Stephanie Brewster Brewer Taylor Alexander (September 1, 1941 – November 20, 2023) was an American mathematician, a professor of mathematics at the University of Illinois at Urbana–Champaign. Her research concerned differential geometry and metric spaces.
Biography Alexander was born in Los Angeles and raised in Vancouver, British Columbia, and London, Ontario. She was a graduate of Mount Holyoke College. 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. After joining the UIUC faculty as a half-time instructor, she became a regular faculty member in 1972. She retired in 2009 and died in 2023.
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.
Books With Vitali Kapovitch and Anton Petrunin, Alexander authored the book An Invitation to Alexandrov Geometry: CAT(0) Spaces (Springer, 2019). S. Alexander, V. Kapovitch, A. Petrunin. Alexandrov geometry—foundations. — AMS, 2024. — (Grad. Stud. Math. 236).
Recognition At Illinois, Alexander won the Luckman Distinguished Undergraduate Teaching Award and the William Prokasy Award for Excellence in Undergraduate Teaching in 1993. 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."
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