- Ph.D. 2002, Brandeis University (supervised by S.-T. Yau).
- Adjunct Assistant Professor, 2002-2003, UCLA.
- Hedrick Assistant Professor, 2003-2006 (on leave in
2005-2006), UCLA.

- Assistant Professor (Tenure-Track), 2005-2011(on leave on 2010-2011), The Chinese University of Hong Kong, Hong Kong.
- Assistant, Associate Professor, 2010-present, Rutgers University at Newark.

Research Interest: Differential Geometry, Algebraic Geometry and Symplectic Geometry.

Algebraic Geometry (GIT, Moduli problem)

- with King-Leung Lee, Zhiyuan Li and Jacob Sturm,
*Asymptotic Chow stability for toric Del Pezzo surfaces*, arXiv:1711.10099

(We proved the asymptotic
Chow polystability for the Kahler-Einstein toric Del Pezzo
surfaces of degree 2, 3 and 4.)

- with Yuguang Zhang, Balanced embedding of degenerating Abelian varieties, arXiv:1605.01860.

(We constructed a family of
balanced embeddings for certain degenerations of principally
polarized Abelian varieties)

- with Chi Li and Chenyang Xu, Quasi-projectivity fo the moduli space of smooth Kahler-Einstein Fano manifolds. arXiv:1502.06532.

(We prove that CM line bundle is nef and big on
the proper moduli space of smoothable Kahler-Einstein Fano
varieties constructed in arXiv:1411.0761
. As a consequence, the moduli space of Kahler-Einstein Fano
manifolds is quasi-projective.)

- with Chi Li and Chenyang Xu, Degeneration of Fano Kahler-Einstein manifolds. arXiv:1411.0761.

- with Chenyang Xu,
*Nonexistence of asymptotic GIT compactification,*arXiv:1212.0173, Duke Math. J. 163, no. 12, (2014) 2217-2241.

- with Jun Li,
*Hilbert Mumford criterion for nodal curves*. arXiv:1108.1727. Compos. Math.**151**(2015), 2076-2130

*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, G_2 Geometry, Isometric embeddings)

- with D. H. Phong, Jian Song and Jacob Sturm, Convergence of the conical Ricci flow on S^2 to a soliton. arXiv:1503.04488.

(This is a continuation of arXiv:1407.1118. We
show that in the unstable case, the limiting metric of conical
Ricci flow is the unique shrinking soliton with cone
singularity $\beta_k[0]+\sum_{j<k}\beta_j[\infty]$.)

- with D. H. Phong, Jian Song and Jacob Sturm, The Ricci flow on the sphere with marked points. arXiv:1407.1118.

(We prove that the conical Ricci flow on
2-sphere converges in all three (stable, semistable and unstable)
cases to a unique conical shrinking Ricci soliton)

- with Ved Datar, Bin Guo and Jian Song, Connecting toric manifolds by
conical Kahler-Einstein metrics. arXiv:1308.6781.
Adv. Math.
**323**(2018) 38-83.

(We prove that for a toric log Fano pair
$(X,D)$, the existence of conical Kahler-Einstein metric is
equivalent to $(X,D)$ being log K-polystable. Moreover, we show
that any two toric manfolds can be connected via a continuous path
of toric log Fano pairs admitting conical Kahler-Einstein metrics
in the Gromov-Hausdorff topology.)

- with Ke Zhu, Isometric embeddings via heat kernel. arXiv:1305.5613, J. Differential Geom. 99, no. 3, (2015) 497-538.

(For any Riemannian manifolds, we constructed a
canonical family of isometric embedding into (or the unit sphere
inside of) Euclidean spaces via a canonical perturbation of heat
kernel embedding.)

- with Naichung Conan Leung and Ke Zhu, Instantons in G_2 manifolds from
J-holomorphic curves in coassociative submanifolds. arXiv:1303.6728.
Proceedings of Gokova Geometry-Topology Conference 2012, 89-111.

(This is a survey of the work in arXiv:1107.1947.)

- with Jian Song,
*The greatest Ricci lower bound, conical Einstein metrics and the Chern number inequality.*arXiv:1207.4839.

(We parially confirm a conjecture of Donaldson
relating the greatest Ricci lower bound to the conical
Kahler-Einstein metric on a Fano manifold. Moreover, we also
establish a Miyaoka-Yau type Chern number inequality for
Fano manifolds.)

- with Naichung Conan Leung and Ke Zhu,
*Thin instantons in G2-manifolds and Seiberg-Witten invariants.*arXiv:1107.1947, J. Differential Geom. 95, no. 3, (2013) 419-483.

- Canonical metrics on stable vector bundles. Comm. Anal. Geom. 13, no. 2, (2005), 253-285.

Symplectic Geometry (Moment map, Symplectic Quotient)

- with Naichung Conan Leung, A quadratic inequality for sum of co-adjoint orbits. Comm. Anal. Geom. 17, no.2, (2009) 265-282.

(Motivated by classical Miyaoka-Yau's Chern
number inequality, we establish a general quadratic inequality for
a sum of co-adjoint orbits. )

- Riemannian moment map. Comm. Anal. Geom. 16, no. 4, (2008) 837-863.

(We extend the Kahler moment map theory to the
Riemannian manifolds with a action of real reductive group.)

- Moment map, Futaki invariant and stability of projective manifold. Comm. Anal. Geom. 12, no. 5, (2004) 1009-1037.

(By applying the moment map theory, we give a
unified proof of several classical result in cscK problem. In
particular, a new proof of S. W. Zhang's result on the geometric
interpretation of Chow stability of a polarized manifold is
given.)