In this episode, I speak with Professor Dominik Wujastyk, Singhmar Chair in Classical Indian Society and Polity at the University of Alberta at Edmonton. He is the Principal Investigator at the Suśruta Project. You can find some of his publications here; this is his entry at Penguin.
Among his teachers at Oxford were Richard Gombrich, Thomas Burrow, Alexis Sanderson (see also here), Robert Zaehner, and later Bimal Krishna Matilal. Among his fellow students was Anne-Marie Gaston (see also here), a performer of Bharatanatyam.
During and after his PhD, he worked at the Wellcome Library.
Sanskrit centres at Pune in India include the Bhandarkar Oriental Research Institute (BORI) and the Centre of Advanced Study of Sanskrit (CASS) at the University of Pune. Perhaps foremost among the scholars he met ae S.D. Joshi and Pandit Vaman Balkrishna Bhagavat.
Here are a few very general links to some of the fields Prof. Wujastyk mentions as good areas for doctoral research these days, Yoga and Tantra. Read more about the temple he discusses in this context here.
This is a useful general introduction to Vyākaraṇa, the Sanskrit study of grammar.
These links are not meant to be exhaustive, but can serve as the basis of your own searches if you are further interested.