Curriculum Vitae

Xiuxiong Chen

Education

• PhD., Pure Mathematics, University of Pennsylvania, 1994.

• M.A., Graduate School of Academic Sinica, Beijing, China, 1989.

• B.A., Pure Mathematics, University of Science and Technology of China, Hefei, China, 1987.

Professional positions

• 09/2010–, Professor, Stony Brook University.

• 01/2007–06/2007, Visiting Professor, Princeton University.

• 2005–2010, Professor, University of Wisconsin at Madison.

• 2002-2005, Associate Professor, University of Wisconsin at Madison.

• 1998-2002, Assistant Professor, Princeton University.

• 1996-1998, NSF Post-doctoral Fellow, Stanford University.

• 1994-1996, Instructor, McMaster University, Canada.

Honors and Awards

• 1996-2000, National Science foundation postdoctoral Fellowship.

• 08/2002, Invited address at International Congress of Mathematicians, Beijing, China.

• 04/2005, Invited address at AMS regional meeting in Newark, Delware.

• 04/09/2010-04/11/2010, Invited lecture at 25th Geometry Festival, Courant Institute.

• 2015, Fellow of the American Mathematical Society.

• 2016, Simons Fellow in Mathematics.

• 2019, Veblen Prize in Geometry.

• 2019, Simons Investigator Award. Xiuxiong Chen Curriculum vitae

PhD. Students and Theses Supervised/co-supervised

• Yingyi Wu (PhD., 2005, University of Science and Technology). Some problems on HCMU metrics in Riemannian Surfaces.

• Brian Weber (PhD., 2007, UW-Madison), Moduli Spaces of Extremal Kahler¨ Manifolds.

• Weiyong He (PhD., 2007, UW-Madison), Extremal Metrics, The Stability Conjecture and the Cal- abi Flow.

• Haozhao Li (PhD, 2007, Peking University), Energy Functionals and Kahler-Ricci¨ Flow.

• Bing Wang (PhD., 2008, UW-Madison), On the Extension of the Ricci flow.

• Yudong Tang (PhD., 2008, UW-Madison), Geodesic Rays and Test Configurations.

• Weidong Yin(PhD., 2009, UW-Madison), Weak Solution of Yang-Mills Flow in Dimension N?4.

• Song Sun (PhD., 2010, UW-Madison), Kempf-Ness theorem and uniqueness of extremal metrics.

• Simone Calamai (PhD., 2010, Universita` degli Studi di Firenze), The Calabi’s Metric for the Space of Kahler¨ Metrics.

• Hongnian Huang, (PhD., 2010, UW-Madison), Calabi Flow on Toric Variety.

• Kai Zheng (PhD., 2010, Chinese Academy of Science), The pseudo-Calabi flow.

• Yajun Yan (PhD., 2010, University of Science and Technology of China), Existence and Uniqueness of Ricci Flow on Surfaces with Initial Curvature Unbounded From Below.

• Yuanqi Wang (PhD., 2011, UW-Madison), On the Ricci flows and Ricci solitons.

• Fang Yuan (PhD., 2012, UW-Madison), The Weak Compactness of Ricci Flow with Ricci Curvature Bounded from Below.

• Xiaojie Wang (PhD., 2014, Stony Brook University), Uniqueness of Ricci Flow Solution on Non- compact Manifolds and Integral Scalar Curvature Bound.

• Long Li (PhD., 2014, Stony Brook University), On the uniqueness of singular Kahler¨ Einstein metrics.

• Seyed Ali Aleyasin (PhD., 2014, Stony Brook University), Space of Kahler¨ metrics on singular and non-compact manifolds.

• Yongqiang Liu (PhD., 2015, University of Science and Technology of China), Divisibility results for Alexander type invariants of hypersurface complements.

• Chengjian Yao (PhD., 2015, Stony Brook University), Conical Kahler-Einstein¨ Metrics and Its Applications.

• Yu Zeng (PhD., 2016, Stony Brook University), Deformations of twisted cscK metrics.

• Robin Sebastian Krom (Ph.D., 2016, ETH Zurich),¨ The Donaldson Geometric Flow

• Gao Chen (PhD., 2017, Stony Brook University), Classification of gravitational instantons with faster than quadratic curvature decay.

