My research is in geometry and dynamics, particularly looking at how techniques from dynamical systems can be used to solve geometric problems. My interests include:
differential geometry
geometric dynamical systems -- geodesic flow, frame flow...
symmetric and homogeneous spaces
homogeneous dynamics
rigidity theory -- see Ralf's "An Invitation to Rigidity Theory" for an idea of what this is
Lie groups
I have done specific work on rank-rigidity and compact forms of homogeneous spaces, as well as shrinking target problems with Jon Chaika.
