There is a vacancy for a position for a Ph.D. student on the FWO research project “Automorphism groups of locally finite trees” (G011012N). The candidate will perform his research in the Algebra research group of the De- partment of Mathematics at Ghent University (Ghent, Belgium), starting at any time during the year 2013, and lasting until December 31, 2016 (2 years + renewal of 2 years).
We will study automorphism groups of locally finite trees, from a combinatorial, geometrical, topological and algebraic point of view. We are particularly interested in two rather complementary situations.
The first situation is given by the action of a Moufang set on the boundary of a locally finite tree. We will be aiming at an axiomatic understanding of the relations between the global action of the group, and the local action induced on the spheres around each vertex of the tree. We want to apply our new knowledge and insights in order to characterize simple p-adic analytic groups within this class of automorphism groups of trees.
The second class of groups that will have our attention, are automorphism groups of trees satisfying Tits’s independence property (P); important examples are given by the Burger–Mozes universal groups U(F) for a prescribed local permutation action F. We will investigate these groups in the case that F is a non-affine sharply two-transitive group, and in the case that F is a rank one group. We will also analyze general groups satisfying property (P), and set our sights on finding connections between group-theoretical properties of F and topological and algebraic properties of U(F).
Candidates should be holder of a Master degree in pure mathematics (or equivalent). Interested candidates should send an email message to Tom De Medts (Tom.DeMedts@UGent.be), including a short CV and a PDF file of their master thesis. Experience in the topics of the project is an advantage but no requirement.