Antoine Clais

Research topics

My work is related to the following topics: hyperbolic groups, Coxeter groups, buildings, cube complexes, quasi-conformal analysis on boundaries, combinatorial modulus of curves, conformal dimension and combinatorial Loewner property.

More precisly, I study the quasi-conformal structures on boundaries of hyperbolic groups. Following ideas of Mostow, Gromov and Pansu, these properties can imply rigidity phenomenon in the group. In particular, I work on boundaries of right-angled hyperbolic buildings of dimension 3 and 4 whose boundaries that are highly suspected to be QI-rigid.

These researches have excited my curiosity in the theories of buildings, hyperbolic geometry and hyperbolic groups and generalizations.

Here are a conference poster and some slides of talk both about combinatorial properties of boundaries of hyperbolic buildings.

Papers
Research articles:

  • Conformal dimension on boundary of right-angled hyperbolic buildings, submitted, arXiv:1602.08611.
  • Propriétés combinatoires du bord d'un groupe hyperbolique , survey in French, Séminaire TSG (Grenoble), 32 (2014-2015), p. 73-96.
  • Combinatorial modulus on boundary of right-angled hyperbolic buildings, Anal. Geom. Metr. Spaces 4 (2016), Art. 1.
  • Transitive parallelism of residues in buildings , Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 4, 625–640.

    Notes:

  • Notes of the minicourse Boundaries of CAT(0) groups and spaces given by Kim Ruane for the conference GEAR : Second Junior Retreat.