Tarantello was born in Pratola Peligna. She did her undergraduate studies at the University of L'Aquila, earning a bachelor's degree there in 1982. She then came to New York University for graduate study at the Courant Institute of Mathematical Sciences, earning a master's degree in 1984 and completing her Ph.D. there in 1986.[1] Her dissertation, Some Results on the Minimal Period Problem for Nonlinear Vibrating Strings and Hamiltonian Systems; and on the Number of Solutions for Semilinear Elliptic Equations, was supervised by Louis Nirenberg.[2]
Tarantello is the author of the book Selfdual Gauge Field Vortices: An Analytical Approach (Progress in Nonlinear Differential Equations and Their Applications 72, Birkhäuser, 2008).[3] With Matthew J. Gursky, Ermanno Lanconelli, Andrea Malchiodi, and Paul C. Yang, she is a co-author of Geometric Analysis and PDEs: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 11–16, 2007 (Lecture Notes in Mathematics 1977, Springer, 2009).[4]