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Brigham Young University
Math Department

Math 686R Section 1

Winter 2014

323 TMCB
3:00-3:50 PM MWF

Instructor: Darrin Doud
Office: 282 TMCB
Office Hours: MWF 4:00 or by appointment

January 6, 2014Introduction to Fermat's Last TheoremDr. Doud
January 8, 2014Projective space, ConicsWil
January 10, 2014Rational Parametrization of conics
Proof of FLT4		Joey
January 13, 2014Weierstrass equations of elliptic curves
Invariants of elliptic curves		Kyle
January 15, 2014The group law on an elliptic curveKevin
January 17, 2014Points of finite order
Nagell-Lutz Theorem		Chris
January 22, 2014Elliptic Functions
Weierstrass p function
j(z)		Chris
January 24, 2014Uniformization theorem
Points of finite order on curves over C
Doud's algorithm		Joey
January 27, 2014Galois representations from elliptic curvesDr. Doud
January 29, 2014Infinite Galois theoryKyle
January 31, 2014The cyclotomic character
Frobenius elements in infinite extensions		Kevin
February 3, 2014Extensions of Local FieldsWil
February 5, 2014Projective Limits and Profinite GroupsDr. Doud
February 7, 2014Infinite extensions of Qp and fundamental characters of niveau n  Kyle
February 10, 2014Computing with Galois representationsDr. Doud
February 12, 2014Introduction to modular formsJoey
February 14, 2014Hecke operators, newforms, and oldformsKevin
February 18, 2014L-functions of modular formsChris
February 19, 2014Shimura's constructionDr. Doud
February 21, 2014Invariants of Galois representationsWil
February 24, 2014Serre's conjecture (examples)Joey
February 26, 2014Conductors of Elliptic CurvesWil
February 28, 2014The Birch–Swinnerton-Dyer ConjectureKyle
March 3, 2014Elliptic Curves and Congruent NumbersChris
March 5, 2014Affine group schemesDr. Doud
March 7, 2014Beginnings of deformations of Galois representationsWil
March 10, 2014More deformations of Galois representationsKevin
March 12, 2014Tangent spacesChris
March 14, 2014Construction of deformation rings of Galois representationsKyle
March 17, 2014Explicit deformations of Galois representations (Boston)Kevin
March 19, 2014Explicit deformations of Galois representations (Boston)Joey
March 21, 2014Explicit deformations of Galois representations (Boston)Dr. Doud
March 24, 2014Hecke Algebras and Galois representations (section 1, 1-4)Kyle
March 26, 2014Hecke Algebras and Galois representations (section 1, 5-8)Kevin
March 28, 2014Hecke Algebras and Galois representations (section 2)Wil
March 31, 2014Hecke Algebras and Galois representations (section 3)Chris
April 2, 2014The proof of Fermat's last theorem (Part I)Joey
April 4, 2014The proof of Fermat's last theorem (Part 2)Joey
April 7, 2014Computing congruent numbersChris
April 9, 2014Solving A4+B4+C4=D4Kyle
April 11, 2014TBAKevin
April 13, 2014Extended Modularity ConjecturesWil

Maintained by Darrin Doud.

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