Bernadette Perrin-Riou

Last updated October 10, 2019

Bernadette Perrin-Riou (born 1 August 1955) is a French number theorist.

Early life

Perrin-Riou was born on 1 August 1955 in Les Vans, Ardèche, France. Her parents had both had a scientific education;^[1] her mother and father were a physicist and chemist, respectively. She was brought up, along with her sisters, in Neuilly-sur-Seine.^[2]^[3]

Les Vans commune in the Ardèche department in the Auvergne-Rhône-Alpes region of southern France.

Ardèche is a department in the Auvergne-Rhône-Alpes region of Southeastern France. It is named after the Ardèche River and had a population of 320,379 as of 2013. Its largest cities are Aubenas, Annonay, Guilherand-Granges, Tournon-sur-Rhône and Privas (prefecture).

France, officially the French Republic, is a country whose territory consists of metropolitan France in Western Europe and several overseas regions and territories. The metropolitan area of France extends from the Mediterranean Sea to the English Channel and the North Sea, and from the Rhine to the Atlantic Ocean. It is bordered by Belgium, Luxembourg and Germany to the northeast, Switzerland and Italy to the east, and Andorra and Spain to the south. The overseas territories include French Guiana in South America and several islands in the Atlantic, Pacific and Indian oceans. The country's 18 integral regions span a combined area of 643,801 square kilometres (248,573 sq mi) and a total population of 67.02 million. France is a unitary semi-presidential republic with its capital in Paris, the country's largest city and main cultural and commercial centre. Other major urban areas include Lyon, Marseille, Toulouse, Bordeaux, Lille and Nice.

Education

She entered the Ecole Normale Supérieure de Jeunes Filles in 1974, completing her undergraduate work in 1977. She then took a research assistant position at the Pierre and Marie Curie University in Paris.^[3] She received an advanced degree from University of Paris-Sud in 1979, working with Georges Poitiou;^[2] she then obtained a doctoral degree from the Pierre and Marie Curie University in 1983. Her thesis advisor was John H. Coates, and her thesis was entitled "Arithmetique des courbes elliptiques et théorie d'Iwasawa" ("Arithmetic of elliptic curves and Iwasawa theory").^[3]

Pierre and Marie Curie University, titled as UPMC from 2007–2017 and also known as Paris 6, was a public research university in Paris, France from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, France.

University of Paris-Sud French University member of the Université Paris-Saclay

Paris-Sud University, also known as University of Paris — XI, is a French research university distributed among several campuses in the southern suburbs of Paris including Orsay, Cachan, Châtenay-Malabry, Sceaux and Kremlin-Bicêtre campuses. The main campus is located in Orsay. This university is a member of the UniverSud Paris and a constituent university of the federal University of Paris-Saclay.

John Henry Coates, FRS is a mathematician who was the Sadleirian Professor of Pure Mathematics at the University of Cambridge in the United Kingdom from 1986 to 2012.

Career

She became maître de conferences at UPMC in 1983, and was then invited to spend a year as a visiting professor at Harvard University; she subsequently became a professor at the same university.^[3]

Harvard University is a private Ivy League research university in Cambridge, Massachusetts, with about 6,700 undergraduate students and about 13,100 postgraduate students. Established in 1636 and named for its first benefactor, clergyman John Harvard, Harvard is the United States' oldest institution of higher learning. Its history, influence, wealth, and academic reputation have made it one of the most prestigious universities in the world. It is cited as the world's top university by many publishers.

In 1994 she moved to a position at University of Paris-Sud in Orsay, which was primarily a research position (that is, with few teaching requirements).^[2] In the same year, she was invited to give an address at the International Congress of Mathematicians, which was held in Zürich,^[3] which she gave on "Fonctions L p-adiques" ("p-adic L-functions").^[4]

Orsay is a commune in the Essonne department in Île-de-France in northern France. It is located in the southwestern suburbs of Paris, France, 20.7 km (12.9 mi) from the centre of Paris.

The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).

Zürich or Zurich is the largest city in Switzerland and the capital of the canton of Zürich. It is located in north-central Switzerland at the northwestern tip of Lake Zürich. The municipality has approximately 409,000 inhabitants, the urban agglomeration 1.315 million and the Zürich metropolitan area 1.83 million. Zürich is a hub for railways, roads, and air traffic. Both Zurich Airport and railway station are the largest and busiest in the country.

Research

Perrin-Riou's research is in number theory, concentrating on p-adic L-functions and Iwasawa theory.^[1]

Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of objects made out of integers or defined as generalizations of the integers.

In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers.

In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa (1959), as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to abelian varieties. More recently, Ralph Greenberg has proposed an Iwasawa theory for motives.

Awards

She was awarded the Ruth Lyttle Satter Prize in Mathematics prize in 1999, a prize established in 1990 for women in maths.^[1]

Related Research Articles

John Torrence Tate Jr. is an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry. He is professor emeritus at the University of Texas at Austin. He was awarded the Abel Prize in 2010.

