The study of Toeplitz operators is a classical subject in several complex variables, deeply intertwined with microlocal analysis. This talk will begin with a brief review of the foundational microlocal frameworks developed by Melin–Sjöstrand, Boutet de Monvel–Sjöstrand, and Boutet de Monvel–Guillemin in the context of CR manifolds. Following this, I will present recent joint work with H. Herrmann, C.-Y. Hsiao, and G. Marinescu. We develop a semi-classical approach for the spectral theory of first-order elliptic self-adjoint Toeplitz operators on compact, strictly pseudoconvex, and embeddable CR manifolds. The primary benefit of our method is that it yields the embeddability of CR manifolds into complex Euclidean spaces not only on the differential geometric level, but also on a precise metric level. If time permits, I will conclude by discussing an extension of this work from my thesis to Levi non-degenerate CR manifolds.
Spectral Asymptotics of Semi-Classical Toeplitz Operators on CR Manifolds
15.06.2026 13:15 - 14:45
Organiser:
Luke Edholm
Location:
BZ09
