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
preprints in reversed chronological order:
Algebraic Geometry (GIT, Moduli problem)
- with Yuguang Zhang, Balanced
degenerating Abelian varieties, arXiv:1605.01860.
- with Chi Li and Chenyang Xu, Quasi-projectivity fo the moduli
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
consequence, the moduli space of Kahler-Einstein Fano manifolds is
(We construct a proper
space parametrizing all smoothable
K-polystable Fano varieties.)
- with Chi Li and Chenyang Xu, Degeneration of Fano
(We show that if a KSBA limit
family of smooth canonically polarized varieties is not asymptotic
Chow semistable then this family does not yield any asymptotic GIT
semistable limit. This answered a longstanding question firstly
by Mumford in the preface of the book ' Geometric Invariant
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
semistable limit, then it must be identical to the KSBA limit.)
(We prove by direct verifying
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
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 intersection
(We construct explicit
embeddings for principally polairzed Abelian varieties and
they converges to the flat metric directly without using Donaldson's
celebrated work on balanced embeddings of cscK manifold.)
(We proved a conjecture of
Donaldon stating that a holomorphic vector bundle over a
polarized manifold being Gieseker stable is equivalent to the fact
the Kodaira embedding into Grassmannian induced by the global
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
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
flow is the unique shrinking soliton with cone singularity
- with D. H. Phong, Jian Song and Jacob Sturm, The Ricci flow on the sphere with
(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
Kahler-Einstein metrics. arXiv:1308.6781.
(We prove that for a toric log Fano pair $(X,D)$, the
of conical Kahler-Einstein metric is equivalent to $(X,D)$ being
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,
(For any Riemannian manifolds, we constructed a canonical family
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.
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
Ricci lower bound to the conical Kahler-Einstein metric on a Fano
manifold. Moreover, we also establish a Miyaoka-Yau type Chern
inequality for Fano manifolds.)
- with Naichung Conan Leung and Ke Zhu, Thin instantons
G2-manifolds and Seiberg-Witten invariants. arXiv:1107.1947,
Differential Geom. 95,
(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'
regular J-holomorphic curves in C. We also explain their
with the Seiberg-Witten invariants for C.)
(We prove that for a Mumford
stable vector bundle over a polarized manifold, the balanced
metrics converges to the twisted Hermitian-Einstein metric. This
vector bundle version of Donaldson's seminal work on balanced
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
(We extend the Kahler moment map theory to the Riemannian
with a action of real reductive group.)
(By applying the moment map theory, we give a unified proof of
classical result in cscK problem. In particular, a new proof of
result on the geometric interpretation of Chow stability of a
manifold is given.)