In 1996, Khmaladze moved with his family from Tbilisi, Georgia, to Sydney, Australia, and from there to Wellington, New Zealand, where in 2002 he was appointed Professor of Statistics after retirement of his predecessor, David Vere-Jones.
A characteristic feature of Khmaladze's work is the search of connection between distant analytical topics.
For example, in Khmaladze (1993), the connections between the theory of spatial martingales and Volterra operators with goodness of fit problems of statistics was demonstrated, and in Khmaladze(2007), the infinitesimal theory for set-valued functions was extended to help with problems of spatial statistics and image analysis.
However, the majority of his mathematical research centers around empirical processes and distribution-free methods of testing statistical hypotheses.
His current applied interests are focused on statistical theory of diversity and Zipf's law.