2 Xiuxiong Chen Curriculum vitae

• Shaosai Huang (PhD., 2018, Stony Brook University), On the collapsing and convergence of Ricci flows and solitons. • Selin Taskent (PhD., 2019, Stony Brook University), Rotationally symmetric Kahler metrics with extremal conditon. • Fangyu Zou (PhD., 2019, Stony Brook University), Monge-Ampere equation on the complement of a divisor and On the Chern-Yamabe flow. • Current students: Jean-Franc¸ois Arbour (Expected 2020), Jiasheng Teh (Expected 2021), Jae Ho Cho (Expected 2021)

Postdocs Supervised or Co-Supervised

• 2003-2006, Lijing Wang (UW-Madison) • 2004-2007, Aobing Li (UW-Madison) • 2013-2017, Lorenzo Foscolo (Stony Brook University) • 2014-2017, Henri Guenancia (Stony Brook University) • 2014-2017, Alex Waldron (SCGP) • 2016-present, Ruobing Zhang. (Stony Brook University) • 2017-present, Yu Li, (Stony Brook University) • 2018-present, Jingrui Cheng, (Stony Brook University)

NSF grants

• NSF Grant DMS 1914719 (2019-2022), Complex Monge Ampere equation and Calabi flow prob- lems. • NSF Grant DMS-1603351 (2015-2017), Conference on Differential Geometry. • NSF Grant DMS-1418942 (2013-2015), Conference on Geometric Analysis and Relativity. • NSF Grant DMS-1515795 (2015-2019), Complex Monge-Ampere` equation, the Kahler-Einstein¨ Problem and constant scalar curvature metric problems • NSF Grant DMS-1211652 (2012-2015), Extremal Kahler¨ metrics, the Kahler¨ Ricci flow and the Calabi flow. • NSF Grant DMS-0907778 (2009-2012), Extremal Kahler¨ Metrics. • NSF Grant DMS-0406346 (2004-2009), Extremal Kahler¨ Metrics. and Geometric Flow Equations. • NSF Grant DMS-0110321 (2001-2004), The Kahler¨ Ricci Flow and the Extremal Kahler¨ Metric. • NSF Grant DMS-0302452, Great Lakes Geometry Conference. • NSF-AMS travel support for International Congress of Mathematicians 2002, Beijing, China. • NSF Post-doctoral Fellowship DMS-9627404 (1996-2000).

3 Xiuxiong Chen Curriculum vitae

Selected Conferences Co-Organized

• Geometry of Manifolds (October 23-October 27, 2017), SCGP.

• Conference on Differential Geometry (July 5- July 9, 2016), Center De Recherches Mathematiques.´

• Geometric flow program (October 13-December 19, 2014), SCGP.

• Geometric Analysis and Relativity (July 6- July 10, 2014), USTC.

• Summer School in Kahler¨ Geometry, June 24- July 5, 2012, SCGP.

• International conference on Nonlinear PDE and applications (August 1- August 6, 2011), USTC.

• Annual Summer School on Geometric Analysis (2003-present), USTC.

• Mini Workshop on Algebraic Geometry (June 17-July 18, 2011),

• Singularity Theory conference, ( July 25 - July 31, 2011), USTC.

• Workshop on Extremal Kahler¨ Metrics (March 21- March 25, 2011), SCGP.

• Differentialgeometrie im Groβen (July 3- July 9, 2011), Oberwolfach.

• Pacific Rim Complex geometry Conference (2006 - 2017).

• Workshop on complex geometry analysis (June 28-July 3, 2009), Banff, Canada.

• School of Differential geometry ( June 8 - June 29, 2008), ICTP, Trieste, Italy.

• Summer school: June 8 - June 20, Conference: June 21 - June 29, 2008, USTC.

• Great Lake geometry conference (April 10 - April 11, 2010), Madison.

Publications

1. On the existence of constant scalar curvature Kahler¨ metric: a new perspective, Ann. Math. Quebec´ 42, (2018), no. 2, pp 169-189.

2. Kahler-Ricci¨ flow, Kahler-Einstein¨ metric, and K-stability (co-authors: S. Sun and B. Wang), Ge- ometry & Topology 22 (2018), no. 6, 3145-3173.

