I went to the EE380 talk at Stanford where Eran Tromer explained the theory.[1][2] The claims were very broad, and I didn't understand exactly what was supposed to have been proven. A lot of material was covered very fast. Watch the video and try to figure it out.

[1] http://web.stanford.edu/class/ee380/ [2] https://www.youtube.com/watch?v=KP8TPeYQyN4