Mathieu Carette

I am a FNRS research fellow (ULB) and am currently a visiting scholar at the University of Illinois at Urbana-Champaign. I recently finished a PhD under the supervision of Bernhard Mühlherr (now at Univesität Giessen) and Richard Weidmann (Heriot-Watt University). I am mainly interested in geometric group theory, and more specifically in groups acting on trees, hyperbolic groups and Coxeter groups. Contact information: Department of Mathematics University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801. USA Email: mcarette at illinois dot edu Office: 227B Illini Hall Phone: +1(217)265-6756

• The automorphism group of accessible groups.
  Preprint (2008) pdf | arXiv | abstract

  Abstract:

  In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by taking extensions of relative automorphism groups of vertex groups, groups of Dehn twists and groups of automorphisms of free products. We apply this description and obtain a criterion for Out(G) to be finitely presented, as well as a necessary and sufficient condition for Out(G) to be finite. Consequences for hyperbolic groups are discussed.

• On the rank of Coxeter groups. (with Richard Weidmann)
  Preprint (2009) pdf | arXiv | abstract

  Abstract:

  We show that the standard generating set of a Coxeter group is of minimal cardinality provided that the non-diagonal entries of the Coxeter matrix are sufficiently large.

• Printemps des sciences 2009
• MATH-F-212 Théorie des nombres
• MATH-F-303 Géométrie
• Desserts du lundi