Kenkichi Iwasawa was a Japanese mathematician who is known for his influence on algebraic number theory.

Susan Howson is a former British mathematician whose research was in the fields of algebraic number theory and arithmetic geometry.

Christophe Breuil is a French mathematician, who works in algebraic geometry and number theory.

In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions, but whose domain and target are p-adic. For example, the domain could be the p-adic integersZ_p, a profinite p-group, or a p-adic family of Galois representations, and the image could be the p-adic numbersQ_p or its algebraic closure.

Jean-Marc Fontaine was a French mathematician. He was one of the founders of p-adic Hodge theory. He was a professor at Paris-Sud 11 University from 1988 to his death.

Marie-France Vignéras is a French mathematician. She is a Professor Emeritus of the Institut de Mathématiques de Jussieu in Paris. She is known for her proof published in 1980 of the existence of isospectral non-isometric Riemann surfaces. Such surfaces show that one cannot hear the shape of a hyperbolic drum. Another highlight of her work is the establishment of the mod-l local Langlands correspondence for GL(n) in 2000. Her current work concerns the p-adic Langlands program.

Guy Henniart is a French mathematician at Paris-Sud 11 University. He is known for his contributions to the Langlands program, in particular his proof of the local Langlands conjecture for GL(n) over a p-adic local field—independently from Michael Harris and Richard Taylor—in 2000.

Hà Huy Khoái is a Vietnamese mathematician working in complex analysis.

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

Leila Schneps is an American mathematician, living in France, employed by Centre national de la recherche scientifique, and based at the Institut de Mathématiques de Jussieu of Pierre and Marie Curie University, France, where she specializes in number theory. In addition to academic publication, she has edited several text books on aspects of mathematics, written a popular book and articles on the use and abuse of mathematics in criminal proceedings, and, under the pseudonym Catherine Shaw, written a series of mathematically themed murder mysteries.

Lawrence Clinton Washington is an American mathematician at the University of Maryland, who specializes in number theory.

Haruzo Hida is a Japanese mathematician, known for his research in number theory, algebraic geometry, and modular forms.

Wiesława Krystyna Nizioł is a Polish mathematician, director of research at CNRS, based at École normale supérieure de Lyon. Her research concerns arithmetic algebraic geometry, and in particular p-adic Hodge theory, Galois representations, and p-adic cohomology.

Yvette Amice was a French mathematician whose research concerned number theory and $p$ -adic analysis. She was president of the Société mathématique de France.

Sarah Livia Zerbes is a German algebraic number theorist at University College London. Her research interests include L-functions, modular forms, p-adic Hodge theory, and Iwasawa theory, and her work has led to new insights towards the Birch and Swinnerton-Dyer conjecture, which predicts the number of rational points on an elliptic curve by the behavior of an associated L-function.

Valérie Berthé is a French mathematician who works as a director of research for the Centre national de la recherche scientifique (CNRS) at the Institut de Recherche en Informatique Fondamentale (IRIF), a joint project between CNRS and Paris Diderot University. Her research involves symbolic dynamics, combinatorics on words, discrete geometry, numeral systems, tessellations, and fractals.

Anupam Saikia is an Indian mathematician and at present professor in the Department of Mathematics at IIT Guwahati, India. He is known for his work related to arithmetic number theory, in particular applications to Iwasawa Theory and p-adic measures. He has also published articles in mathematical cryptography.

Emmanuel Trélat is a French mathematician.

References

1 2 3 "1999 Satter Prize" (PDF). Notices of the AMS. 46 (4): 467–468. April 1999.
1 2 3 Charlene Morrow and Teri Peri, ed. (1998). Notable Women in Mathematics. Greenwood Press. pp. 161–164.
1 2 3 4 5 "Bernadette Perrin-Riou". MacTutor History of Mathematics. February 2010. Retrieved 8 October 2019.
↑ Bernadette Perrin-Riou (1994). Fonctions Lp-adiques [p-adic L-functions](PDF). International Congress of Mathematicians (in French). I. pp. 400–410.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[RLSPrize-1] 1 2 3 "1999 Satter Prize" (PDF). Notices of the AMS. 46 (4): 467–468. April 1999.

[NWiM-2] 1 2 3 Charlene Morrow and Teri Peri, ed. (1998). Notable Women in Mathematics. Greenwood Press. pp. 161–164.

[MacTutor-3] 1 2 3 4 5 "Bernadette Perrin-Riou". MacTutor History of Mathematics. February 2010. Retrieved 8 October 2019.

[4] Bernadette Perrin-Riou (1994). Fonctions Lp-adiques [p-adic L-functions](PDF). International Congress of Mathematicians (in French). I. pp. 400–410.