Ralph Greenberg

Who is Ralph Greenberg?

Ralph Greenberg is an American mathematician who has made notable contributions to number theory, in particular Iwasawa theory.

He attended Princeton University, earning his doctorate in 1971 under the supervision of Kenkichi Iwasawa.

Greenberg's results include a proof of the Mazur–Tate–Teitelbaum conjecture as well as a formula for the derivative of a p-adic Dirichlet L-function at s = 0. Greenberg is also well known for his many conjectures. In his PhD thesis, he conjectured that the Iwasawa μ- and λ-invariants of the cyclotomic Zₚ-extension of a totally real field are zero, a conjecture that remains open as of September 2012. In the 1980s, he introduced the notion of a Selmer group for a p-adic Galois representation and generalized the "main conjectures" of Iwasawa and Mazur to this setting. He has since generalized this setup to present Iwasawa theory as the theory of p-adic deformations of motives. He also provided an arithmetic theory of L-invariants generalizing his aforementioned work with Glenn Stevens.

He was an invited speaker in International Congress of Mathematicians 2010, Hyderabad on the topic of "Number Theory."