Black Sea deluge is one theory for the initial dispersal of Indo-European speakers. Although wikipedia I don't think mentions this directly, the idea is that forced relocation caused the spread of the language. The timeline is approximately in line with what other theories suggest as well. And yes, Ukraine would have been the center. Or more correctly, what is now at the bottom of the Black Sea south of Ukraine.

http://en.wikipedia.org/wiki/Black_Sea_deluge_hypothesis