Jean Lannes (mathematician)

Jean E. Lannes (born September 21, 1947 in Pauligne ) is a French mathematician who deals with algebraic topology , especially homotopy theory.

Hans-Werner Henn (left) and Jean Lannes in Oberwolfach 2009

Lannes received his doctorate in 1975 from the University of Paris-South (Univ. Paris XI) in Orsay . He was then a professor there and at the University of Paris-Diderot (Univ. Paris VII). Currently (2009) he is professor at the École polytechnique and director of the Center de Mathématiques Laurent Schwartz (CMLS). He was a visiting scholar at the Institute for Advanced Study (1979/80) and the Massachusetts Institute of Technology (MIT).

Lannes dealt, among other things, with the homotopy theory of classifying spaces of groups. He proved the generalized Sullivan conjecture (which was also independently proven by Gunnar Carlsson and Haynes Miller ) in the mid-1980s . The mod p cohomology of the classifying spaces of certain finite groups (elementary Abelian p groups, for which the generalized Sullivan's conjecture was formulated) also played an important role. The connection between the cohomology theory of these finite groups and that of classifying spaces of groups is examined in Lannes' theory. A "T-functor" that he introduced plays an important role here. Lannes thus led an important development in algebraic topology in the 1980s. Employees included Lionel Schwartz and Hans-Werner Henn .

Lannes also studied Vassiliev's knot invariants .

He was invited speaker at the International Congress of Mathematicians (ICM) in Zurich in 1994 ( Applications dont la source est un classifiant ).

Fabien Morel is one of his PhD students .

Fonts

• Sur la cohomologie modulo p des p-groupes abeliennes elementaires. In: Elmer Rees, John DS Jones (Eds.): Homotopy Theory. Proceedings of the Durham Symposium 1985 (= Lecture Note Series. 117). Cambridge University Press, Cambridge et al. 1987, ISBN 0-521-33946-4 , pp. 97-116.
• Cohomology of groups and function spaces. Preprint 1986 (not published).
• with Lionel Schwartz : A propos de conjectures de Serre et Sullivan. In: Inventiones Mathematicae . Vol. 83, 1986, pp. 593-604 .
• with Saïd Zarati: Sur les U-injectifs. In: Annales Scientifiques de l'École Normale Supérieure. Series 4, Vol. 19, No. 2, 1986, pp. 303-333, (on- line ).
• Sur les espaces fonctionels dont le source est le classifiant d'un -group abélien élémentaire. ${\displaystyle p}$In: Publications Mathématiques de l'IHÉS. Vol. 75, 1992, pp. 135-244 .
• with Jean Barge: Suites de Sturm, indice de Maslov et périodicité de Bott (= Progress in Mathematics. 267). Birkhäuser, Basel et al. 2008, ISBN 978-3-7643-8709-9 .
• with Gaëtan Chenevier: Automorphic Forms and Even Unimodular Lattices. Kneser Neighbors of Niemeier Lattices (= results of mathematics and its border areas . Volume 3, 96). Springer, Cham 2018, ISBN 978-3-319-95890-3 .

literature

• Hans-Werner Henn , Dieter Doll : Algebraic topology. In: Gerd Fischer , Friedrich Hirzebruch , Winfried Scharlau , Willi Törnig (eds.): A century of mathematics 1890–1990. Festschrift for the anniversary of the DMV (= documents on the history of mathematics. 6). Vieweg, Braunschweig et al. 1990, ISBN 3-528-06326-2 , pp. 673-716.
• Lionel Schwartz: Unstable Modules over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture (= Chicago Lectures in Mathematics Series. ). University of Chicago Press, Chicago IL et al. 1994, ISBN 0-226-74202-4 .

Web links

• Conference in his honor in Djerba