My research is in analysis and geometry; more specifically, I work on the interactions between several complex variables, multivariable operator theory, harmonic analysis, and their applications to noncommutative geometry. 

• A new index theorem for monomial ideals by resolutions, J. Funct. Anal. 275 (2018), 735-760. (with R. Douglas, X. Tang, and G. Yu) (Link, PDF)

• Index Theory for Toeplitz Operators on Algebraic Spaces, PhD thesis, Washington University in St. Louis (2019). (Link, PDF)

• An index theorem for quotients of Bergman spaces on egg domains, Annals of K-Theory 6 (2021), 357-380. (with X. Tang) (Link, PDF)

• p-Summable commutators in Bergman spaces on generalized egg domains, Complex Analysis and Operator Theory 16:21 (2022), 1-28. (Link, PDF)

• Essential normality of Bergman modules over intersections of complex ellipsoids, Studia Mathematica 267 (2022), 347-359. (Link, PDF)

• Perturbations of principal submodules in the Drury-Arveson space, Journal of Noncommutative Geometry 17 (2023), 211-232. (with X. Tang) (Link, PDF)