Staffilani has been the Abby Rockefeller Mauze Professor of Mathematics at the Massachusetts Institute of Technology since 2007. She received her undergraduate degree from the University of Bologna in 1989 and her M.S. and Ph.D. from the University of Chicago. Following a Szegö assistant professorship at Stanford University, she had faculty appointments at Stanford, Princeton University and Brown University before joining the MIT mathematics faculty in 2002.
Staffilani is an analyst with a concentration on dispersive nonlinear partial differential equations. At Stanford, she received the Harold M. Bacon Memorial Teaching Award and the Frederick E. Terman Award for young faculty. She was a Sloan fellow from 2000 to 2002, a member of the Institute for Advanced Study in Princeton in 1995 and 2003, and a member of the Radcliffe Institute for Advanced Study at Harvard University in 2009.
She is an elected member of the Massachusetts Academy of Science, a fellow of the American Mathematical Society, a member of the American Academy of Arts and Sciences and a member of the National Academy of Sciences. In 2017, she received a Guggenheim Fellowship and a Simons Fellowship in Mathematics. In 2018 she received the MIT Earll M. Murman Award for Excellence in Undergraduate Advising.