Some of my research interests include studying problems that arise from or involve materials. I have studied composite materials using multiple scales analysis to study problems related to conductivity over heterogeneous electrode surfaces. This work required a deep analysis of the partial differential equations (PDEs) modeling the phenomena using asymptotic scales as well as a rigorous numerical solution of the PDEs. Another field of my research includes modeling and analyzing data using a data mining/machine learning approach based on spectral graph theory methods, probability and statistics. Large data sets are modeled on manifolds using a graph Laplacian approach. My recent work in this area involves using a graph theory based learning algorithm to perform a pattern analysis of synaptic activity induced by seizure-like events as well as using spectral graph theory based dimension reduction algorithms to analyze simulated radar and ladar data.
partial differential equations, asymptotics, numerical analysis, graph theory, probability and statistics