Jean E. Lannes (born 21 September 1947 in Pauligne) is a French mathematician, specializing in

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

and

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topolog ...

. Lannes completed his secondary studies at the Lycée Louis-le-Grand in Paris and graduated in 1966 from the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

. He received his doctorate in 1975 from the

University of Paris-Saclay Paris-Saclay University (french: Université Paris-Saclay) is a public research university based in Paris, France. It is one of the 13 prestigious universities that emerged from the division of the University of Paris, also known as the Sorbonne. ...

(Paris 12). Afterwards he was a professor there and at the

Paris Diderot University Paris Diderot University, also known as Paris 7 (french: Université Paris Diderot), was a French university located in Paris, France. It was one of the inheritors of the historic University of Paris, which was split into 13 universities in 197 ...

(Paris 7). In 2009 he became a professor at the

École polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

and ''Directeur des recherches'' at the Centre de mathématiques Laurent-Schwartz (CMLS); he is now professor emeritus. He was a visiting scholar at several academic institutions, including the Institute for Advanced Study (1979/80) and the Massachusetts Institute of Technology (MIT). Lannes is known for his research on the homotopy theory of classifying spaces of groups. He proved in the mid-1980s the generalized Sullivan conjecture (which was also proven independently by

Gunnar Carlsson Gunnar E. Carlsson (born August 22, 1952 in Stockholm, Sweden) is an American mathematician, working in algebraic topology. He is known for his work on the Segal conjecture, and for his work on applied algebraic topology, especially topological ...

and

Haynes Miller Haynes Robert Miller (born January 29, 1948 in Princeton, New Jersey) is an American mathematician specializing in algebraic topology. Miller completed his undergraduate study at Harvard University and earned his PhD under the supervision of John ...

). The mod ''p'' cohomology of the classifying spaces of certain finite groups (elementary Abelian ''p''-groups, for which the generalized Sullivan conjecture was formulated) played an important role in the proof. The connection between the cohomology theory of these finite groups and the classifying spaces of groups is illuminated by the work of Lannes. He introduced the

T

-functor on the category of unstable algebra over the

Steenrod algebra In algebraic topology, a Steenrod algebra was defined by to be the algebra of stable cohomology operations for mod p cohomology. For a given prime number p, the Steenrod algebra A_p is the graded Hopf algebra over the field \mathbb_p of order p, c ...

. Lannes thus led an important development of algebraic topology in the 1980s. He has collaborated extensively with Lionel Schwartz, Hans-Werner Henn, and Saîd Zarati. Lannes has also done research on the knot invariants of Vassiliev. He was an invited speaker at the

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 Nevanlinna Prize (to be rename ...

(ICM) in Zurich in 1994. His doctoral candidates include

Fabien Morel Fabien Morel (born 22 January 1965, in Reims) is a French algebraic geometer and key developer of A¹ homotopy theory with Vladimir Voevodsky. Among his accomplishments is the proof of the Friedlander conjecture, and the proof of the complex cas ...

. In 2007 there was a conference in Djerba in honor of Lannes's 60th birthday.

Selected publications

* with Lionel Schwartz:
Online
* ''Cohomology of groups and function spaces'', Preprint 1986 (not published) * ''Sur la cohomologie modulo

p

des

p

-groupes abeliennes elementaire'', Proc. Durham Symposium 1985, Cambridge University Press 1987 * with Saîd Zarati: ''Sur les U-injectifs'', Annales Scient. ENS, vol. 19, 1986, pp. 303–333
Online
* * with H. W. Henn and L. Schwartz: Localizations of unstable A-modules and equivariant mod ''p'' cohomology. Mathematische Annalen, 301(1), 1995 23-68. * with Jean Barge: ''Suites de Sturm, indice de Maslov et périodicité de Bott'', Birkhäuser 2008 * with Gaëtan Chenevier : Automorphic Forms and Even Unimodular Lattices, Springer 2019

References

External links

* {{DEFAULTSORT:Lannes, Jean 1947 births Living people 20th-century French mathematicians 21st-century French mathematicians Lycée Louis-le-Grand alumni École Normale Supérieure alumni Academic staff of Paris-Saclay University Academic staff of École Polytechnique Topologists