These structures first arose in Hitchin's program of characterizing geometrical structures via functionals of differential forms, a connection which formed the basis of Robbert Dijkgraaf, Sergei Gukov, Andrew Nietzke and Cumrun Vafa's 2004 proposal that topological string theories are special cases of a topological M-theory.
He is known for proposing with Cumrun Vafa the Gopakumar-Vafa duality and Gopakumar-Vafa invariants.