Here are some of the issues that concern me at the moment:

1. There is strong evidence (eg., omega/T scaling and fractional exponents
in the magnetic dynamics) that the picture of T=0 SDW transition, or
fluctuating magnetic order parameter, fails at the quantum critical point
of at least some heavy fermion metals. Does the Fermi surface indeed undergo
a jump at the QCP (as, eg, the local quantum criticality would expect)?

2. What is the precise nature of the non-Fermi liquid excitations at a
quantum critical point where Kondo screening is destroyed? Spin-charge
separation?

3. There are experimental indications for non-Fermi liquid behavior near
first-order quantum transitions. What are the low-lying excitations in
such cases?

4. I also have some interest in the non-equilibrium aspects of quantum
critical points, a topic that has hardly been systematically explored.