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[7] over the real numbers, a result that resolves an issue mathematicians have worked on for at least two decades.
In 2013 he became a fellow of the American Mathematical Society.[9] Vakil was elected as its president in 2024 and began his two-year term on 1 February 2025.[10]
Mathematics contests
He was a member of the Canadian team in three International Mathematical Olympiads, winning silver, gold (perfect score), and gold in 1986, 1987, and 1988 respectively. He was also 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.[11]