3. Gravitational instantons with faster than quadratic curvature decay (II) (co-author: G. Chen), J. Reine Angew. Math. 726 (2018), https://doi.org/10.1515/crelle-2017-0026.

4. Space of Ricci flows (II)–part A: moduli of singular Calabi-Yau spaces (co-author: B. Wang), Forum Math. Sigma (2017), Vol. 5, e32, 103 pp, doi:10.1017/fms.2017.28.

5. On the regularity problem of complex Monge-Ampere` equations with conical singularities (co- author: Y. Q. Wang), Ann. Inst. Fourier (Grenoble) 67 (2017), no. 3, 969-1003.

6. A note on Ricci flow with Ricci curvature bounded below (co-author: F. Yuan), J. Reine Angew. Math. 726 (2017), 29-44.

7. Approximation of weak geodesics and subharmonicity of Mabuchi energy (co-authors: L. Li, M. Paun),˘ Calc. Var. Partial Differential Equations 55 (2016), no. 4, Art. 106, 28 pp.

4 Xiuxiong Chen Curriculum vitae

8. The interior regularity of the Calabi flow on a toric surface (co-authors: H. N. Huang, L. Sheng), Calc. Var. Partial Differential Equations 55 (2016), no. 4, Art. 106, 28 pp.

9. C2,α-estimate for Monge-Ampere` equations with Holder-continuous¨ right hand side (co-author: Y. Q. Wang), Ann. Global Anal. Geom. 49 (2016), no. 2, 195-204.

10. Bessel functions, heat kernel and the conical Kahler-Ricci¨ flow (co-author: Y. Q. Wang), J. Funct. Anal. 269 (2015), no. 2, 551-632.

11. On four-dimensional anti-self-dual gradient Ricci solitons (co-author: Y. Q. Wang), J. Geom. Anal. 25 (2015), no. 2, 1335-1343.

12. Kahler-Einstein¨ metrics on Fano manifolds. III: Limits as cone angle approaches 2π and comple- tion of the main proof (co-authors: S. K. Donaldson, S. Sun), J. Amer. Math. Soc. 28 (2015), no. 1, 235-278.

13. Kahler-Einstein¨ metrics on Fano manifolds. II: Limits with cone angle less than 2π (co-authors: S. K. Donaldson, S. Sun), J. Amer. Math. Soc. 28 (2015), no. 1, 199-234.

14. Kahler-Einstein¨ metrics on Fano manifolds. I: Approximation of metrics with cone singularities (co-authors: S. K. Donaldson, S. Sun), J. Amer. Math. Soc. 28 (2015), no. 1, 183-197.

15. Calabi flow, geodesic rays, and uniqueness of constant scalar curvature Kahler¨ metrics (co-author: S. Sun), Ann. of Math. (2) 180 (2014), no. 2, 407-454.

16. Integral bounds on curvature and Gromov-Hausdorff limits (co-author: S. K. Donaldson), J. Topol. 7 (2014), no. 2, 543-556.

17. Kahler-Einstein¨ metrics and stability (co-authors: S. K. Donaldson, S. Sun), Int. Math. Res. Not. 2014, no. 8, 2119-2125.

18. Liouville energy on a topological two sphere (co-author: M. J. Zhu), Commun. Math. Stat. 1 (2013), no. 4, 369-385.

19. On the conditions to extend Ricci flow (III) (co-author: B. Wang), Int. Math. Res. Not. 2013, no. 10, 2349-2367.

20. Volume estimates for Kahler-Einstein¨ metrics and rigidity of complex structures (co-author: S. K. Donaldson), J. Differential Geom.93 (2013), no. 2, 191-201.

21. Volume estimates for Kahler-Einstein¨ metrics: the three-dimensional case (co-author: S. K. Don- aldson), J. Differential Geom.93 (2013), no. 2, 175-189.

22. The pseudo-Calabi flow (co-author: K. Zheng), J. Reine Angew. Math. 674 (2013), 195-251.

23. Space of Kahler¨ metrics (V): Kahler¨ quantization (co-author: S. Sun), Metric and differential ge- ometry, 19-41, Progr. Math., 297, Birkhauser/Springer,¨ Basel, 2012.

