This will give you some, as a similar question came up a few hours ago, and /u/rusoved linked to this Historical Linguistics AMA.

He may pop in here at some point, too, to address more directly your question, but here's a start from the linguistics side of things. Historical linguists have partially reconstructed the Proto-Indo-European language using the languages in the IE family, and have used word correspondences between those languages to make a geographical approximation as to where the speakers of the language might have originated. The search for the origins of speakers of PIE is mostly for the scholarly purposes: understanding who they were, what the were like, where they went, etc.