Curriculum Vitae Education Professional Positions Honors And

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 Ka¨hler Manifolds. • Weiyong He (PhD., 2007, UW-Madison), Extremal Metrics, The Stability Conjecture and the Calabi Flow. • Haozhao Li (PhD, 2007, Peking University), Energy Functionals and Ka¨hler-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 Ka¨hler 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 Noncompact Manifolds and Integral Scalar Curvature Bound. • Long Li (PhD., 2014, Stony Brook University), On the uniqueness of singular Ka¨hler Einstein metrics. • Seyed Ali Aleyasin (PhD., 2014, Stony Brook University), Space of Ka¨hler 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 Ka¨hler-Einstein Metrics and Its Applications. • Yu Zeng (PhD., 2016, Stony Brook University), Deformations of twisted cscK metrics. • Robin Sebastian Krom (Ph.D., 2016, ETH Zu¨rich), 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-François 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 problems. • 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-Ampe`re equation, the Ka¨hler-Einstein Problem and constant scalar curvature metric problems • NSF Grant DMS-1211652 (2012-2015), Extremal Ka¨hler metrics, the Ka¨hler Ricci flow and the Calabi flow. • NSF Grant DMS-0907778 (2009-2012), Extremal Ka¨hler Metrics. • NSF Grant DMS-0406346 (2004-2009), Extremal Ka¨hler Metrics. and Geometric Flow Equations. • NSF Grant DMS-0110321 (2001-2004), The Ka¨hler Ricci Flow and the Extremal Ka¨hler 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 Mathe´matiques. • Geometric flow program (October 13-December 19, 2014), SCGP. • Geometric Analysis and Relativity (July 6- July 10, 2014), USTC. • Summer School in Ka¨hler 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 Ka¨hler 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 Ka¨hler metric: a new perspective, Ann. Math. Que´bec 42, (2018), no. 2, pp 169-189. 2. Ka¨hler-Ricci flow, Ka¨hler-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. <a href="/goto?url=https://doi.org/10.1515/crelle-2017-0026" target="_blank">Reine Angew. Math. 726 (2018), https://doi.org/10.1515/crelle-2017-0026. </a>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-Ampe`re 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. Pa˘un), 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-Ampe`re equations with Ho¨lder-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 Ka¨hler-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. Ka¨hler-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. Ka¨hler-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. Ka¨hler-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 Ka¨hler 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. Ka¨hler-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 Ka¨hler-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 Ka¨hler-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 Ka¨hler metrics (V): Ka¨hler quantization (co-author: S. Sun), Metric and differential geometry, 19-41, Progr. Math., 297, Birkhaüser/Springer, Basel, 2012. 24. The complex Monge-Ampe`re equation on compact Ka¨hler manifolds (co-author: W. Y. He), Math. Ann. 354 (2012), no. 4, 1583-1600. 25. The Ka¨hler 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 Ka¨hler 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 Ka¨hler-Ricci flow (co-authors: G. Tian, Z. Zhang), Trans. Amer. Math. Soc. 363 (2011), no. 6, 2849-2863. n230. Moduli spaces of critical Riemannian metrics with L 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 Ka¨hler Ricci flow (co-author: B. Wang), J. Geom. Anal. 20 (2010), no. 2, 335-353. 33. Stability of Ka¨hler-Ricci flow (co-author: H. Z. Li), J. Geom. Anal. 20 (2010), no. 2, 306-334. 34. A note on Ka¨hler-Ricci soliton (co-authors: S. Sun, G. Tian), Int. Math. Res. Not. 2009, no. 17, 3328-3336. 35. Ka¨hler-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 Ka¨hler 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), Geóme´trie diffe´rentielle, physique mathe´matique, mathe´matiques et socie´te´. I. Aste´risque No. 321 (2008), 139-167. 38. The Ka¨hler-Ricci flow on Ka¨hler 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 Ka¨hler metrics and foliations by holomorphic discs (co-author: G. Tian), Publ. Math. Inst. Hautes Etudes Sci. no. 107 (2008), 1-107. 40. On conformally Ka¨hler, 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 Ka¨hler 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 Ka¨hler-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 Ka¨hler 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-Ampe`re equations (co-author: G. Tian), C. R. Math. Acad. Sci. Paris 340 (2005), no. 5, 337-340. 50. Uniqueness of extremal Ka¨hler metrics (co-author: G. Tian), C. R. Math. Acad. Sci. Paris 340 (2005), no. 4, 287-290. 51. A new parabolic flow in Ka¨hler manifolds, Comm. Anal. Geom. 12 (2004), no. 4, 837-852. 52. The space of Ka¨hler metrics II (co-author: E. Calabi), J. Differential Geom.61 (2002), no. 2, 173- 193. 53. Recent progress in Ka¨hler geometry, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 273-282, Higher Ed. Press, Beijing, 2002. 54. Ricci flow on Ka¨hler-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 Ka¨hler manifolds (co-author: G. Tian), C. R. Acad. Sci. Paris Se´r. 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 Ka¨hler 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 geometry and topology (Tianjin, 1986-87), 63-70, Lecture Notes in Math., 1369, Springer, Berlin, 1989. Preprints 1. On the constant scalar curvature Ka¨hler metrics, apriori estimates (co-author: J. R. Cheng), preprint, arXiv:1712.06697. 2. On the constant scalar curvature Ka¨hler metrics, existence results (co-author: J. R. Cheng), preprint, arXiv:1801.00656. 3. On the constant scalar curvature Ka¨hler metrics, general automorphism group (co-author: J. R. Cheng), preprint, arXiv:1801.05907. 4. Geodesically Convexity of Small Neighborhood in Space of Ka¨hler 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. Pa˘un and Y. Zeng), preprint, arXiv:1506.01290. 8

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