Jane Piore Gilman (born 1945)^[1] is an American mathematician, a distinguished professor of mathematics at Rutgers University.^[2] Her research concerns topology and group theory.

Gilman is one of three children of physicist Emanuel R. Piore.^[3] She did her undergraduate studies at the University of Chicago, graduating in 1965,^[2] and received her Ph.D. from Columbia University in 1971. Her thesis, supervised by Lipman Bers, was entitled Relative Modular Groups in Teichmüller Spaces.^[4] She worked for a year as an instructor at Stony Brook University before joining Rutgers in 1972.^[2]

Gilman is the author of a monograph on the problem of testing whether pairs of elements of PSL(2,R) (the group of orientation-preserving isometries of the hyperbolic plane) generate a Fuchsian group (a discrete subgroup of PSL(2,R)). It is Two-generator Discrete Subgroups of PSL(2, R) (Memoirs of the American Mathematical Society 117, 1995).^[5] With Irwin Kra and Rubí E. Rodríguez she is the co-author of a graduate-level textbook on complex analysis, Complex Analysis: In the Spirit of Lipman Bers (Graduate Texts in Mathematics 245, Springer, 2007; 2nd ed., 2013).^[6]

In 2014 she was elected as a fellow of the American Mathematical Society "for contributions to topology and group theory, and for service to her department and the larger community."^[7]