My research lies at the intersection of complex geometry, symplectic geometry, and functional analysis. More specifically, I am interested in Bergman kernel asymptotics and Berezin–Toeplitz quantization.
Publications
- Fubini–Study forms on punctured Riemann Surfaces, with X. Ma and L. Wang, CR Math. Acad. Sci. Paris 363 (2025), 603–615. arXiv:2506.05863.
Abstract
In this paper we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré metric near the punctures, and a holomorphic line bundle that polarizes the metric. We show that the quotient of the induced Fubini–Study forms by Kodaira maps of high tensor powers of the line bundle and the Poincaré form near the singularity grows polynomially uniformly on a neighborhood of the singularity as the tensor power tends to infinity, as an application of the method in [5].
Preprints
- Asymptotics for Toeplitz operators with symbol an indicator function, arXiv:2606.24503 (2026).
Abstract
We prove an off-diagonal expansion of the kernel of the Toeplitz operator whose symbol is the indicator function of a compact domain with smooth boundary in a complete symplectic manifold of bounded geometry. Using our approach, we extend two results to the non-compact setting: the first concerns the asymptotics of the trace of polynomials in this operator, and the second establishes a Weyl law for this Toeplitz operator.