Colette Moeglin (born 1953) is a French mathematician, working in the field of

automorphic form In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G o ...

s, a topic at the intersection of

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

Career and distinctions

Moeglin is a Directeur de recherche at the

Centre national de la recherche scientifique The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

and is currently working at the Institut de mathématiques de Jussieu. She was a

speaker Speaker most commonly refers to: * Speaker, a person who produces speech * Loudspeaker, a device that produces sound ** Computer speakers Speaker, Speakers, or The Speaker may also refer to: Arts and entertainment * "Speaker" (song), by David ...

at the 1990

International Congress of Mathematicians 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). The Fields Medals, the IMU Abacus Medal (known before ...

, on decomposition into distinguished subspaces of certain spaces of square-integral automorphic forms. She was a recipient of the Jaffé prize of the

French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

in 2004, "for her work, most notably on the topics of enveloping algebras of Lie algebras, automorphic forms and the classification of square-integrable representations of reductive classical p-adic groups by their cuspidal representations". She was the chief editor of the ''Journal of the Institute of Mathematics of Jussieu'' from 2002 to 2006. She became a member of the

Academia Europaea The Academia Europaea is a pan-European Academy of humanities, letters, law, and sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europe ...

in 2019.

Mathematical contributions

She has done work both in the pure representation theory of

Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Eucli ...

s real or ''p''-adic (the study of unitary representations of those groups) and in the study of the "automorphic spectrum" of arithmetic groups (the study of those unitary representations which have an arithmetic significance), especially in the area of the Langlands programme. A prominent example of her achievements in the former is her classification, obtained with

Jean-Loup Waldspurger Jean-Loup Waldspurger (born 2 July 1953) is a French mathematician working on the Langlands program and related areas. He proved Waldspurger's theorem, the Waldspurger formula, and the local Gan–Gross–Prasad conjecture for orthogonal groups ...

, of the non-cuspidal discrete factors in the decomposition into irreducible components of the spaces of square-integrable invariant functions on adelic general linear groups. For this purpose it was first necessary to write down in a rigorous form the general theory of

Eisenstein series Eisenstein series, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written down directly. Originally defined for the modular group, Eisenstein series can be generalize ...

laid down years earlier by Langlands, which they did in a seminar in Paris the content of which was later published in book form. Another notable work in the domain, with Waldspurger and

Marie-France Vignéras Marie-France Vignéras (born 1946) 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 su ...

, is a book on the Howe correspondence. With Waldspurger, Moeglin completed the proof of the local

Gan–Gross–Prasad conjecture In mathematics, the Gan–Gross–Prasad conjecture is a restriction problem in the representation theory of real or Lie groups posed by Gan Wee Teck, Benedict Gross, and Dipendra Prasad. The problem originated from a conjecture of Gross a ...

for generic L-packets of representations of orthogonal groups in 2012. She did much work on the programme of

James Arthur James Andrew Arthur (born 2 March 1988) is an English singer and songwriter. He rose to fame after winning the ninth series of ''The X Factor'' in 2012. His debut single, a cover of Shontelle's " Impossible", was released by Syco Music aft ...

to classify automorphic representations of classical groups, and she was invited to present Arthur's ultimate solution to his conjectures at the Bourbaki seminar.

Selected publications

References

External links

Homepage at IMJ
{{DEFAULTSORT:Moeglin, Colette Living people 20th-century French mathematicians 21st-century French mathematicians 1953 births Members of Academia Europaea