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Elizabeth Louise Mansfield (born 1957) is a UK based, Australian-born mathematician at the University of Kent. Her research focuses on applications of Lie groups to differential and difference systems.

Early life and education
Mansfield was born in Sydney, Australia. She attended what is now Pymble Ladies College and then the Australian International Independent School in North Ryde, Sydney. Her mother was the noted ceramic artist, author and publisher, Janet Mansfield. https://maas.museum/inside-the-collection/2013/02/08/in-memory-of-janet-mansfield-oam-1934-2013-australian-potter-author-and-publisher/

Mansfield was educated at the University of Sydney. After completing a BSc (1978) and an MSc (1981) there, she attended the Graduate School in Mathematics at the University of Wisconsin-Madison, USA for three years but returned to Sydney after the death of her supervisor, Professor Charles Conley (https://en.wikipedia.org/wiki/Charles_C._Conley). She subsequently completed a PhD in Differential Groebner Bases under the supervision of E.D. Fackerell in 1992. Her first research position was with Alan McIntosh at Macquarie University in Sydney. Subsequently, she held a post-doctoral research position at the University of Exeter, working with Peter Clarkson.

Mathematical work
Mansfield moved to Kent in 1995 and was appointed as Professor in 2005. She was the first ever female lecturer in mathematics and then the first ever female mathematics professor at the University of Kent. Mansfield first became known for her PhD thesis, on the subject of nonlinear, overdetermined differential systems of polynomial type, accompanied by software written in the computing language MAPLE. Related theorems were subsequently proved, to the satisfaction of the mathematical community, by Evelyne Hubert (E. Hubert, Factorization free decomposition algorithms in differential algebra, Journal of Symbolic Computations, 2000, volume 29(4-5) pp 641-662). The software was used in the study of reductions of nonlinear partial differential equations in the search for exact analytic solutions, in work with Peter Clarkson.

Noether’s Theorem is a key result in mathematical physics, giving conservation laws for variational systems, such as conservation of energy, linear and angular momentum. With Peter Hydon, Mansfield developed a rigorous variational complex for difference systems, independently of any continuum limit.

The key innovation in this work was the replacement of continuity used in the smooth variational complex, with that of adjacency. Noether’s Second Theorem was also extended to difference systems.

Mansfield has also worked on the modern, Lie group based moving frame, writing the text, A Practical Guide to the Invariant Calculus, published by Cambridge University Press in 2010.

Book
Practical Guide to the Invariant Calculus, Cambridge University Press, 2010. 

Recognition
Mansfield is a Fellow of the Institute of Mathematics and its Applications.

She is an editor of the LMS Journal for Computation and Mathematics.

She is a member of the Editorial Board for the Journal of Foundations of Computational Mathematics.

Mansfield has held positions of responsibility within four professional and learned societies: she has been on the Board of Foundations of Computational Mathematics (2002-2014), she was Vice President (2011-2013) of the Association of Computing Machinery’s Special Interest Group in Symbolic and Algebraic Manipulation.

She has been a Council Member of the London Mathematical Society (2011-2014), , and has been a vice president of the Institute of Mathematics and its Applications (2015-2018).

Mansfield was a member of EPSRC’s Mathematics Strategic Advisory Team and sits on the Scientific Advisory Board of the Australian Mathematical Sciences Institute.