My general interest is in the field of correlated electron
systems, in particular unconventional superconductivity,
cuprate physics, non-Fermi-liquid behavior, competing orders, 
and induced orders by proximity effects. 

My interest in quantum critical phenomena currently concentrates on

A: the transition from homogeneous superconductivity to
inhomogeneous superconductivity at critical doping in cuprates

B: quantum phase transitions in superconductor-ferromagnet
nano-scale heterostructures

Some key questions:

A)
-What is the nature of the order parameter(s) in underdoped cuprates?
Is there an additional (hidden) order in the underdoped SC state?
-Are the enhanced spin fluctuations in underdoped cuprates primarily relevant to
or a secondary result of the competing phases in the quantum critical region?

B)
-How does an S-F-S Josephson junction behave when tuned to the transition
between the zero-junction and the pi-junction ground state?
-How does superconductivity penetrate into ferromagnetic domain walls?
Is crossed Andreev reflection relevant?