Looking at a map of Language groups in India, the Indo-Aryan languages are mostly in the North/Center, while the Dravidian Languages are mostly in the South/Center. Sinhala seems to be one of the exceptions though, an Indo-Aryan language spoken at Southern most tip of the subcontinent. Was there some sort of mass migration or conquest of Sri Lanka by Indo-Aryan speakers that bypassed the other Dravidian speaking areas?
See my answer on Sinhalese origins here. The short answer is population migration from Bengal around the 5th or 6th century BCE.
