** **

** ****Jian Song
**宋 劍

Professor

Department
of Mathematics

Rutgers,
The State University of New Jersey

Hill
526, Busch Campus

110
Frelinghuysen Road, Piscataway, NJ 08854-8019

Email:
jiansong@math.rutgers.edu

Phone:
848.445.7983

Fax:
732.445.5530

I do
research in differential geometry, global complex geometry, geometric analysis
and partial differential equations.

Here
is my CV.

**Teaching **

Spring 2017: Elementary
partial differential equations (640:423)

**Publication
and preprints **

*- Degeneration of Kahler-Einstein
manifolds of negative scalar curvature*, arXiv

*- Geometric estimates for complex Monge-Ampere
equations, *with X. Fu and B. Guo, arXiv

*- Connecting toric conical Kahler-Einstein manifolds, *with
V. Datar, B. Guo and X.
Wang, Adv. Math. 323 (2018), 38-83, arXiv

*- The Kahler-Ricci
flow through singularities, *with G. Tian, Invent. Math. 207 (2017), no. 2, 519-595, arXiv

*- On Feldman-Ilmanen-Knopf
conjecture for the blow-up behavior of the Kahler-Ricci
flow, *to appear in Math. Res. Lett., with B. Guo, Math. Res. Lett. 23 (2016), no. 6, 1681-1719, arXiv

*- Geometric convergence of the Kahler-Ricci flow on complex surfaces of general type, *with
B. Guo and B. Weinkove,
I.M.R.N. 2016, no. 18, 5652-5669, arXiv

*- Schauder estimates for equations
with cone metrics, I, *with B. Guo,* *arXiv

*- Convergence of the conical Ricci flow on S^2
to a soliton, *with D.H. Phong, J. Sturm and X. Wang, arXiv

*- Riemannian geometry of Kahler-Einstein
currents II: an analytic proof of KawamataÕs base
point free theorem*, arXiv

*- The Ricci flow on the sphere with marked
points, *with D.H. Phong, J. Sturm and X. Wang,
arXiv

*- Riemannian geometry of Kahler-Einstein
currents*, arXiv

*- A remark on Kahler
metrics with conical singularities along a simple normal crossing divisor*,
with V. Datar, Bull. of Lond. Math. Soc., 47 (2015), no. 6, 1010-1013, arXiv

*- The degenerate J-flow and the Mabuchi energy
on minimal surfaces of general type, *with B. Weinkove, Universitatis Iagellonicae Acta Mathematica, no. 50, (2013), 89-106, arXiv

*- Ricci flow and birational
surgery*, arXiv

*- Degeneration of Kahler-Ricci
solitons on Fano manifolds,
*with D.H. Phong and J. Sturm, Universitatis Iagellonicae Acta Mathematica, No. 52 (2015),
29-43, arXiv

*- The greatest Ricci lower bound, conical Einstein metrics and
the Chern number inequality,with*
X. Wang, Geom. Topol., 20 (2016), no. 1, 49-102, arXiv

*- The J-flow on Kahler
surfaces: a boundary case, *with H. Fang, M. Lai and B. Weinkove, Anal. PDE 7 (2014), no. 215-226, arXiv

*- Some Type I solutions of Ricci flow with
rotational symmetry,* I.M.R.N., no. 16, 7365-7381, arXiv

* *

*- On a conjecture of Candelas and de la Ossa, *to
appear in Comm. Math. Phys. 334 (2015), no. 2, 697--717*, arXiv*

*- Bounding scalar curvature for global
solutions of the Kahler-Ricci flow, *with
G. Tian, American Journal of Mathematics, vol. 138,
no. 3, 2016, arXiv

*- The Kahler-Ricci
flow on projective bundles, *with B. Szekelyhidi and B. Weinkove, Int.
Math. Res. Not. IMRN 2013, no. 2, 243-257, arXiv

*- Contracting exceptional divisors by the Kahler-Ricci flow II, *with B. Weinkove, Proc. Lond. Math. Soc.
(3) 108 (2014), no. 6, 1529-1561,* arXiv*

*- Metric flips with Calabi
ansatz, *with Y. Yuan, Geom. Func. Anal. 22 (2012), no. 1, 240-265, arXiv

