Meeting Times:
Tuesdays and Thursdays
11:00 AM - 12:30 PM in 153 Sloan

Instructor:
Edray Herber Goins
goins@caltech.edu


Suggested Textbook

Modular Forms and Fermat's Last Theorem
Cornell, Silverman, Stevens, Eds.
Springer Verlag

Course Objective

This course will cover Wiles' proof of Fermat's Last Theorem. We will present a survey of topics surrounding deformations of Galois representations, including Tate's construction of p-adic Galois representations associated to elliptic curves, Shimura's construction of p-adic Galois representations associated to modular forms, Mazur's concept of the universal deformation ring of a residual Galois representation, Hida's theory of a p-adic family of modular forms, and Diamond's axiomatic approach for proving modularity using Galois cohomology and Hecke modules. We will discuss generalizations of Wiles' results towards the modularity of abelian varieties and complex Galois representations.

Prerequisites

The prerequisites for this course are Ma 120 and Ma 160 for an understanding of Galois theory, the p-adic numbers, and the structure of primes in number fields.

Grading Policy

There will be no homework or exams. The final grade will be determined by a final project which will consist of a presentation in class on a research paper from a related field.

Office Hours

Thursdays from 2:00 PM - 4:00 PM in 276 Sloan.