Resume (Here is my CV):
- Ph.D. 2002, Brandeis University (supervised by S.-T.
- Adjunct Assistant Professor, 2002-2003, UCLA.
- Hedrick Assistant Professor, 2003-2006 (on leave in
- 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.
Interest: Differential Geometry, Algebraic
Geometry and Symplectic Geometry.
preprints in reversed chronological order:
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
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.)
(We construct a proper
algebraic space parametrizing all smoothable K-polystable Fano
- with Chi Li and Chenyang Xu, Degeneration of Fano
Kahler-Einstein manifolds. arXiv:1411.0761.
(We show that if a KSBA limit
of family of smooth canonically polarized varieties is not
asymptotic GIT Chow semistable then this family does not yield any
asymptotic GIT Chow semistable limit. This answered a longstanding
question firstly asked by Mumford in the preface of the book ' Geometric
Invariant Theory'. In fact, we show that the semi-stable
filling minimizes the GIT height and the KSBA limit minimizes the
degree of CM line bundle. Since the latter is the limit of the
formers, if there is a asymptotic GIT Chow semistable limit, then it
must be identical to the KSBA limit.)
(We prove by direct verifying
the Hilbert-Mumford criterion that a slope stable polarized weighted
pointed nodal curve is Chow asymptotic stable. In particular, this
solves a question raised by Mumford and Gieseker.)
(We introduce a cohomological
invariant for any family GIT problem. This is an analogue of
Falting's height introduced by Zhang. As an application, we
establish the converse to the Cornalba-Harris' theorem.
As a special case, we reinterpret Donaldson-Futaki invariant as a
(We construct explicit
balanced embeddings for principally polairzed Abelian varieties
and prove they converges to the flat metric directly without
using Donaldson's celebrated work on balanced embeddings of
(We proved a conjecture of
Donaldon stating that a holomorphic vector bundle over a
polarized manifold being Gieseker stable is equivalent to the fact
that the Kodaira embedding into Grassmannian induced by the global
sections can be balanced.)
Differential Geometry (Einstein metric, G_2 Geometry, Isometric
- 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
show that in the unstable case, the limiting metric of conical
Ricci flow is the unique shrinking soliton with cone
- 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
- 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.
- 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
- 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.
(For two nearby disjoint
coassociative submanifolds C and C' in a G_2 manifold, we
construct thin instantons with boundaries lying on C and C'
from regular J-holomorphic curves in C. We also explain their
relationship with the Seiberg-Witten invariants for C.)
(We prove that for a Mumford
stable vector bundle over a polarized manifold, the balanced
Bergman metrics converges to the twisted Hermitian-Einstein
metric. This is a vector bundle version of Donaldson's seminal
work on balanced embedding of a polarized cscK manifold.)
Symplectic Geometry (Moment map, Symplectic Quotient)
(Motivated by classical Miyaoka-Yau's Chern
number inequality, we establish a general quadratic inequality for
a sum of co-adjoint orbits. )
(We extend the Kahler moment map theory to the
Riemannian manifolds with a action of real reductive group.)
(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