24. The complex Monge-Ampere` equation on compact Kahler¨ manifolds (co-author: W. Y. He), Math. Ann. 354 (2012), no. 4, 1583-1600.

25. The Kahler¨ Ricci flow on Fano manifolds (I) (co-author: B. Wang), J. Eur. Math. Soc. (JEMS) 14 (2012), no. 6, 2001-2038.

5 Xiuxiong Chen Curriculum vitae

26. Space of Ricci flows I (co-author: B. Wang), Comm. Pure Appl. Math. 65 (2012), no. 10, 1399- 1457.

27. The Kahler¨ Ricci flow on Fano surfaces (I) (co-author: B. Wang), Math. Z. 270 (2012), no. 1-2, 577-587.

28. The space of volume forms (co-author: W. Y. He), Int. Math. Res. Not. 2011, no. 5, 967-1009.

29. On the weak Kahler-Ricci¨ flow (co-authors: G. Tian, Z. Zhang), Trans. Amer. Math. Soc. 363 (2011), no. 6, 2849-2863.

n 30. Moduli spaces of critical Riemannian metrics with L 2 norm curvature bounds (co-author: B. We- ber), Adv. Math. 226 (2011), no. 2, 1307-1330.

31. The Calabi flow on toric Fano surfaces (co-author: W. Y. He), Math. Res. Lett. 17 (2010), no. 2, 231-241.

32. Remarks on Kahler¨ Ricci flow (co-author: B. Wang), J. Geom. Anal. 20 (2010), no. 2, 335-353.

33. Stability of Kahler-Ricci¨ flow (co-author: H. Z. Li), J. Geom. Anal. 20 (2010), no. 2, 306-334.

34. A note on Kahler-Ricci¨ soliton (co-authors: S. Sun, G. Tian), Int. Math. Res. Not. 2009, no. 17, 3328-3336.

35. Kahler-Ricci¨ flow with small initial energy (co-authors: H. Z. Li, B. Wang), Geom. Funct. Anal. 18 (2009), no. 5, 1525-1563.

36. Space of Kahler¨ metrics. III — On the lower bound of the Calabi energy and geodesic distance, Invent. Math. 175 (2009), no. 3, 453-503.

37. Test configuration and geodesic rays (co-author: Y. D. Tang), Geom´ etrie´ differentielle,´ physique mathematique,´ mathematiques´ et societ´ e.´ I. Asterisque´ No. 321 (2008), 139-167.

38. The Kahler-Ricci¨ flow on Kahler¨ manifolds with 2-non-negative traceless bisectional curvature operator (co-author: H. Z. Li), Chin. Ann. Math. Ser. B 29 (2008), no. 5, 543-556.

39. Geometry of Kahler¨ metrics and foliations by holomorphic discs (co-author: G. Tian), Publ. Math. Inst. Hautes Etudes Sci. no. 107 (2008), 1-107.

40. On conformally Kahler,¨ Einstein manifolds (co-authors: C. Lebrun, B. Weber), J. Amer. Math. Soc. 21 (2008), no. 4, 1137-1168.

41. On the Calabi flow (co-author: W. Y. He), Amer. J. Math. 130 (2008), no. 2, 539-570.

42. On Kahler¨ manifolds with positive orthogonal bisectional curvature, Adv. Math. 215 (2007), no. 2, 427-445.

43. Ricci flow on surfaces with degenerate initial metrics (co-author: W. Y. Ding), J. Partial Differential Equations 20 (2007), no. 3, 193-202.

44. Singular angles of weak limiting metrics under certain integral curvature bounds (co-authors: Q. Chen, W. Y. He), Pacific J. Math. 231 (2007), no. 1, 35-49.

45. A note on uniformization of Riemann surfaces by Ricci flow (co-authors: P. Lu, G. Tian), Proc. Amer. Math. Soc. 134 (2006), no. 11, 3391-3393.

6 Xiuxiong Chen Curriculum vitae

46. Ricci flow on Kahler-Einstein¨ manifolds (co-author: G. Tian), Duke Math. J. 131 (2006), no. 1, 17-73.

47. On the lower bound of energy functional E1 (I) — A stability theorem on the Kahler¨ Ricci flow, J. Geom. Anal. 16 (2006), no. 1, 23-38.

