Who was Steven Zelditch?
Steven Zelditch was an American mathematician who specialized in global analysis, complex geometry, and mathematical physics. He was born on September 13, 1953, and passed away on September 11, 2022. Zelditch received his bachelor's degree in mathematics from Harvard University in 1975 and his Ph.D. from the University of California, Berkeley in 1981, under the supervision of Alan Weinstein.
Career and Education
Zelditch's academic career spanned over four decades, with notable positions at Columbia University, Johns Hopkins University, and Northwestern University. He was a Ritt Assistant Professor at Columbia University from 1981 to 1985, an assistant professor at Johns Hopkins University from 1985 to 1989, an associate professor from 1989 to 1992, and a professor from 1992 to 2010. In 2010, he moved to Northwestern University, where he was the Wayne and Elizabeth Jones Professor of Mathematics.
Research and Contributions
Zelditch's research focused on the spectral and scattering theory of the Laplace operator on Riemannian manifolds, particularly the asymptotic and distribution of its eigenfunctions. He made significant contributions to the field, including the study of quantum ergodicity, equidistribution of eigenfunctions in billiard geometries, and quantum ergodic restriction theorems to separating hypersurfaces. One of his notable papers, published in 2009, demonstrated that one can recover the shape of a convex, analytic planar domain with up-down symmetries from its Laplace spectrum.
Awards and Recognition
Zelditch's work was recognized with several awards and honors. He was elected a Fellow of the American Mathematical Society in 2012 and shared the Stefan Bergman Prize in 2013 with Xiaojun Huang for their research on the Bergman kernel. Zelditch was also an invited speaker at the International Congress of Mathematicians in Beijing in 2002, where he presented a talk on the asymptotics of polynomials and eigenfunctions.
Legacy and Impact
Zelditch's contributions to mathematics have had a lasting impact on the field. His work on the inverse spectral problem and the study of quantum ergodicity have opened up new areas of research, and his papers have been widely cited and built upon by other mathematicians. The Tian-Yau-Zelditch theorem, which provides a complete asymptotic expansion of the Bergman kernel near the diagonal, is a testament to his innovative approach to mathematical physics.
FAQ
What was Steven Zelditch's area of expertise? Zelditch was a mathematician who specialized in global analysis, complex geometry, and mathematical physics.
What was the focus of Zelditch's research? Zelditch's research focused on the spectral and scattering theory of the Laplace operator on Riemannian manifolds, particularly the asymptotic and distribution of its eigenfunctions.
How was Zelditch's work recognized? Zelditch was elected a Fellow of the American Mathematical Society in 2012 and shared the Stefan Bergman Prize in 2013 with Xiaojun Huang for their research on the Bergman kernel.