The answers are subjective by definition, but looking at the numbers behind the Google Research awards announced yesterday can provide some quick insights. Going by the grants as a proxy for what are where are the current hottest areas of research, here's what we get:
A total of 105 grants were awarded. 81 universities in all got the awards, in 19 different research areas.
Here are the top research areas:
As far as institutions go, MIT, Georgia Tech and CMU got 5 grants each, with Cornell and Standford getting 3 each.