Current  Activity Colossal magnetoresistance oxides:- The very actively explored family of doped manganites, namely Re1-xAx MnO3 where Re is a trivalent rare earth and A are alkaline earths, pose a new and difficult challenge in many body physics because local (Jahn-Teller) electron lattice coupling, electron electron correlation, Hund's rule ferromagnetic spin exchange, are all present and strong. A new microscopic two fluid approach has been developed which has the potential to illuminate the entire field. The idea is the necessary coexistence of two different kinds of orbital states at each site. With one, a large Jahn-Teller distortion and consequent energy lowering is associated and with the other, not. The former leads, in a lattice, to nearest localized states in the relevant antiadiabatic regime, and the latter to a correlated broad band. The simultaneous but necessary coexistence of these two qualitatively different kinds of electron fluids, possible for strong Jahn-Teller coupling and on including quantum lattice effects, is shown to lie behind the very rich and hitherto puzzling phenomena in manganites. For example, the insulator to ferromagnetic metal transition as a function of doping x and temperature T, colossal negative magnetoresistance, transport properties of the ferromagnetic and paramagnetic phases, the ubiquitous `two phase' coexistence, large quantum effects (isotopic mass) on the ferromagnetic Tc, and properties of electron doped manganites have all been qualitatively and quantitatively explained including the strong correlation effects nonperturbatively. Extensions to orbital correlations/order, electronic inhomogeneities, polaron dynamics etc. are in progress.     2.   High Temperature Superconductivity:- (a) Effective low energy theory for cuprates: Role of internal and overall phase fluctuations and implications for the pseudogap phase, theory of the underdoped regime. (b) Electronic properties of the superconducting phase: Quasiparticles and quasiparticle transport in the mixed state, vortex dynamics, inelastic neutron peak, phase fluctuation effects, effect of impurities (esp. Zn), vortex induced idxy order, and bound electronic states in the vortex core.     3.  Biophysics:-  Origin and significance of long tailed distributions in gene expression. Chromatin, gene  transcription, coarse  grained models for DNA.