Dongzhe (Denzel) Zheng

Ph.D. Researcher, MAE, Princeton University
Gordon Y.S. Wu Fellow in Engineering, Princeton University
Co-founder, Conjectas
Master, Part III of the Mathematical Tripos, University of Cambridge
Bachelor of Science in Mathematics, University of New Hampshire

∴ Academic Projects

Co-founder · Public Alpha

Conjectas — The Conjecture Commons

Open problems & conjectures · AI-assisted proofs · Lean formalization · Contribution ledger · Citable claims · Field graph

Co-founded a decentralized, open academic collaboration platform for hard mathematical conjectures and unsolved problems. Conjectas combines AI-assisted proof attempts, Lean theorem-proving tracks, review-credit accounting, a contribution ledger, citable scholarly claims, and graph-based field maps so that proposing conjectures, reviewing arguments, and formalizing proofs can become visible, attributable, and reusable.

◊ Scientific Machine Learning

Accepted · ICML 2026

Topology-Preserving Neural Operator Learning via Hodge Decomposition

Dongzhe Zheng, Tao Zhong, Christine Allen-Blanchette

International Conference on Machine Learning (ICML) 2026 · Regular Paper [Avg. Review Rating: 5/6 (est. Top 1% via PaperCopilot)]

Introducing a hybrid Eulerian–Lagrangian architecture, Hodge Spectral Duality (HSD), that exploits Hodge orthogonality to decouple unlearnable topological features from learnable geometric dynamics. Combining discrete differential forms with an auxiliary ambient space, the method markedly improves accuracy, efficiency, and fidelity to physical invariants when solving field equations on geometric meshes.

⚛ Physics

Accepted · March 16, 2026

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

Dongzhe Zheng

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.

Accepted · May 8, 2026

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

Dongzhe Zheng

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 \(\mathcal{E}_{\Lambda,L}\) correlates with the many-body gap in Harper–Hofstadter and kagome models far more sharply than the conventional Berry-curvature proxy \(\sigma_B\), giving a quantitative single-particle criterion for zero-field topological many-body phases.

Provisionally Accepted · May 26, 2026

Linear Visibility of the Higgs Mode and Odd-Frequency Mixing Mechanism in Time-Reversal Symmetry Breaking Kagome Superconductors

Dongzhe Zheng

Journal of Physics: Condensed Matter (JPCM)

Proving that in time-reversal-symmetry-breaking superconductors, the unique symmetry-allowed channel through which a pseudoscalar background field activates the Higgs mode is odd-frequency mixing—static coupling is strictly forbidden. This identifies a previously unrecognized selection rule for TRSB collective-mode coupling.

⎈ 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.

∫ Mathematics

Submitted · Letters in Mathematical Physics

State Complex of Toroidal Six-Vertex Height Functions: CAT(0) Covers and Circle Homotopy

Dongzhe Zheng

Studying the state complex of plaquette flips for toroidal six-vertex height functions, connecting CAT(0) cube complex methods with the topology of constrained configuration spaces. The main result is a homotopy classification: every interior slope sector has CAT(0) lifted state complex and quotient homotopy type \(S^1\), while boundary sectors are frozen with explicit binomial counts. As an application, flat \(U(1)\) twists of the Rokhsar–Kivelson Hamiltonian are classified by a single sweep holonomy, yielding an exact zero-mode criterion.