Jessica A. Shepherd Purcell is an American mathematician specializing in low-dimensional topology whose research topics have included hyperbolic Dehn surgery and the Jones polynomial. She is a professor of mathematics at Monash University in Melbourne, Australia.^[1]

Purcell credits a high school mathematics teacher, Mr. Pehrson, for her interest in mathematics.^[2] She majored in mathematics as an undergraduate at the University of Utah, with a minor in computer science. She was a co-winner of the 1998 Alice T. Schafer Prize for Excellence in Mathematics by an Undergraduate Woman of the Association for Women in Mathematics,^[3][4] and graduated summa cum laude in 1998.^[1]

After earning a master's degree in mathematics at the University of Michigan in 1999,^[1] Purcell completed her Ph.D. at Stanford University in 2004. Her dissertation, Cusp Shapes of Hyperbolic Link Complements and Dehn Filling, was supervised by Steven Kerckhoff.^[1][5]

After postdoctoral research at the University of Texas at Austin and University of Oxford, Purcell became an assistant professor at Brigham Young University in 2007.^[1] She was named a Sloan Research Fellow in 2011,^[1][6] and earned tenure at Brigham Young in 2013. After visits to Monash University and at the Institute for Advanced Study as a Von Neumann Fellow, she moved to Monash as an associate professor in 2015, became an ARC Future Fellow in 2017, and was named full professor in 2019.^[1]

She chaired the Women in Mathematics Special Interest Group of the Australian Mathematical Society for 2018–2019 and 2019–2020.^[7]

Purcell is the author of the book Hyperbolic Knot Theory (Graduate Studies in Mathematics 209, American Mathematical Society, 2020).^[8] With David Futer and Efstratia Kalfagianni she is a coauthor of Guts of Surfaces and the Colored Jones Polynomial (Lecture Notes in Mathematics 2069, Springer, 2012).^[9]

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