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Topic: Ken Ribet

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Epsilon conjecture

John Coates

Raoul Bott

Andrew Wiles

Robert Langlands

Yutaka Taniyama

Sun Ke

Goro Shimura

Saharon Shelah

Iwasawa theory

Mikio Sato

Kunihiko Kodaira

University of California, Berkeley

Masatoshi Koshiba

Gerard Debreu

	NOVA \| Transcripts \| The Proof \| PBS
		KEN RIBET: Now, one way of looking at it is that you have all elliptic curves, and then you have the modular elliptic curves, and you want to prove that there are the same number of each.
		KEN RIBET: Well, I was at this conference on L functions and elliptic curves, and it was kind of a standard conference and all of the people were there.
		KEN RIBET: Andrew Wiles is probably one of the few people on earth who had the audacity to dream that you could actually go and prove this conjecture.
	www.pbs.org /wgbh/nova/transcripts/2414proof.html (6232 words)

	Archived publications by Kenneth Ribet
		Agashe, Amod; Ribet, Kenneth A.; Stein, William A. The modular degree, congruence primes and multiplicity one to appear.
		Ribet, Kenneth A.; Stein, William A. Lectures on Serre's conjectures.
		Ribet, Kenneth A. Galois representations attached to eigenforms with Nebentypus.
	math.berkeley.edu /~ribet/Articles (0 words)

	Ken Kolodner: Hammered Dulcimer and Fiddle Website
		As a major part of the rebirth of the hammered dulcimer in the US, Ken is recognized as one of "one of today's most accomplished, musical hammered dulcimer artists...
		Viewed by many players as one of the most influential player in the United States, Ken is widely known for an expressive and improvisational style and for creative ensemble playing.
		With Helicon (with Chris Norman and Robin Bullock) and Greenfire (with Laura Risk) and in solo performance, with Baltimore as his home base, Ken has toured extensively throughout North America and Europe and has taught at countless festivals and music camps.
	www.kenkolodner.com (0 words)

	Ken Ribet - BAMA (Site not responding. Last check: )
		Ribet is known for his work in number theory and algebraic geometry.
		Dr. Ribet was elected to the American Academy of Arts and Sciences in 1997 and the National Academy of Sciences in 2000.
		Ribet was inducted as a Vigneron d'honneur by the Jurade de Saint Emilion in 1988.
	mathematicaladventures.org /Ribet.html (273 words)

	Ribet (Site not responding. Last check: )
		Wiles, Ribet, Shimura-Taniyama-Weil and FLT A collection of links based on the former e-math gopher archive.
		Ribet, C Features mushroom prints, California oak trees, California landscapes and many other art prints.
		Modular Forms and Hecke Operators Notes by William A. Stein of a course by Ken Ribet.
	www.serebella.com /encyclopedia/article-Ribet.html (133 words)

	Ken Ribet (Site not responding. Last check: )
		Kenneth A. Ribet is an American mathematician, currently a professor of mathematics at the University of California, Berkeley.
		Ribet established the epsilon conjecture, and thereby proved that Fermat's Last Theorem would follow from the Taniyama-Shimura conjecture.
		Crucially it also followed that the full conjecture was not needed, but a special case sufficed.
	www.wapipedia.com /wikipedia/mobiletopic.aspx?cur_title=Ken_Ribet (120 words)

	Kenneth Alan Ribet - Red Enciclopedia
		Kenneth Alan Ribet o Ken Ribet è un matematico statunitense, attualmente professore di matematica all’Università di Berkeley, in California.
		Ribet ha stabilito la congettura epsilon, e quindi ha dimostrato che l'ultimo teorema di Fermat si può derivare dalla congettura di Taniyama-Shimura.
		Quando era allievo della Far Rockaway High School, Ribet, anche se la sua materia di studio principale era la chimica, faceva parte di una squadra per le competizioni di matematica.
	www.redhostingdns.com /index.php?title=Kenneth_Alan_Ribet (191 words)

