The Berger–Kazdan comparison theorem served as a fundamental component in the proof of the Blaschke conjecture and the systematic classification of Wiedersehen manifolds. Since the mid-twentieth century, Jerry Kazdan has contributed extensively to the fields of differential geometry and partial differential equations, shaping academic approaches to Riemannian metrics and scalar curvature problems through his research and teaching.
Academic Foundation
Born in Detroit in 1937, Kazdan pursued his undergraduate studies at Rensselaer Polytechnic Institute, earning a bachelor's degree in 1959. He continued his academic training at New York University, completing a master's degree in 1961. In 1963, he received his PhD from the Courant Institute of Mathematical Sciences at New York University. His doctoral dissertation, titled A Boundary Value Problem Arising in the Theory of Univalent Functions, was written under the supervision of Paul Garabedian.
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Following the completion of his doctoral degree, Kazdan served as a Benjamin Peirce Instructor at Harvard University. In 1966, he moved to the University of Pennsylvania, where he accepted a position as a Professor of Mathematics. During his tenure at the university, he mentored students including Dennis DeTurck, who later collaborated with him on regularity theorems in Riemannian geometry.
Research and Publications
Kazdan maintained a long-term research partnership with Frank Warner, focusing on the problem of prescribing the scalar curvature of a Riemannian metric. Their collective work includes several influential papers published throughout the 1970s, such as the 1974 article Curvature functions for compact 2-manifolds and the 1975 publication Scalar curvature and conformal deformation of Riemannian structure. In addition to his research papers, he authored textbooks including Lectures on Complex Numbers and Infinite Series in 1966, Calculus Two: Linear and Nonlinear Functions in 1971, Intermediate Calculus And Linear Algebra in 1975, and Prescribing the Curvature of a Riemannian Manifold in 1985.
Recognition and Awards
The mathematical community recognized Kazdan’s contributions to expository writing in 1999 when he was awarded the Paul R. Halmos - Lester R. Ford Award for his article titled Solving equations, an elegant legacy. Later, in 2012, he became a fellow of the American Mathematical Society, an organization in which he holds active membership.
Fast facts
- Born: 1937, Detroit
- PhD: 1963, Courant Institute of Mathematical Sciences
- Specialization: Differential geometry and partial differential equations
- Notable Collaboration: Frank Warner
- Professional Role: Professor of Mathematics, University of Pennsylvania
- AMS Fellowship: 2013
- Lester R. Ford Award: 1999
Questions readers ask
What is the significance of the Berger–Kazdan comparison theorem?
It provided a critical step in proving the Blaschke conjecture and aided in the classification of Wiedersehen manifolds.
Which institution granted Kazdan his PhD?
He earned his doctoral degree from the Courant Institute of Mathematical Sciences at New York University in 1963.
Achievements
- Held posts at Harvard University and University of Pennsylvania
