I'm sure their mathematical models are very beautiful, but the facts just don't support this theory at all. The "wheel" argument against this theory is just too damning, and their counterargument is weak: that nearly 4000 years after the language family split up, words for wheel, axle, and yoke managed to spread to nearly all daughter languages as loan words. But the problem is that these supposed loan words words reflect the same sound changes as all of the basic, inherited vocabulary. Thus the wheel vocab must be inherited from the same point in time as words like thou/tu/du.

Not to mention that the material culture found at the Ukraine sites is a much better match for what we know about early Indo-European culture.