Daphne Gilbert

Daphne Jane Mansergh was born in 1944 in Working, Surrey, England.^[1] She was the second of five children of Philip Nicholas Seton Mansergh, an Anglo-Irish historian, and Diana Mary Keeton, a squash and lawn tennis blue.^[4] Her interest in mathematics began when she attended the Perse School For Girls in Cambridge.^[1] On her nature walks, she would notice organic geometric patterns.^[1] Although her parents encouraged her to pursue domestic sciences, she insisted on studying mathematics, physics, and chemistry.^[1] In 1961, Gilbert began her studies of mathematics at New Hull (now Murray Edwards College) in Cambridge.^[1] She paused her studies a year later to devote her time to raising a family. In 1977, she went back to New Hull to continue her study of mathematics, earning her bachelor’s degree in 1980.^[1][5] Gilbert’s doctoral dissertation, completed in 1984^[5] under the supervision of David Pearson,^[1] developed what became known as the Gilbert–Pearson theory of Subordinacy for Schrödinger Operators.^[2]

Gilbert began her career at New Hull after earning her PhD in 1984.^[5] She continued her research and development, publishing an extension to the theory in 1989 called “On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints."^[6] Daphne Gilbert extended the subordinacy theory of Schrödinger operators, originally developed with her advisor David Pearson for systems defined on the half-line, to apply to the whole line.^[3] This allowed the analysis of particle behavior in both directions rather than only from a fixed starting point.^[3]

In 1990, she joined Sheffield Hallam University, in Sheffield, South Yorkshire, England, where she continued her mathematical research.^[1] Here, she lectured, supervised PhD candidates with uplifting guidance and dedication,^[7] developed new degree programs, and developed new masters programs within mathematics fields.^[1] Gilbert then proceeded to become Head of Department of Pure and Applied Mathematics at the Dublin Institute of Technology in 1999, where she rose to professor before her retirement.^[1][8] She continued conducting research and developing the Mathematical Science Department at DIT.^[9] Gilbert coauthored numerous research articles between June 2000 and July 2013,^[10] including several published after her retirement. She retired in 2008 and was granted emeritus status.^[1]

Gilbert and David Pearson developed the Gilbert-Pearson Theory of Subordinacy of Schrödinger Operators,^[2] published in 1984.^[5] Their theory gave mathematicians and physicists a new way to understand how quantum particles behave over time and how their possible energy states can be identified. In mathematical terms, their theory provides a framework for analyzing and quantifying the behavior of quantum states, and was the first to apply subordinacy theory to continuum half-line Schrödinger operators, establishing a new method for studying their spectral properties.^[11] Gilbert then continued to follow up with her “On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints,”^[6] which developed the subordinacy theory for the whole continuum of Schrödinger operators.^[11]

• On Subordinacy and Analysis of the Spectrum of One-Dimensional Schrödinger Operators,^[2] Gilbert and Pearson, August 8, 1985
• On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints,^[6] Gilbert, 1989
• The Derivation of Minimal Test Sets for Combinational Logic Circuits using Genetic Algorithms,^[12] Takhar and Gilbert, 1997
• Bounds for the points of spectral concentration of Sturm-Liouville problems,^[13] Gilbert and Harris, June 2000
• On the Recovery of a Differential Equation from Its Spectral Functions,^[14] Gilbert and Harris, October 2001
• Bounds for the Points of Spectral Concentration of One-dimensional Schrödinger Operators,^[15] Gilbert and Harris and Riehl, January 2004
• The spectral function for Sturm–Liouville problems where the potential is of Wigner–von Neumann type or slowly decaying,^[16] Gilbert and Harris and Riehl, June 2004
• Zeros of the Jost Function for a Class of Exponentially Decaying Potentials,^[17] Gilbert and Kerouanton, 2005
• Higher Derivatives of Spectral Functions Associated with One-Dimensional Schrödinger Operators,^[18] Gilbert and Harris and Riehl, December 2008
• Higher derivatives of spectral functions associated with one-dimensional Schrödinger operators II,^[19] Gilbert and Harris and Riehl, July 2013
• Eigenfunction expansions associated with the one-dimensional Schrödinger operator,^[20] Gilbert, October 2015

Gilbert met her husband, Paul Gilbert (1942–2022), a philosophy student turned professor,^[24] during her studies at New Hull in 1961.^[1] After getting married the next year, Daphne paused her studies to concentrate on her family. Even though Paul supported her ambitions, Daphne stayed home for 15 years.^[1] Together they had Benjamin, Hester, Matthew, and Emily Gilbert.^[1] Gilbert died on March 12, 2024, at the Claremont House Care Home in Beverley.^[25]