*- Contracting exceptional divisors by the KŠhler-Ricci flow, *with B. Weinkove, Duke Math. J. 162 (2013), no.2, 367-415, arXiv

*- Convergence of the Kahler-Ricci
flow on singular Calabi-Yau varieties, with Y. Yuan,
ALM 21, Advances in Geometric Analysis (volume dedicated to Professor Shing-Tung Yau), 119-138, 2012*

*- Finite time extinction of the Kahler-Ricci flow, *Math. Res. Lett., 21 (2014), no. 6,
1435-1449,* arXiv*

*- The Kahler-Ricci
flow on Hirzebruch surfaces,*
with B. Weinkove, J. Reine Angew. Math. 659 (2011), 141-168, arXiv

*- The modified Kahler-Ricci
flow and solitons, *with D.H. Phong, J. Sturm and B. Weinkove,
Comment. Math. Helv. 86 (2011), no. 1, 91-112, arXiv

*- Canonical measures and Kahler-Ricci
flow, *with G. Tian, J. Amer. Math. Soc. 25
(2012), no. 2, 303-353, arXiv

*- Test configurations, large deviations and
geodesic rays on toric varieties,*
with S. Zelditch, Adv. Math. 229 (2012), no. 4
2338-2378, arXiv

*- Bergman metrics and geodesics in the space
of KŠhler metrics on toric
varieties, *with S. Zelditch, Anal. PDE 3 (2010),
no. 3, 295-358, arXiv

*- The Kahler-Ricci
flow with positive bisectional curvature, *with D.H. Phong, J. Sturm and B. Weinkove,
Invent. Math. 173 (2008), no. 3, 651-665, arXiv

*- The Kahler-Ricci flow
and the $\bar\partial$ operator on vector fields, *with
D.H. Phong, J. Sturm and B. Weinkove,
J. Differential Geom. 81 (2009), no. 3, 631-647, arXiv

*- Constructions of Kahler-Einstein
metrics with negative scalar curvature, *with B. Weinkove, Math. Ann. 347 (2010), no. 1, 59-79, arXiv

*- Convergence of Bergman geodesics on CP^1, *with
S. Zelditch, Ann. Inst. Fourier (Grenoble) 57 (2007),
no. 7, 2209-2237, arXiv

*- On Donaldson's flow of surfaces in a hyperkahler four-manifold, *with
B. Weinkove, Math. Z. 256 (2007), no. 4, 769-787, arXiv

*- The Moser-Trudinger
inequality on Kahler-Einstein manifolds, *with
D.H. Phong, J. Sturm and B. Weinkove,
Amer. J. Math. 130 (2008), no. 3, 651-665, arXiv

*- The Kahler-Ricci
flow on surfaces of positive Kodaira dimension, *with
G. Tian, Invent. Math. 170 (2007), no. 3, 609-653, arXiv

*- Energy functionals
and canonical Kahler metrics, *with
B. Weinkove, Duke Math. J. 137 (2007), no. 1,
159-184, arXiv

*- The Kahler-Ricci flow on Kahler surfaces, *Proceedings of Gokova Geometry-Topology Conference 2006, 123-135

*- On the convergence and singularities of the
J-flow with applications to the Mabuchi energy,with*
B. Weinkove, Comm. Pure Appl. Math. 61 (2008), no. 2,
210-229, arXiv

*- The α-invariant on Toric
Fano Manifolds, *Amer. J. Math. 127
(2005), no. 6, 1247-1259, arXiv

*- The α-invariant on CP^2 blown up at two
points, *Trans. Amer. Math. Soc. 357 (2005), no. 1, 45-57, arXiv

**Notes**

*1. Lecture notes on the Kahler-Ricci
flow*, with B. Weinkove, ÔAn introduction
to the Kahler-Ricci flowÕ, 89-188, Lecture Notes in
Math., 2086, Springer, Cham, 2013, arXiv

*2. Complex Monge-Ampere
equations,* with D.H. Phong and J. Sturm, Surveys
in Differential Geometry, vol. 17, 327-411 (2012), arXiv

*3. The Szego kernel
on an orbifold circle bundle,*
thesis at Columbia University, 2004

**Seminar and Conference**

Complex analysis and geometry seminar, Rutgers

Analysis, complex geometry and mathematical physics: a
conference in honor of Duong H. Phong,
2013

Summer school in complex geometry, Rutgers,
2013