A short outline of the areas of research that I have been working on is detailed below.
Physics of Non-equilibrium Stationary States
Physics of disordered systems
A general formulation of non-equilibrium phenomena is an open problem in physics. The relatively recent formulation of a class of non-equilibrium phenomena characterizable by long term steady states via the large deviation principle (LDP) has been remarkably successful in encapsulating features that frequently arise in equilibrium cases. For instance, in the simple exclusion process steady states can be shown to undergo dynamical phase transitions. Likewise, in models of self-assembly and growth LDP can be used to study classes of phase transitions and extract dynamical critical exponents.
The interplay of disorder with strongly correlated phases like superfluids can lead to exotic behavior. One instance is the emergence of new exotic quantum disordered phases like the Bose-glass. Another is the counterintuitive order-by-disorder type of behavior evident in the re-entrant superfluid phase (RSF). Inhomogeneities can further make things interesting by allowing coexistence of ordered/disordered domains - interesting boundary effects are possible. A fascinating area yet to be fully explored is quasi-equilibrium but away from linear-response types of behavior; examples include topological structures like vortices and loops, quantum glassiness etc.
Phenomenologically speaking, superconductivity is characterized by the reduction of the resistivity of a material to zero below a certain transition temperature. Associated effects include the Meisner effect that leads to expulsion of magnetic fields from the interior of superconductors (leading to the floating effect seen in the central image). Although, the microscopic mechanism for a class of superconductors was given by the famous BCS theory of superconductivity we still do not know how it comes about in other more general contexts. There is active research being pursued to identify the pairing mechanism in high temperature superconductors -- the hunt is on for room temperature superconducting materials. More exotic forms of superconductors such as topological variants are of interest primarily for quantum information processing -- again, another very active area of research.