Zelditch was a pioneer in the mathematical theory of quantum chaos. He made the first major breakthrough in this subject shortly after receiving his PhD, in work culminating in his 1987 paper on quantum ergodicity for Riemann surfaces. His subsequent work spanned a tremendous range of fields in mathematics and mathematical physics, making progress in and drawing ideas from probability, string theory, general relativity, complex geometry, partial differential equations, and spectral and scattering theory. Zelditch's celebrated work in spectral geometry included, in 2019, the strongest positive result to date in this area (in collaboration with his former student Hamid Hezari): you can hear the shape of a nearly circular ellipse.
Among the unifying features of Zelditch's work were his taste for problems involving asymptotic expansions and his use of random objects as proxies for hard-to-reach deterministic ones. He was a winner of the 2013 Stefan Bergman prize, whose citation stated that with his "strikingly original vision, he has found deep and diverse relations between the Bergman kernel and many other areas, including complex geometry, probability, and mathematical physics." His work on the Bergman kernel included the celebrated Tian-Yau-Zelditch expansion in complex geometry.
In his prolific career, Zelditch authored more than 180 publications and supervised 13 PhD students. He was an invited speaker at the International Congress of Mathematicians in Beijing in 2002. In 2013 he was named a Fellow of the American Mathematical Society. Zelditch served on many editorial boards, including the Annales Scientifiques de l'École Normale Supérieure, Analysis & PDE, the American Journal of Mathematics, Communications in Mathematical Physics, Journal of Geometric Analysis, the Journal of Mathematical Physics and Pure and Applied Mathematics Quarterly.
Above all else, Zelditch loved to talk mathematics. He had an infectious enthusiasm and a profligate generosity with his seemingly endless stream of ideas. When news of his illness spread in the mathematical community, his colleagues quickly organized an online 69th birthday conference, with an eminent cast of speakers from all over the world. He was, characteristically, on the Zoom call until the day before his death, still eager to hear about the latest developments. The mathematical community at large, and Northwestern's department in particular, will sorely miss him.
Steve Zelditch is survived by his wife, Ursula Porod, and their two sons Benjamin and Phillip.