Pierre-Emmanuel Caprace

Pierre-Emmanuel Caprace (* 1981 ) is a Belgian mathematician.

In 1999 he received the bronze medal at the International Mathematical Olympiad. Caprace received his doctorate in 2005 from the Free University of Brussels under Bernhard Mühlherr ( Abstract Homomorphisms of Split Kac-Moody Groups ). He teaches at the Catholic University of Leuven.

He deals with geometrically interesting groups and their algebraic structure, for example Kac-Moody groups.

In 2015 he and Nicolas Monod received the Berwick Prize for their work on isometric groups of CAT (0) spaces . After the official appreciation, they thereby expanded the rich classical theory of lattices in semi-simple groups and extensions of this theory by Mikhail Leonidowitsch Gromow and others. They proved (algebraic and geometric) product decomposition theorems in the sense of Georges de Rham , whereby symmetrical spaces and Euclidean buildings follow in a beautiful way from the condition that stabilizers in infinity act cocompactly on the inside, which generalizes classical theorems of rigidity of rank (laudation).

Fonts

• with Nicolas Monod: Isometry groups of non-positively curved spaces, part 1, Structure theory, part 2, Discrete subgroups, Journal of Topology, Volume 2, 2009, pp. 661–700, 701–746, Arxiv , Arxiv, part 2
• with T. De Medts: Trees, contraction groups, and Moufang sets, Duke Math. J.,. Volume 162, 2013, pp. 2413-2449.
• with Koji Fujiwara: Rank one isometries of buildings and quasi-morphisms of KacMoody groups, Geom. Funct. Anal., Vol. 19, 2010, pp. 1296-1319.
• with N. Monod: Decomposing locally compact groups into simple pieces, Math. Proc. Cambridge Philos. Soc., Vol. 150, No. 1, 2011, pp. 97-128.
• with M. Sageev: Rank rigidity for CAT (0) cube complexes, Geom. Funct. Anal., Volume 21, 2011, pp. 4, 851-891.
• with C. Reid, G. Willis: Locally normal subgroups of simple locally compact groups, CR Math. Acad. Sci. Paris, Volume 351, 2013, pp. 657-661.
• with N. Monod: Fixed points and amenability in non-positive curvature, Math. Ann., Volume 356, 2013, pp. 1303-1337.
• with Ph. Wesolek: Elementary totally disconnected locally compact groups, Proc. Lond. Math. Soc., Volume 110, 2015, pp. 1387-1434.
• with B. Mühlherr: Isomorphisms of Kac-Moody groups, Invent. Math., Vol. 161. 2005, pp. 361-388.
• with Bertrand Rémy: Simplicity and superrigidity of twin building lattices, Invent. Math., Vol. 176, 2009, pp. 169-221.

Web links

• Homepage

Individual evidence

1. ↑ Caprace as a participant in the Int. Math. Olympics
2. ↑ Pierre-Emmanuel Caprace in the Mathematics Genealogy Project (English)
3. ↑ Appreciation of the Berwick Prize for Monod, Caprace at EPFL, Lausanne