Brief Resume (Here is my CV):

Research Interest: Differential Geometry, Algebraic Geometry and Symplectic Geometry.
Papers and preprints in reversed chronological order:

Algebraic Geometry
(GIT, Moduli problem)

        (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 varieties.)
        (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 intersection formula.)
        (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  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 that the Kodaira embedding into Grassmannian induced by the global sections can be balanced.)

Differential Geometry (Einstein metric, G_2 Geometry, Isometric embeddings)

        (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 $\beta_k[0]+\sum_{j<k}\beta_j[\infty]$.)
        (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)
        (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.)
        (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.)
        (This is a survey of the work in arXiv:1107.1947.)
        (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.)
        (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 Zhang's result on the geometric interpretation of Chow stability of a polarized manifold is given.)


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