My main research area is computational neuroimaging, where non invasive brain imaging modalities such as magnetic resonance imaging (MRI), diffusion tensor imaging (DTI) and functional-MRI are used to map spatiotemporal dynamics of the human brain. Computational neuroimaging deals with the computational problems arising from the quantification of the structure and the function of the human brain. My research has been concentrated on the methodological development of quantifying anatomical shape variations and functional differences in both normal and clinical populations using various mathematical, computational and statistical techniques. A major challenge in the field is caused by the massive amount of nonstandard high dimensional non-Euclidean imaging and network data that are difficult to analyze using available techniques. This requires new computational solutions that are formulated in a differential geometric and algebraic topological setting in addressing more complex scientific hypotheses. Other than computational neuroimaging, my interest lies in topological data analysis (persistent homology), shape analysis, network analysis, image analysis, functional data analysis, diffusion equations and persistent homology.