I've been doing real (commutative) algebra and geometry for some time already. Recently Im working with the algebraic geometry of theoretical kinematics, algebraic number theory and computer algebra. I'm dealing with general inverse kinematic solutions of 6R/P manipulators and path planning of these manipulators in the Study quadric defined by their kinematic structure. Ocassionally I also look at the $3x+1$ problem (aka. Collatz conjecture).