, April 27

Number Field Sieve Lecture 3 (Bill Hart) 20090427.sws

Wednesday, April 29

Modular abelain varieties and BSD 1; factoring projects due

Friday, May 1

Modular abelain varieties and BSD 2

Week 6

Monday, May 4

Modular forms, modular curves, and Hecke operators

Wednesday, May 6

Bounding torsion on modular abelian varieties

Friday, May 8

Computing Tamagawa numbers of modular abelian varieties

Week 7

Monday, May 11

Modular Symbols

Wednesday, May 13

Manin Symbols

Friday, May 15

Cuspidal and Boundary Modular Symbols; basis of modular forms

Week 8

Monday, May 18

Computing newforms

Wednesday, May 20

Explicit Modular Abelian Varieties: 1

Friday, May 22

Explicit Modular Abelian Varieties: 2

Week 9

Monday, May 25

No class -- memorial day

Wednesday, May 27

Computing the Endomorphism Ring

Friday, May 29

The Isogeny Class of a Modular Abelian Varieties 20090529-ssmod-example.sws

Week 10

Monday, June 1

Supersingular Graph Method

Wednesday, June 3

Brandt Modules (Quaternion Algebras) 1

Friday, June 5

Brandt Modules (Quaternion Algebras) 2