Teaching

Fall 2014: Multivariable Calculus 640:251   

Publication and preprints

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

Riemannian geometry of Kahler-Einstein currents, arXiv:1404.0445

A remark on Kahler metrics with conical singularities along a simple normal crossing divisor, with V. Datar, arXiv:1309.5013

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

Ricci flow and birational surgery, arXiv:1304.2607

Degeneration of Kahler-Ricci solitons on Fano manifolds, with D.H. Phong and J. Sturm, arXiv:1211.5849

The degenerate J-flow and the Mabuchi energy on minimal surfaces of general type, with B. Weinkove, to appear in Universitatis Iagellonicae Acta Mathematica, arXiv:13091810

The greatest Ricci lower bound, conical Einstein metrics and the Chern number inequality, with X. Wang, arXiv:1207.4839

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:1204.4068

Some Type I solutions of Ricci flow with rotational symmetry, to appear in I.M.R.N., arXiv:1203.2688

On a conjecture of Candelas and de la Ossa, to appear in Comm. Math. Phys., arXiv:1201.4358

Bounding scalar curvature for global solutions of the Kahler-Ricci flow, with G. Tian, arXiv:1111.5681

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

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

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

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

The Kahler-Ricci flow through singularities, with G. Tian, arXiv:0909.4898

Finite time extinction of the Kahler-Ricci flow, arXiv:0905.0939

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

I do research in differential geometry, global complex geometry, geometric analysis and partial differential equations. Here is my CV.

Seminar and Conference

Complex analysis and geometry seminar, Rutgers

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

Summer school in complex geometry, Rutgers

Notes

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

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

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