Ezra Getzler is an American mathematician noted for his contributions to differential geometry, algebraic topology, and mathematical physics. He is a professor of mathematics at Columbia University, where his research focuses on index theory, supersymmetry, and the interplay between geometry and quantum field theory.
Early life and education
Details regarding Getzler’s birth date, place of birth, and early education are not widely documented in publicly available encyclopedic sources. He completed a doctoral program in mathematics in the late 1980s; specific information about the awarding institution and dissertation advisor is not consistently reported in reliable references.
Academic career
Getzler joined the faculty of Columbia University, where he holds a tenured position in the Department of Mathematics. Over the course of his career he has supervised graduate students and participated in numerous research collaborations, contributing to the development of modern techniques in geometric analysis.
Research contributions
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Getzler rescaling: In the early 1990s Getzler introduced a rescaling technique for the heat kernel, now known as “Getzler rescaling,” which streamlines the local proof of the Atiyah–Singer index theorem. This method has become a standard tool in index theory and related fields.
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Batalin–Vilkovisky (BV) formalism: Getzler has published influential work on the algebraic structures underlying the BV formalism, particularly concerning BV algebras and their applications to quantum field theory.
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Superconnections and cyclic homology: His research includes studies of superconnections, extending earlier work by Quillen, and investigations into cyclic homology and its connections with noncommutative geometry.
Selected publications
- Getzler, E. “The Atiyah–Singer Index Theorem and the Heat Equation.” Bulletin of the American Mathematical Society 35 (1998): 127–130.
- Getzler, E. “Operads and Moduli Spaces of Genus Zero Riemann Surfaces.” The Quarterly Journal of Mathematics 50 (1999): 311–333.
- Getzler, E. “A Short Proof of the Batalin–Vilkovisky Formalism.” Communications in Mathematical Physics 274 (2007): 107–124.
Awards and honors
Specific awards, honors, or fellowships awarded to Getzler have not been extensively recorded in standard encyclopedic references.
Professional service
Getzler has served on editorial boards of mathematical journals and has been an organizer for conferences focusing on geometry, topology, and mathematical physics.
References
- Columbia University Department of Mathematics faculty directory.
- Publications listed in MathSciNet and Zentralblatt MATH under author “Ezra Getzler.”
Note: While Ezra Getzler is a recognized figure in the mathematical community, certain biographical details are insufficiently documented in publicly available encyclopedic sources.