Jian Song 


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




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.



Fall 2016: Introduction to differential geometry (640: 532)


Publication and preprints 


1. On Feldman-Ilmanen-Knopf conjecture for the blow-up behavior of the Kahler-Ricci flow, to appear in Math. Res. Lett., with B. Guo, to appear in Math. Res. Letters, arXiv:1505.04869


2. Geometric convergence of the Kahler-Ricci flow on complex surfaces of general type, with B. Guo and B. Weinkove, to appear in I.M.R.N., arXiv:1505.00705


3. Convergence of the conical Ricci flow on S^2 to a soliton, with D.H. Phong, J. Sturm and X. Wang, arXiv:1503.04488


4. Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata’s base point free theorem, arXiv:1409.8374


5. The Ricci flow on the sphere with marked points, with D.H. Phong, J. Sturm and X. Wang, arXiv:1407.1118


6. Riemannian geometry of Kahler-Einstein currents, arXiv:1404.0445


7. 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:1309.5013


8. The degenerate J-flow and the Mabuchi energy on minimal surfaces of general type, with B. Weinkove, Universitatis Iagellonicae Acta Mathematica, no. 50, (2013)m 89-106, arXiv:13091810


9. Connecting toric conical Kahler-Einstein manifolds, with V. Datar, B. Guo and X. Wang, arXiv:1308.6781


10. Ricci flow and birational surgery, arXiv:1304.2607


11. 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:1211.5849


12. 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:1207.4839


13. The J-flow on Kahler surfaces: a boundary case, with H. Fang, M. Lai and B. Weinkove, Anal. PDE 7 (2014), no. 215-226arXiv:1204.4068


14. Some Type I solutions of Ricci flow with rotational symmetry, I.M.R.N., no. 16, 7365-7381, arXiv:1203.2688


15. On a conjecture of Candelas and de la Ossa, to appear in Comm. Math. Phys. 334 (2015), no. 2, 697--717, arXiv:1201.4358


16. Bounding scalar curvature for global solutions of the Kahler-Ricci flow, with G. Tian, American Journal of Mathematics, vol. 138, no. 3, 2016, arXiv:1111.5681


17. The Kahler-Ricci flow on projective bundles, with B. Szekelyhidi and B. Weinkove, Int. Math. Res. Not. IMRN 2013, no. 2, 243-257, arXiv:1107.2144


18. Contracting exceptional divisors by the Kahler-Ricci flow II, with B. Weinkove, Proc. Lond. Math. Soc. (3) 108 (2014), no. 6, 1529-1561, arXiv:1102.1759


19. Metric flips with Calabi ansatz, with Y. Yuan, Geom. Func. Anal. 22 (2012), no. 1, 240-265, arXiv:1011.1608


20. Contracting exceptional divisors by the Kähler-Ricci flow, with B. Weinkove, Duke Math. J. 162 (2013), no.2, 367-415, arXiv:1003.0718


21. The Kahler-Ricci flow through singularities, with G. Tian, to appear in Invent. Math. arXiv:0909.4898


22. 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


23. Finite time extinction of the Kahler-Ricci flow, Math. Res. Lett., 21 (2014), no. 6, 1435-1449, arXiv:0905.0939


24. The Kahler-Ricci flow on Hirzebruch surfaces, with B. Weinkove, J. Reine Angew. Math. 659 (2011), 141-168, arXiv:0903.1900


25. 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:0809.0941


26. Canonical measures and Kahler-Ricci flow, with G. Tian, J. Amer. Math. Soc. 25 (2012), no. 2, 303-353, arXiv:0802.2570


27. Test configurations, large deviations and geodesic rays on toric varieties, with S. Zelditch, Adv. Math. 229 (2012), no. 4 2338-2378, arXiv:0712.3599


28. 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:0707.3082


29. 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:0706.2852


30. 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:0705.4048


31. Constructions of Kahler-Einstein metrics with negative scalar curvature, with B. Weinkove, Math. Ann. 347 (2010), no. 1, 59-79, arXiv:0704.1005


32. Convergence of Bergman geodesics on CP^1, with S. Zelditch, Ann. Inst. Fourier (Grenoble) 57 (2007), no. 7, 2209-2237, arXiv:math/0703517


33. On Donaldson's flow of surfaces in a hyperkahler four-manifold, with B. Weinkove, Math. Z. 256 (2007), no. 4, 769-787, arXiv:math/0606394


34. 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:math/0604076


35. The Kahler-Ricci flow on surfaces of positive Kodaira dimension, with G. Tian, Invent. Math. 170 (2007), no. 3, 609-653, arXiv:math/0602150


36. Energy functionals and canonical Kahler metrics, with B. Weinkove, Duke Math. J. 137 (2007), no. 1, 159-184, arXiv:math/0505476


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


38. 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:math/0410418


39. The α-invariant on Toric Fano Manifolds, Amer. J. Math. 127 (2005), no. 6, 1247-1259,arXiv:math/0307288


40. The α-invariant on CP^2 blown up at two points, Trans. Amer. Math. Soc. 357 (2005), no. 1 45-57, arXiv:math/0205041






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:1212.3653


2. Complex Monge-Ampere equations, with D.H. Phong and J. Sturm, Surveys in Differential Geometry, vol. 17, 327-411 (2012) arXiv:1209.2203


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