Paul-Henry Leemann

Assistant professor at the department of pure mathematics, XJTLU.


Curriculum Vitæ


Research Interests:

My research interests lie in geometric and combinatorial group theory, in graph theory and in symbolic dynamic. I am particularly interested in groups acting on rooted trees and their (weakly) maximal subgroups, limits and coverings of (Schreier) graphs, rigidity phenomenon in Cayley and Schreier graphs and graphs associated to dynamical systems. For more details, here is a recent researchproject.pdf.

I did my PhD thesis under Tatiana Smirnova-Nagnibeda supervision.

Publications and Preprints:

  1. Most rigid representation and Cayley index of finitely generated groups
    with M. de la Salle
    arXiv
  2. Subgroup induction property for branch groups
    with D. Francoeur
    arXiv
  3. Weakly maximal subgroups of branch groups
    arXiv
  4. Wreath products of groups acting with bounded orbits
    with G. Schneeberger
    Accepted in l’Enseignement mathématiques (2022)
    arXiv
  5. Property FW and wreath products of groups: a simple approach using Schreier graphs
    with G. Schneeberger
    To appear in Expositiones Mathematicae (2022)
  6. Cayley graphs with few automorphisms: the case of infinite groups
    with M. de la Salle
    Annales Henri Lebesgue, Vol. 5 (2022)
  7. Up to a double cover, every regular connected graph is isomorphic to a Schreier graph
    Bulletin of the Belgian Mathematical Society – Simon Stevin, Vol. 28, Issue 3 (2022)
    (arXiv )
  8. Finitely generated subgroups of branch groups and subdirect products of just infinite groups
    with R. Grigorchuk and T. Nagnibeda
    Izvestia: Mathematics, Vol. 85 (2021)
  9. Cayley graphs with few automorphisms
    with Mikael de la Salle
    Journal of Algebraic Combinatorics, Vol. 53 (2021)
    ( arXiv )
  10. Schreier graphs: Transitivity and Coverings
    International Journal of Algebra and Computation, Vol. 26 Issue 1 (2016)
    (arXiv)
  11. Weakly maximal subgroups in regular branch groups
    with K. Bou-Rabee and T. Nagnibeda
    Journal of Algebra, Vol. 455 (2016)
  12. Lamplighter groups, de Bruijn graphs, spider-web graphs and their spectra
    with R. Grigorchuk and T. Nagnibeda
    Journal of Physics A: Mathematical and Theoretical, Vol. 49 Number 20 (2016)
    ( arXiv )

Some projects:

  1. Limits of Rauzy graphs of subshifts of finite type and horocyclic products of trees
    with V. Kaimanovich and T. Nagnibeda
  2. Limits of Rauzy graphs of languages of subexponential complexity
    with T. Nagnibeda and A. Skripchenko
  3. De Bruijn Graphs, Lamplighter Groups and Spectral Computations
    with T. Nagnibeda
    See
  4. Strong block subgroup decomposition for the first Grigorchuk group
    with D. Francoeur, R. Grigorchuck and T. Nagnibeda
  5. Closed subgroups of the first Grigorchuk group
  6. Cayley graphs with few automorphisms: the case of countable groups

Conferences organisation:

Co-organizer of one week conference on self-similar groups, as part of the thematic trimester Groups Acting on Fractals, 30 May-3 June 2022, Institut Henri Poincaré, France

Co-organizer of the Kervaire Seminar Baum-Connes conjecture, 24-29 Octobre 2021, Les Diablerets, Switzerland

Co-organizer of the Kervaire Seminar Geometry of Groups 2013, 10-15 March 2013, Les Diablerets, Switzerland


Talks (selected) and Slides:

Conference Talks:

August 2021
World Of Group Craft, inline conference. Wreath product of groups acting with bounded orbits.
June 2018
Trees Dynamics and Locally Compact Groups, Heinrich Heine University, Dusseldörf, Germany. Profinite completion of weakly maximal subgroups of branch groups.
January 2017
GAMME's meeting, Sète, France. Sous-groupes faiblement maximaux du groupe de Grigorchuk. De l’existence à la construction d’IRS.
June 2015
De Bruijn Graphs, Lamplighter Groups and Spectral Computations, Joint AMS-EMS-SPM Meeting, Porto, Portugal. Talk given by T. Nagnibeda. Slides
November 2014
Paroles aux jeunes chercheurs en géométrie et dynamique, GDR Platon 3341 CNRS, Université de Bordeaux, France. Un critère de transitivité pour les graphes de Schreier.
June 2014
Workshop in Algebra and Geometry, Université de Berne, Switzerland. Transitivity of Schreier graphs and strongly simple groups.
Septembre 2013
Geometric and Analytic Group Theory, Ventotene, Italy. Transitivity of Schreier graphs.

Seminar Talks:

Mars 2022
Colloquium of the Université de Fribourg, Switzerland. Cayley graphs with few automorphisms
Mai 2021
Groups and Geometry seminar, Université de Genève, Switzerland. Produit en couronne et groupes agissant avec des orbites bornées.
April 2021
Algebra Seminar, Lincoln University, United-Kingdom. Branch groups and the subgroup induction property
April 2021
Séminaire Géométrie, Algèbre, Algèbre d'opérateurs, Université de Clermont-Ferrand, France. Graphes de Cayley avec peu d’automorphismes
March 2021
Group theory seminar, ENS, Paris, France. De Bruijn graphs, spider web graphs and Lamplighter groups
February 2021
Symmetry in Newcastle, University of Newcastle, Australia. Rigidity of Cayley graphs
December 2020
Groups and Analysis seminar, Université de Neuchâtel, Switzerland. Propriété FW et produit en couronne : le point de vue des graphes médians.
November 2020
Colloquium of the Université de Neuchâtel, Switzerland. Groupes et graphes : phénomènes de rigidités.
March 2020
Groups and Geometry seminar, Université de Genève, Switzerland. Weakly maximal subgroups of branch groups.
Jully 2019
Darboux's seminar, Université de Montpellier, France. Rigidité des graphes de Cayley.
September 2015
Graduate Seminar, Université de Genève, Suisse. Weakly maximal subgroups of regular branch groups.
May 2015
Ergodic and Geometric Group Theory Seminar, EPFL, Lausanne, Suisse. Tarski's monster are strongly simple.