Steven Zelditch

He has done research on the spectral and scattering theory of the Laplace operator on Riemannian manifolds and especially the asymptotic and distribution of its eigenfunctions (e.g. quantum ergodicity, equidistribution of eigenfunctions in billiard geometries, quantum ergodic restriction theorems to separating hypersurfaces).

In a seminal paper in 2009, Zelditch showed that one can recover the shape of a convex, analytic planar domain with up-down symmetries from its Laplace spectrum.

In 2019, with his coauthor, Zelditch showed that ellipses of small eccentricity are spectrally determined amongst all smooth, convex planar domains.

The Tian-Yau-Zelditch theorem in this case gives a complete asymptotic expansion of the Bergman kernel near the diagonal.

In 2002 he was an invited speaker with talk Asymptotics of polynomials and eigenfunctions at the International Congress of Mathematicians in Beijing.