Kenneth Ribet intends to continue his work on the number theory associated with modular forms, modular curves, abelian varieties and Galois groups. Ribet is especially interested in number fields arising from torsion points on abelian varieties. While many questions in this subject are technical in nature, they are ultimately rooted in the classical problem of finding all whole number or fractional solutions to a family of equations.
Kenneth Ribet studies the arithmetic of modular forms, Galois representations and abelian varieties. His research lies at the intersection of algebraic geometry and algebraic number theory, two flourishing fields of mathematics. Ribet is best known for his contribution to the proof of Fermat's Last Theorem: Ribet proved a technical result about Galois representations, sometimes known as Serre's epsilon conjecure, which relates Fermat's Last Theorem to the Shimura-Taniyama conjecture for elliptic curves. More recently, Ribet contributed to the proof of a Fermat's conjecture to the effect that three distinct positive perfect n'th powers (where n is bigger than 2) can never form an arithmetic progression.
