Chabauty Limits of the Diagonal Subgroup in SL(n,Q_p)- Arielle Leitner (Weizmann)
Abstract: A conjugacy limit group is a limit of a sequence of conjugates of the positive diagonal subgroup C in SL(n) in the Chabauty topology. In low dimensions, there are finitely many limits up to conjugacy, and we explain why there are more limits over Q_p than over R. In higher dimensions there are infinitely many limits up to conjugacy. We can understand limits of C by understand how to go to infinity in the building (you won't need to know what a building is for this talk, we'll explain the geometry with low dimensional examples). We use the geometry of the building to classify limits of C. This is joint work with C. Ciobotaru and A. Valette. The hidden agenda of this talk is to convince you that Q_p is friendly, and things that we do over R and C can work over Q_p as well.
Sequences of Hitchin representations of Tree-Type- Giuseppe Martone (Michigan)
Abstract: Let S be an oriented surface of genus greater than 1. The Teichmuller space of S can be described as a connected component of the space of representations of the fundamental group of S into the Lie group PSL(2,R). The Hitchin component generalizes this classical picture to the Lie group PSL(d,R). Hitchin representations are a prominent subject of study in the field of Higher Teichmuller theory. Motivated by classical work of Thurston, one wishes to understand the asymptotic behavior of sequences of Hitchin representations. In this talk we describe non-trivial sufficient conditions on a diverging sequence of Hitchin representations so that its limit can be described as an action on a tree. In other words, we single out sequences whose asymptotic behavior is similar to diverging sequences in the Teichmuller space. Our non-trivial conditions are given in terms of Fock-Goncharov coordinates on moduli spaces of positive tuples of flags.