李逸

兼职教授

Email: yilicms _at_ simis.cn
研究方向：微分几何、几何流
办公室：

简历

李逸现任东南大学数学学院和东南大学丘成桐中心教授。他于2012 年从哈佛大学获得数学博士学位。

李逸教授的研究兴趣包括微分几何、复几何、几何分析、几何流、非线性几何型偏微分方程、相对论。并已在国际一流学术期刊上发表了超过25篇论文。

教育经历

  • 2007-2012    哈佛大学    基础数学     博士
  • 2004-2007    浙江大学    基础数学     硕士
  • 2000-2004    宁波大学    基础数学     学士

工作经历

  • 2024-            上海数学与交叉学科研究院    兼职教授
  • 2019-            东南大学和东南大学丘成桐中心    教授
  • 2016-2018    卢森堡大学    助理研究员
  • 2013-2016    上海交通大学    特别副研究员
  • 2012-2013    约翰霍普金斯大学    讲师

荣誉和获奖

  1. 2016 Shanghai Jiao Tong University Teaching Achievement Grand Prize, with Liang Jin, Zhu Zuonong and Li Weimin.
  2. 3rd Prize, Teaching Competition for Young Teachers in Shanghai Jiao Tong University, 2016

Publication (In preparation)

  1. Li, Yi. CR twistor space and exceptional Lie groups, 2023.
  2. Li, Yi. A project on Einstein scalar field equations.
  3. Li, Yi. Geometry on Ricc-harmonic metrics.
  4. Li, Yi; Yuan, Yuan. On a new geometric flow over Kahler manifolds III: long time behavior, in preparation, 2021.

论著

  1. Li, Yi; Zhang, Qianwei. Existence of solutions to a class of Kazdan-Warner equations on finite graphs, preprint, arXiv: 2308.10002, 2023 (submitted)
  2. Li, Yi. Curvature pinching estimate under the Laplacian G_2 flow, preprint, arXiv: 2307.14289, 2023 (submitted)
  3. Li, Yi. Curvature estimates on a parabolic flow of Fei-Guo-Phong, preprint, arXiv: 2210.16842, 2022 (submitted)
  4. Li, Yi. A new notion on weighted Riemann curvature, Rendiconti del Circolo Matematico di Palermo Series 2, 2023.
  5. Li, Yi; Li, Chuanhuan; Xu, Kairui. Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures, The Journal of Geometric Analysis, 33, 282 (2023).
  6. Li, Yi; Li, Chuanhuan. List’s flow with bounded integral curvature on noncompact complete Riemannian manifolds, preprint, 2022
  7. Li, Yi; Zhang, Miaosen. A local curvature estimate for the Ricci-harmonic flow on complete Riemannian manifolds, preprint, http://arxiv.org/abs/2112.02576 (submitted)
  8. Li, Yi. Local curvature estimates for the Ricci-harmonic flow, Nonlinear Analysis, 222(2022), No. 112961, 53pp.
  9. Li, Yi; Yuan, Yuan. Local curvature estimates along the k-LYZ flow, J. Geom. Phys., 164(2021), 104162, 21pp.
  10. Li, Yi. Local curvature estimates for the Laplacian flow, Cal. Var. PDE., 60(2021), no. 1, Paper No. 28, 37pp.
  11. Li, Yi; Yuan, Yuan; Zhang, Yuguang. On a new geometric flow over Kahler manifolds, Comm. Analysis and Geometry, 28(2020), no. 6, 1251-1288.
  12. Zhu, Xiaorui; Li, Yi. Harnack estimates for a heat-type equation under the geometric flow, Potential Analysis, 52(2020), 469-496. MR4067300
  13. Li, Yi. Generalized Ricci flow II: existence for noncompact complete manifolds, Differential Geometry and its Applications, 66(2019), 106-154. MR3913713
  14. Li, Yi. Scalar curvature along the Ricci flow, preprint, 2019 (submitted).
  15. Li, Xiangdong; Li, Songzi; Li, Yi. Uniqueness and local curvature estimates for a class of generalized Ricci flow, preprint, 2019.
  16. Li, Yi. Long time existence and bounded scalar curvature in the Ricci-harmonic flow, J. Differential Equations, 265(2018), no. 1, 69-97. MR3782539
  17. Li, Yi; Zhu, Xiaorui. Harnack estimates for a nonlinear equation under Ricci flow, Differential Geometry and its Applications, 56(2018), 67-80. MR3759353
  18. Wu, Guoqiang; Li, Yi. Heat kernel estimates along the Ricci-harmonic flow, preprint, 2017 (submitted)
  19. Li, Yi. Long time existence of Ricci-harmonic flow, Front. Math. China, 11(2016), no. 5, 1313-1334. MR3547931
  20. Li, Yi; Zhu, Xiaorui. Harnack estimates for a heat-type equation under the Ricci flow, J. Differential Equations, 260(2016), no. 4, 3270-3301. MR343499
  21. Li, Yi. Li-Yau-Hamilton estimates and Bakry-Emery Ricci curvature, Nonlinear Anal., 113(2015), 1-32. MR3281843
  22. Li, Yi; Liu, Kefeng. A geometric heat flow for vector fields, Sci. China Math., 58(2015), no. 4, 673-688.MR3319305
  23. Zhu, Xiaorui; Li, Yi.Li-Yau estimates for a nonlinear parabolic equation on manifolds,Math. Phys. Anal. Geom., 17(2014), no. 3-4, 273-288. MR3291929
  24. Li, Yi. A priori estimates for Donaldson’s equation over compact Hermitian manifolds, Cal. Var. PDE., 50(2014), no. 3-4, 867-882. MR3216837
  25. Li, Yi. On an extension of the Hk-mean curvature flow for closed convex hypersurfaces, Geom. edicata,172(2014), 147-154. MR3253775
  26. Li, Yi. Eigenvalues and entropies under the harmonic-Ricci flow, Pacific J. Math.,267 (2014), no. 1, 141-184. MR3163480
  27. Li, Yi. Mabuchi and Aubin-Yau functionals over complex surfaces, J. Math. Anal. Appl., 416(2014), no. 1, 81-98. MR3182749
  28. Li Yi. On an extension of the Hk-mean curvature flow, Sci. China Math., 55(2012), no. 1, 99-118. MR2873806
  29. Li, Yi. Generalized Ricci flow I: higher derivatives estimates for compact manifolds, Analysis & PDE, 5(2012), no. 4, 747-775. MR3006641
  30. Li, Yi. Mabuchi and Aubin-Yau functionals over complex manifolds, arXiv: 1004.0553, preprint.
  31. Li, Yi. Mabuchi and Aubin-Yau functionals over complex three-folds, arXiv: 1003.5307, preprint.
  32. Li Yi. Harnack inequality for the negative power Gaussian curvature flow, Proc. Amer. Math. Soc., 139(2011), no. 10, 3707-3717. MR2813400 (2012g: 53137)
  33. Chen Lin; Li Yi; Liu Kefeng. Localization, Hurwitz numbers and the Witten conjecture, Asian J. Math., 12(2008), no. 4, 511-518. MR2481688 (2009m: 14084)
  34. Li Yi. Some results of the Marino-Vafa formula, Math. Res. Lett., 13(2006), no. 6, 847-864. MR2280780 (2007g: 14071)
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