48. The structure of HCMU metric in a K-surface (co-authors: Q. Chen, Y. Y. Wu), Int. Math. Res. Not. 2005, no. 16, 941-958.

49. Partial regularity for homogeneous complex Monge-Ampere` equations (co-author: G. Tian), C. R. Math. Acad. Sci. Paris 340 (2005), no. 5, 337-340.

50. Uniqueness of extremal Kahler¨ metrics (co-author: G. Tian), C. R. Math. Acad. Sci. Paris 340 (2005), no. 4, 287-290.

51. A new parabolic flow in Kahler¨ manifolds, Comm. Anal. Geom. 12 (2004), no. 4, 837-852.

52. The space of Kahler¨ metrics II (co-author: E. Calabi), J. Differential Geom.61 (2002), no. 2, 173- 193.

53. Recent progress in Kahler¨ geometry, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 273-282, Higher Ed. Press, Beijing, 2002.

54. Ricci flow on Kahler-Einstein¨ surfaces (co-author: G. Tian), Invent. Math. 147 (2002), no. 3, 487-544.

55. Calabi flow in Riemann surfaces revisited: a new point of view, Int. Math. Res. Not. 2001, no. 6, 275-297.

56. Ricci flow on Kahler¨ manifolds (co-author: G. Tian), C. R. Acad. Sci. Paris Ser.´ I Math. 332 (2001), no. 3, 245-248.

57. Existence of extremal metrics on almost homogeneous manifolds of cohomogeneity one. Loo-Keng Hua: a great mathematician of the twentieth century (co-author: D. Guan), Asian J. Math. 4 (2000), no. 4, 817-829.

58. The space of Kahler¨ metrics, J. Differential Geom.56 (2000), no. 2, 189-234.

59. On the lower bound of the Mabuchi energy and its application, Int. Math. Res. Not. 2000, no. 12, 607-623.

60. Obstruction to the existence of metric whose curvature has umbilical Hessian in a K-surface, Comm. Anal. Geom. 8 (2000), no. 2, 267-299.

61. Extremal Hermitian metrics on Riemann surfaces, Calc. Var. Partial Differential Equations 8 (1999), no. 3, 191-232.

62. Remarks on the existence of branch bubbles on the blowup analysis of equation −∆u = e2u in dimension two, Comm. Anal. Geom. 7 (1999), no. 2, 295-302.

63. Extremal Hermitian metrics on Riemannian surfaces, Int. Math. Res. Not. 1998, no. 15, 781-797.

64. Weak limits of Riemannian metrics in surfaces with integral curvature bound, Calc. Var. Partial Differential Equations 6 (1998), no. 3, 189-226.

7 Xiuxiong Chen Curriculum vitae

65. Extremal Hermitian metrics with curvature distortion in a Riemann surface, Thesis (PhD.)-University of Pennsylvania. 1994.

66. Deformation of surfaces preserving principal curvatures (co-author: C. K. Peng), Differential ge- ometry and topology (Tianjin, 1986-87), 63-70, Lecture Notes in Math., 1369, Springer, Berlin, 1989.

Preprints

1. On the constant scalar curvature Kahler¨ metrics, apriori estimates (co-author: J. R. Cheng), preprint, arXiv:1712.06697.

2. On the constant scalar curvature Kahler¨ metrics, existence results (co-author: J. R. Cheng), preprint, arXiv:1801.00656.

3. On the constant scalar curvature Kahler¨ metrics, general automorphism group (co-author: J. R. Cheng), preprint, arXiv:1801.05907.

4. Geodesically Convexity of Small Neighborhood in Space of Kahler¨ Potentials (co-authors: M. Feld- man and J. C. Hu), preprint, arXiv:1805.02373.

5. Gravitational instantons with faster than quadratic curvature decay (I) (co-author: G. Chen), preprint, arXiv:1505.01790.

6. Gravitational instantons with faster than quadratic curvature decay (III) (co-author: G. Chen), preprint, arXiv:1603.08465.

7. On deformation of extremal metrics (co-authors: M. Paun˘ and Y.Zeng), preprint, arXiv:1506.01290.

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