	[No title]
		\par \par }{\b\fs20 KEN RIBET}{\fs20 : Sophie Germain.
		\par \par }{\b\fs20 KEN RIBET}{\fs20 : The problem is that Frey didn't really prove that his elliptic curve was not modular.He gave a plausibility argument which he hoped could be filled in by experts, and then the experts started working on it.
		\par \par }{\b\fs20 KEN RIBET}{\fs20 : Now one way of looking at it is that you have all elliptic curves and then you have the modular elliptic curves and you want to prove that there are the same number of each.
	members.fortunecity.com /templarseries/horizon/fermat.rtf (4773 words)

	Ribet talk (Site not responding. Last check: )
		At MU, Ken Ribet spoke on FLT Oct. 27 to a large group of enthusiastic faculty and students from MU and surrounding high schools.
		Ribet has been a professor at the University of California-Berkeley for almost 20 years.
		Ribet won half of the first Prix Fermat in 1989 for showing that the Shimura-Taniyama conjecture implies FLT.
	www.math.missouri.edu /~news/issue3/ribet.html (242 words)

	HRUMC XII - More Information
		Ribet is known for his work in number theory and algebraic geometry.
		Ribet was elected to the American Academy of Arts and Sciences in 1997 and the National Academy of Sciences in 2000.
		Ribet was inducted as a Vigneron d'honneur by the Jurade de Saint Emilion in 1988.
	www.skidmore.edu /academics/mcs/pages/hrumc12in.htm (491 words)

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		"Ribet and Wiles studied this curve under the assumption that there exist a nonzero integer c such that a^n + b^n = c^n." (Ribenboim, p.
		The variables of Fermat's equation are in the x, y variables of the ellipitic curve equation; therefore, Freys, Ribet, Wiles and Taniyama-Shimura assumption that the constant of the elliptic curve equation (equ 11), a and b, represent Fermat's equation is invalid.
		In addition, Fermat's elliptic curve equation is derive using the integer solution equations of n=2 (equ 13); therefore, n>2 cannot be represent with the elliptic curves.
	www.psyclops.com /hawking/forum/printmsg.cgi?period=current&msg=67653 (1681 words)

	Ken Ribet Gives Arnold Ross Lecture
		Ribet was introduced by Victoria Powers (Emory University) and Glenn Stevens (Boston University), former and current chairs of the Arnold Ross Lecture Series Committee, respectively.
		Ribet did get two of the three problems correct, however, so he felt like it was worth it.
		During the question-and-answer session, Ribet spoke about his role in the proof of Fermat's Last Theorem--proving a connection between the theorem and elliptic equations.
	www.ams.org /ams/arl2005.html (0 words)

	Math Forum Discussions
		Lang once came to visit Berkeley he was put in Ribet's office.
		Ribet had written in the book, right after the part in the introduction that
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.org /kb/message.jspa?messageID=384734&tstart=0 (211 words)

	A Mathematical Lie
		The lie, due to Harvard mathematician Barry Mazur, was broadcast in a TV program, "The Proof," in October 1997 and repeated in a book based on the program and in a Scientific American article, "Fermat's Last Stand," by Simon Singh and Kenneth Ribet, in November 1997.
		A 1996 page in Daney's site shows that Mazur, Ribet, Singh, and Peterson were wrong about the history of the known relationships between elliptic curves and modular forms.
		Combined with earlier work of Ribet, the work of Wiles and Taylor is said to constitute a proof of Fermat's last theorem.
	log24.com /log03/1130.htm (0 words)

	Modular Forms Course
		You might want to visit Ken Ribet's Home Page.
		These are the notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
		They were created by several of us students and assembled by Lawren Smithline.
	modular.math.washington.edu /MF.html (96 words)

