Research
Brief Resume:
- Ph.D. 2002, Brandeis University (Supervised by Professor Shing-Tung Yau)
- Assistant Adjunct/Hedrick Assistant Professor, 2002-2005, UCLA
- Assistant Professor (Tenure Track), 2005-2010, The Chinese University of Hong Kong
- Assistant, Associate Professor, Professor 2010-present, Rutgers University at Newark
- https://orcid.org/0000-0003-1935-1786
Research Interest:
- Differential Geometry
- Algebraic Geometry
- Symplectic Geometry
Papers and Preprints:
Algebraic Geometry (Geometric Invariant Theory and Moduli)
- with Kenneth Ascher, Dori Bejleri, Harold Blum, Kristin DeVleming, Giovanni Inchiostro and Yuchen Liu,
Moduli of boundary polarized Calabi-Yau pairs, (2023), arXiv 2307.06522 - GIT stability, K-stability and the moduli space of Fano varieties.Moduli of K-stable varieties, Springer INdAM Ser., 31, Springer, Cham, (2019), 153-181
- with Chi Li and Chenyang Xu, Algebraicity of the Metric Tangent Cones and Equivariant K-stability, arXiv:1805.03393. J. Amer. Math. Soc. 34 (2021), no. 4, 1175-1214.
- with King-Leung Lee, Zhiyuan Li and Jacob Sturm, Asymptotic Chow stability for toric Del Pezzo surfaces, Math. Res. Lett. 26 (2019), no.6, 1759-1787, arXiv:1711.10099
- with Yuguang Zhang, Balanced embedding of degenerating Abelian varieties, arXiv:1605.01860
- with Chi Li and Chenyang Xu, Quasi-projectivity fo the moduli space of smooth K\”ahler-Einstein Fano manifolds.. Ann. Sci. \’Ecole Norm. Sup. (4) 51 (2018) no.3, 739-772, arXiv:1502.06532
- with Chi Li and Chenyang Xu, On the proper moduli spaces of smoothable K\”ahler-Einstein Fano varieties, Duke Math. J. 168 (2019), no. 8, 1387-1459, arXiv:1411.0761
- with Chenyang Xu, Nonexistence of asymptotic GIT compactification, Duke Math. J. 163, no. 12, (2014) 2217-2241, arXiv:1212.0173
- with Jun Li, Hilbert Mumford criterion for nodal curves, Compos. Math. 151 (2015), 2076-2130, arXiv:1108.1727
- Height and GIT weight. Math. Res. Lett. 19 (2012), 909–926
- with Hok-Pun Yu, Theta function and Bergman metric on Abelian varieites, New York J. Math. 15 (2009), 19-35
- Balance point and stability of vector bundle over a projective manifold, Math. Res. Lett. 9 no. 2-3, (2002), 393-411
Differential Geometry (Einstein metric, G2 Geometry and Isometric Embedding)
- with Jian Song and Jacob Sturm, An analytic proof of stable reduction theorem, (2020), arXiv:2009.13596
- with Jian Song and Jacob Sturm, Continuity of Weil-Petersson potential, (2020), arXiv:2008.11215
- with Jian Song and Jacob Sturm, Riemannian geometry of K\”ahler-Einstein currents III: compactness of K\”ahler-Einstein manifolds of negative scalar curvature, (2020), arXiv:2003.04709
- with Duong H. Phong, Jian Song and Jacob Sturm, The Ricci flow on the sphere with marked points. J. Differential Geom. 114 (2020), no. 1, 117-170.
- with Ved Datar, Bin Guo and Jian Song, Connecting toric manifolds by conical Kahler-Einstein metrics. Adv. Math. 323 (2018) 38-83, arXiv:1308.6781
- with Ke Zhu, Isometric embeddings via heat kernel. J. Differential Geom. 99, no. 3, (2015) 497-538, arXiv:1305.5613
- with Naichung Conan Leung and Ke Zhu, Instantons in G_2 manifolds from J-holomorphic curves in coassociative submanifolds.. Proceedings of Gokova Geometry-Topology Conference 2012, 89-111, arXiv:1303.6728
- with Jian Song, The greatest Ricci lower bound, conical Einstein metrics and the Chern number inequality, Geom. Topol. 20 (2016), no. 1, 49-102, arXiv:1207.4839
- with Naichung Conan Leung and Ke Zhu, Thin instantons in G2-manifolds and Seiberg-Witten invariants. J. Differential Geom. 95, no. 3, (2013) 419-483, arXiv:1107.1947
- Canonical metrics on stable vector bundles. Comm. Anal. Geom. 13, no. 2, (2005), 253-285
Symplectic Geometry(Moment Map and Symplectic Quotient)
- with King-Leung Lee and Jacob Sturm, Moment map, convex function and extremal point, arXiv:2208.03724.
- with Naichung Conan Leung, A quadratic inequality for sum of co-adjoint orbits. Comm. Anal. Geom. 17, no.2, (2009) 265-282
- Riemannian moment map. Comm. Anal. Geom. 16, no. 4, (2008) 837-863
- Moment map, Futaki invariant and stability of projective manifold. Comm. Anal. Geom. 12, no. 5, (2004) 1009-1037