Analysis of random objects - theory-backed methods and inference for analyzing metric space valued data with applications in brain imaging studies, child neurological development, traffic network analysis, social network analysis, genetics and compositional data.

Functional and longitudinal data analysis and its overlap with metric geometry- studying samples of dynamic metric space data, examples being time varying networks, distributions or tree valued data.

Modeling and inference for dynamic networks- generating mechanisms and network archeology.

Online learning problems- analysis of streaming object data.