Dongzhe (Denzel) Zheng

Ph.D. Researcher, MAE, Princeton University
Gordon Y.S. Wu Fellow in Engineering, Princeton University
Master of Mathematics, University of Cambridge

⚛ Physics

Accepted · March 16, 2026

Toroidal Loop-Current Order in Kagome \(AV_3Sb_5\): Zero-Field Diode and Anomalous Hall

Journal of Physics: Condensed Matter (JPCM)

Resolving the phenomenological coexistence of charge density wave-driven anomalous Hall effect (AHE) and zero-field superconducting diode effect (SDE) in kagome metals. This work establishes a unified theoretical framework connecting microscopic orbital current patterns to macroscopic transport signatures.

Minor Revision

Operator-norm Control of Projected Density Algebras in Chern Bands: Toeplitz Correspondence and Adiabatic Equivalence to the Lowest Landau Level

Journal of Physics A: Mathematical and Theoretical

Turning the founding question of the fractional Chern insulator (FCI) field—in what precise sense is a Chern band "close to" the lowest Landau level?—from a decade of heuristic band-geometry correlations into rigorous, quantitative control: operator-norm bounds on the projected density algebra that cleanly separate geometric effects (Berry curvature, Fubini–Study metric) from interband-mixing dispersion, with quasi-adiabatic continuation then tying single-particle algebraic deviation to many-body gap stability. A new finite-volume indicator correlates sharply with the many-body gap in Harper–Hofstadter and kagome models, giving a quantitative single-particle criterion for zero-field topological many-body phases.

Long-Term Vision

Rigorous Bridges Between Microscopic Quantum Geometry and Emergent Many-Body Topology

Theoretical Framework

To build controlled bridges between microscopic quantum-geometric and algebraic structure and macroscopic topological response in correlated matter—asking when collective ordering and band geometry can be faithfully read as emergent gauge configurations and projected operator algebras, across kagome metals, moiré platforms, and beyond.

Underneath this program sits the founding question of the FCI field, chased heuristically for over a decade: once a system is incompressible, what is really the right notion of "closeness" between a Chern band and the lowest Landau level—and is it the one everyone implicitly uses?

∫ Mathematics

Preprint

Picard Groups of Completed Period Images and the Deng–Robles Problem

Badre Mounda, Dongzhe Zheng

arXiv:2603.09709

We reduce the Deng–Robles problem—namely, whether the completed image of a degenerate period map can be naturally characterized as an intrinsic Proj-type algebro-geometric object—to a structural problem concerning Picard group generation, and provide a complete proof in the case where the pure period image is one-dimensional.

Preprint

Pseudoconvexity and Algebraization of the Generalized Satake–Baily–Borel Completion

ResearchGate

We establish the local pseudoconvexity and holomorphic extension input needed for the \(\theta\)-bundle algebraization of generalized Satake–Baily–Borel completions, using a new anisotropic weighted \(L^2\)-\(\bar\partial\) method adapted to degenerate Hodge metrics; this upgrades the analytic completion to an algebraic one in the weight-2 Hermitian and Calabi–Yau 3 cases.

⎈ Control

Accepted · April 6, 2026

A Posteriori Second-Order Guarantees for Bolza Problems via Collocation

Dongzhe Zheng, Wenjie Mei

IEEE Control Systems Letters (L-CSS)

Providing a posteriori second-order sufficient conditions for Bolza-type optimal control problems solved via collocation methods, enabling rigorous local optimality verification of numerically computed trajectories.