Carlos Tschudi Simpson (born 30 June 1962) is an American mathematician, specializing in algebraic geometry.
Simpson received his Ph.D. in 1987 from Harvard University, where he was supervised by Wilfried Schmid; his thesis was titled Systems of Hodge Bundles and Uniformization.
He is research director of the Centre national de la recherche scientifique.
In his Ph.D. dissertation, Simpson studied the notion of system of Hodge bundles, which can be seen as a special case of the higher dimensional generalization of Higgs bundles introduced earlier by Nigel Hitchin.
[3] Simpson was an Invited Speaker with talk Nonabelian Hodge theory at the International Congress of Mathematicians in 1990 at Kyoto.