Tengren Zhang

My research interests revolve around discrete group actions on homogeneous spaces, with a particular focus on Anosov subgroups and higher Teichmuller theory.

An Anosov subgroup is a specific type of discrete subgroup of a non-compact semisimple Lie group G. These subgroups are important as they engender “well-behaved” actions of the discrete group on select G-homogeneous spaces. Today, these are central objects in the study of geometric structures. On the other hand, higher Teichmuller theory is the study of connected components of the character variety of representations from a cocompact lattice in PSL(2,R) to G, that contain only discrete and faithful representations. These components are called the higher Teichmuller spaces. Anosov subgroups and higher Teichmuller theory share an intrinsic connection: in all existing examples, the images of the representations in the higher Teichmuller spaces are Anosov subgroups.