This has shifted over the years. For the longest time as I was growing up it was
interest in Black Holes. As I learned more Physics I came to realize my interest
really was at the fundamental question "What is the Quantum Nature of Gravity ?"
So for Physics, it would be unlikely union of GR with QM (QFT) (doesn't work yet)...
For Math, it would a whole bunch Differential Geometry/Complex Analysis/Abstract
Algebra (with Spinors & Lie Groups mixed in)...
Though I still have passing interest in Astrophysics & Cosmology...
Maddog