1.  Mathematical Biology: Modeling the spread and control of emerging and re-emerging diseases.  I am currently focussed on modeling the impact of climate change on the spread of vector-borne diseases.  The overall objective is to contribute to the effort to formulate effective public health policy to curtail the spread of such diseases.

2.  Applied Dynamical Systems:  Qualitative theory of nonlinear dynamical systems (with emphasis on studying the existence and asymptotic stability of associated steady-state solutions, and characterizing various bifurcation types).

3.  Computational Mathematics (Scientific Computing):  The design of robust numerical methods that are dynamically-consistent with the associated continuous-time dynamical system being discretized.  In particular, I am interested in designing numerical methods that capture the essential properties of the continuous-time system being solved (such as boundedness and positivity of solutions, capturing the correct asymptotic stability properties, characterizing the correct bifurcation types etc.)  I am also interested in the design of numerical methods for solving partial differential equations on a parallel architecture.