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My research is centered around leveraging curvature in differential geometry to understand fundamental concepts and problems in algebraic, complex, and arithmetic geometry. This typically involves using methods from geometric analysis and partial differential equations.


1. Second-Order Estimates for Collapsed Limits of Ricci-flat Kähler Metrics.
(arXiv.2106.13343)Canad. Math. Bull. (here).


2. The Schwarz Lemma in Kähler and Non-Kähler Geometry. 
(arXiv.2109.06331)Asian J. Math. (here).


3. The Schwarz Lemma: An Odyssey. 
(arXiv.2110.04989). Rocky Mountain J.  Math. (

4. On the Nonnegativity of the Dirichlet Energy of a Weighted Graph​. 
Bull. Aust.  Math. Soc. (here).


5. An Eigenvalue Characterization of the Dual EDM Cone​.
Bull. Aust. Math. Soc. (here).

6. Remarks on the Quadratic Orthogonal Bisectional Curvature. 
(​​arXiv.2211.05362). J.  Geom. (here).


7. On the Weighted Orthogonal Ricci Curvature. (with Kai Tang).
(arXiv.2111.00346). J.  Geom and Phys. (here).

8. On the Gauduchon curvature of Hermitian manifolds. (with James Stanfield).
(arXiv.2211.05973). Int. J. of Math. (here).


1. Twisted Kähler--Einstein Metrics and Collapsing​. 


2. On the Altered Holomorphic Curvatures of Hermitian Manifolds. (with Kai Tang).

3. Some Remarks on the Wu--Yau Theorem. 


​4. (ε,𝛿)--Quasi-Negative Curvature and Positivity of the Canonical Bundle. (with Kai Tang).

5. A General Schwarz Lemma for Hermitian Manifolds. (with James Stanfield).

6. Hermitian metrics with vanishing second Chern Ricci curvature. (with Artem Pulemotov).


Photo courtesy of Glen Wheeler

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