Ralph Greenberg Explained

Ralph Greenberg
Birth Place:	Chester, Pennsylvania
Nationality:	American
Fields:	Mathematics
Workplaces:	University of Washington
Alma Mater:	University of Pennsylvania Princeton University
Doctoral Advisor:	Kenkichi Iwasawa

Ralph Greenberg (born 1944) is an American mathematician who has made contributions to number theory, in particular Iwasawa theory.

He was born in Chester, Pennsylvania^[1] and studied at the University of Pennsylvania, earning a B.A. in 1966, after which he attended Princeton University, earning his doctorate in 1971 under the supervision of Kenkichi Iwasawa.^[2]

Greenberg's results include a proof (joint with Glenn Stevens) of the Mazur–Tate–Teitelbaum conjecture as well as a formula for the derivative of a p-adic Dirichlet L-function at

s =0 (joint with Bruce Ferrero). 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 \Z _{p} -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 Barry 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 Stevens.

Greenberg was an invited speaker in International Congress of Mathematicians 2010, Hyderabad on the topic of "Number Theory."^[3]

In 2012, he became a fellow of the American Mathematical Society.^[4]

In the late 1990s and early 2000s, Greenberg publicly disputed NASA conspiracy theorist and pseudoscientist Richard C. Hoagland's mathematical interpretations of the so-called "D&M Pyramid" and surrounding features found on the Cydonia Planitia region of Mars as being conclusive signs of extraterrestrial intelligence and challenged him to a public debate. Hoagland has yet to respond.^[5]

External links

• https://sites.math.washington.edu/~greenber/update.html

Notes and References

1. Web site: The Institute for Advanced Studies, Annual Report 1981/82. . January 9, 2020.
2. Web site: Curriculum Vita.
3. Web site: ICM Plenary and Invited Speakers since 1897. International Congress of Mathematicians.
4. Web site: List of Fellows of the American Mathematical Society. 2013-01-19.
5. Web site: Letter to Richard Hoagland.