- 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 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 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.

(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
Zhang's
result on the geometric interpretation of Chow stability of a
polarized
manifold is given.)