Jian Song 

 

Description: Macintosh HD:Users:jiansong:Dropbox:homepage:2015:DSCF4356.jpg

 

 

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 Kawamata’s 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 Kähler-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 Kähler 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, ‘An introduction to the Kahler-Ricci flow’, 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