18.786 - Galois Representations (Spring 2014)

 

Instructor: Sug Woo Shin

Grader: John Binder (binderj@math)

Office: Room E18-426

Time/Place for class: TR 9:30-11, Room E17-133

Office Hours: F 3-4 or by appointment

Email: swshin [at] math . xxx .edu (you know what xxx is)


COURSE DESCRIPTION

The goal of this course is to understand how to prove the automorphy of Galos representations, as initiated by Wiles and substantially developed by many others, mainly in the two dimensional case perhaps under some simplifying hypotheses. Along the way I hope to get to some details in Wiles's proof of Fermat's Last Theorem (as a consequence of his work on the Shimura-Taniyama-Weil conjecture that ``every elliptic curve over $\Q$ is modular'', which can be rephrased as the automorphy of certain Galois representations). There is little overlap with what used to be taught in the old 18.786 before the recent revision of the catalogue.

Prerequisites: Basic knowledge of algebraic number theory and commutative algebra. Familiarity with elliptic curves, modular forms, and class field theory would be helpful but not strictly required. (See syllabus for suggestion on background reading.)

Text Book: There is no textbook but see syllabus for main references.


UPDATE

[05.01.2014] Note that Tue May 6 is a class holiday.

[04.29.2014] Problem set 10 is now available. (Due Thu May 8)

Recall: Grad students who passed the quals are granted exemption.