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Research Institute in Mathematics and Physics

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Research Institute in Mathematics and Physics

Group theory

irmp | Louvain-la-Neuve

We are interested in the algebraic structure of infinite groups, possibly endowed with a non-discrete topology. The groups under study often act naturally actions on some geometric space. In addition to the classical framework of Lie groups, semi-simple algebraic groups and their discrete subgroups, generalizations are considered, notably to the Kac–Moody groups. These particular examples are brought in perspective in a more global analysis of topological groups, for which the central questions are rigidity, linearity, finiteness properties, and the existence and the classification of networks.
 

Faculty members

  • Pierre-Emmanuel CAPRACE
  • Timothée MARQUIS

Post-doctoral researchers

  • Sebastian BISCHOF
  • François THILMANY

PhD Student

  • Max CARTER
  • Robynn CORVELEYN
  • Maximilien FORTE
  • Alex LOUÉ 
  • Justin VAST
  • P.-E. Caprace et Koji Fujiwara. Rank one isometries of buildings and quasi-morphisms of Kac­Moody groups. Geom. Funct. Anal. 19 (2010), pp.1296--­1319.
  • P-E. Caprace et N. Monod, Decomposing locally compact groups into simple pieces. Math. Proc. Cambridge Philos. Soc. 150 Nr. 1 (2011), pp. 97--128.
  • P-E. Caprace et M. Sageev, Rank rigidity for CAT(0) cube complexes. Geom. Funct. Anal. 21 (2011), no. 4, 851--891.
  • P-E. Caprace et T. De Medts, Trees, contraction groups, and Moufang sets. Duke Math. J. 162 (2013), no. 13, 2413--2449.
  • P-E. Caprace et N. Monod, Fixed points and amenability in non-positive curvature. Math. Ann. 356 (2013), no. 4, 1303--1337.
  • Ph. Wesolek, Elementary totally disconnected locally compact groups. Proc. Lond. Math. Soc. (3) 110 (2015), no. 6, 1387--1434.
  • T. Marquis, Abstract simplicity of locally compact Kac-Moody groups. Compos. Math. 150 (2014), no. 4, 713–728.
  • P-E. Caprace et T. Stulemeijer, Totally disconnected locally compact groups with a linear open subgroup. Int. Math. Res. Not. 2015 Nr. 24 (2015), pp. 13800–13829.
  • P-E. Caprace, C. Reid et G. Willis, Locally normal subgroups of totally disconnected groups. Part I: General theory. Forum Math. Sigma 5 (2017), e11, 76 pp. 
  • P-E. Caprace, C. Reid et G. Willis, Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups. Forum Math. Sigma 5 (2017), e12, 89 pp. 
  • A. Le Boudec, C∗-simplicity and the amenable radical. Invent. Math. 209 (2017), no. 1, 159–174.
  • N. Radu, A classification theorem for boundary 2-transitive automorphism groups of trees.  Invent. Math. 209 (2017), no. 1, 1–60.
  • P-E. Caprace et N. Monod (éditeurs), New directions in locally compact groups. London Mathematical Society Lecture Note Series (447), Cambridge UP.
  • T. Marquis, An introduction to Kac-Moody groups over fields, EMS Textbooks in Mathematics, 2018.
  • T. Marquis. Cyclically reduced elements in Coxeter groups. Annales Scientifiques de l'école normale supérieure. Fasc.2, Tome 54, 2021 pp. 483-502
  • P.-E. Caprace, Mehrdad Kalantar, Nicolas Monod. A type I conjecture and boundary representations of hyperbolic groups. Proceedings of the London Mathematical Society. Volume127, Issue2 August 2023 pp. 447-486.