	Level-lowering for mod 2 modular forms (Site not responding. Last check: )
		In 1985, Ken Ribet proved a "level-lowering" theorem in the theory of mod p modular forms, valid for forms of level Gamma_0(N) and primes p>2.
		As a consequence of this result he was able to prove that the Taniyama-Shimura conjecture implied Fermat's Last Theorem.
		Taylor's approach to settling infinitely many new cases of a conjecture of Artin was based on these ideas of Wiles and Ribet, but unfortunately he needed to work with p=2, where Ribet's work, as it stood, did not apply.
	www.math.jussieu.fr /projets/tn/STN/00/resume-Buzzard.html (136 words)

	Review of Fermat's Enigma
		Two years later, Princeton professor Ken Ribet proved the link and now there was no longer any doubt: prove the Taniyama-Shimura conjecture and you proved Fermat's Last Theorem.
		Now that Ribet had linked it to Fermat, dismay set in: by this time, most mathematicians believed that anything that would lead to a solution of Fermat was doomed to failure.
		The trigger was Ken Ribet's 1986 proof that solving the Tamiyama-Shimura conjecture would lead directly to a proof of Fermat's Last Theorem.
	www.leegruenfeld.com /reviews/fermat.htm (1889 words)

	Scientific American: Are mathematicians finally satisfied with Andrew Wiles's proof of Fermat's Last Theorem? Why has ...
		It was already known before Wiles's proof that Fermat's Last Theorem would be a consequence of the modularity conjecture, combining it with another big theorem due to Ken Ribet and using key ideas from Gerhard Frey and Jean-Pierre Serre.
		And Wiles is no exception: his proof grows out of work by Frey, Serre and Ribet that connects Fermat's statement with the theory of elliptic curves.
		Once that connection was established, and one knew that proving the Modularity Conjecture for elliptic curves would yield a proof of Fermat's Last Theorem, there was reason to be hopeful.
	www.sciam.com /print_version.cfm?articleID=000DBA55-B698-1C71-9EB7809EC588F2D7 (1025 words)

	ribet.html (Site not responding. Last check: )
		Many mathematicians contributed to the proof---among them Frey, Ribet, Serre, Taylor and Wiles---and it has captured the public imagination in a way that is rare in mathematics.
		The Math Department is pleased to welcome Ken Ribet to the University of Missouri for a public lecture on this great accomplishment.
		The talk does not require any sort of higher mathematics; it is intended for people who are interested in mathematics, and are willing to think about equations and numbers.
	www.math.missouri.edu /~elias/graduatestudies/ribet.html (94 words)

	Amazon.com: "Ken Ribet": Key Phrase page
		See all pages with references to "Ken Ribet".
		One of those toiling to prove and complete the connection between the Taniyama-Shimura conjecture and Fermat's Last Theorem was Ken Ribet, a professor at the University of California at Berkeley.
		That was proved by Ken Ribet in 1986, showing that the truth of the Modularity Conjecture entails Fermat's Last Theorem.
	www.amazon.com /phrase/Ken-Ribet (0 words)

	Math 254 (Number Theory) (Site not responding. Last check: )
		Prospective students in number theory are encouraged to attend.
		If you're shopping for an advisor in number theory, check out the Web pages of Robert Coleman, Hendrik Lenstra, Arthur Ogus, Bjorn Poonen, Ken Ribet, and Paul Vojta.
		J.S. Milne has printable notes from a variety of courses, including Algebraic Number Theory (and the class field theory notes mentioned above).
	www-math.mit.edu /~kedlaya/math254b.html (400 words)

	Mathematical Sciences Research Institute - Workshop Calendar
		Organized By: Jeff Brock, Ken Bromberg, Richard Canary, Howard Masur, Alan Reid, Maryam Mirzakhani, and John Smillie
		To this end it is hoped to limit lectures to 4 hours a day, allowing plenty of time for informal interactions.
		During the conference there will be a dinner to honor Ken Ribet on his 60th birthday.
	www.msri.org /calendar/index_workshops (0 words)

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