Vakil is an algebraic geometer and his research work spans over enumerative geometry, topology, Gromov-Witten theory, and classical Algebraic Geometry. He has solved several old problems in Schubert calculus. Among other results, he proved that all Schubert problems are enumerative over the real numbers, a result that resolves an issue mathematicians have worked on for at least two decades. Vakil has also proved several results regarding the Murphy's law in algebraic geometry.
Vakil has received many awards, including an NSF Career Fellowship, a Sloan Research Fellowship, an American Mathematical Society Centennial Fellowship, a G. de B. Robinson Prize for the best paper published in the Canadian Journal of Mathematics and the Canadian Mathematical Bulletin, and the André-Aisenstadt Prize from the Centre de Recherches Mathématiques at the Université de Montréal.
He has participated with the Canadian team in three IMO's winning two gold and one silver medals and was the fourth person to be a four-time Putnam Fellow in the history of the contest. Also, he has been the coordinator of weekly Putnam preparation seminars at Stanford.