Stephanie B. Alexander

Stephanie Brewster Brewer Taylor Alexander (September 1, 1941 – November 20, 2023)^[1] was an American mathematician, a professor of mathematics at the University of Illinois at Urbana–Champaign.^[2] Her research concerned differential geometry and metric spaces.^[3]

Stephanie Alexander at Oberwolfach.

Biography

Alexander was born in Los Angeles and raised in Vancouver, British Columbia, and London, Ontario. She was a graduate of Mount Holyoke College.^[4]

She earned her Ph.D. from UIUC in 1967, under the supervision of Richard L. Bishop, with a thesis entitled Reducibility of Euclidean Immersions of Low Codimensions.^[5] After joining the UIUC faculty as a half-time instructor, she became a regular faculty member in 1972.^[3] She retired in 2009^[6] and died in 2023.^[4]

Mathematical Work

Alexander's most significant achievements were in relation to the study of metric spaces with curvature bounds. Of particular importance was her work with Bishop to establish a concept of curvature bounds in the style of Alexandrov geometry for semi-Riemannian manifolds and Lorentzian manifolds, an early step towards the development of synthetic geometry in a Lorentzian setting.^[7]

Books

• With Vitali Kapovitch and Anton Petrunin, Alexander authored the book An Invitation to Alexandrov Geometry: CAT(0) Spaces (Springer, 2019).

Recognition

• At Illinois, Alexander won the Luckman Distinguished Undergraduate Teaching Award and the William Prokasy Award for Excellence in Undergraduate Teaching in 1993.^[6]
• In 2014 she was elected as a fellow of the American Mathematical Society "for contributions to geometry, for high-quality exposition, and for exceptional teaching of mathematics."^[8]