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李逸
教授
数学学院
应用数学系
电话:
邮箱:
yilicms@seu.edu.cn, yilicms@gmail.com,yilicms@163.com
地址:
四牌楼校区逸夫建筑馆15楼1511
邮编:
210096
  • 博士生导师。 研究兴趣: 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、广义相对论及其应用
    工作经历: (1) 2019/3-至今,东南大学数学学院和东南大学丘成桐中心,教授, (2) 2018/12-2019/2,东南大学丘成桐中心,访问学者 (3) 2016/12-2018/11,卢森堡大学数学系,助理研究员, (4) 2014/3-2014/6,访问学者,上海数学中心, (5) 2013/6-2016/11,上海交通大学数学系,特别副研究员, (5) 2012/6-2013/5,美国约翰霍普金斯大学数学系,讲师。
    教育经历: (1) 2007/9-2012/5,美国哈佛大学数学系,博士, (2) 2004/9-2007/6,浙江大学数学系,硕士, (3) 2000/9-2004/6,宁波大学数学系,学士。
  • Publications


    (19) Zhu, Xiaorui; Li, Yi. Harnack estimates for a heat-type equation under the geometric flow, Potential Analysis, 52(2020), 469-496. MR4067300


    (18) Li, Yi. Generalized Ricci flow II: existence for noncompact complete manifolds, Differential Geometry and its Applications, 66(2019), 106-154. MR3913713


    (17) Li, Yi; Yuan, Yuan; Zhang, Yuguang. On a new geometric flow over Kahler manifolds, to appear in Comm. Analysis and Geometry(CAG#1891, https://www.intlpress.com/site/pub/pages/journals/items/cag/_home/acceptedpapers/index.php)


    (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


    (15) Li, Yi; Zhu, Xiaorui. Harnack estimates for a nonlinear equation under Ricci flow, Differential Geometry and its Applications, 56(2018), 67-80. MR3759353


    (14) Li, Yi. Long time existence of Ricci-harmonic flow, Front. Math. China, 11(2016), no. 5, 1313-1334. MR3547931


    (13) 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


    (12) Li, Yi. Li-Yau-Hamilton estimates and Bakry-Emery Ricci curvature, Nonlinear Anal., 113(2015), 1-32. MR3281843


    (11) Li, Yi; Liu, Kefeng. A geometric heat flow for vector fields, Sci. China Math., 58(2015), no. 4, 673-688.MR3319305


    (10) 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


    (9) Li, Yi. A priori estimates for Donaldson's equation over compact Hermitian manifolds, Cal. Var. PDE., 50(2014), no. 3-4, 867-882. MR3216837


    (8) Li, Yi. On an extension of the Hk-mean curvature flow for closed convex hypersurfaces, Geom. edicata, 172(2014), 147-154. MR3253775


    (7) Li, Yi. Eigenvalues and entropies under the harmonic-Ricci flow, Pacific J. Math., 267(2014), no. 1, 141-184. MR3163480


    (6) Li, Yi. Mabuchi and Aubin-Yau functionals over complex surfaces, J. Math. Anal. Appl., 416(2014), no. 1, 81-98. MR3182749


    (5) Li Yi. On an extension of the Hk-mean  curvature flow, Sci. China Math., 55(2012), no. 1, 99-118. MR2873806


    (4) Li, Yi. Generalized Ricci flow I: higher derivatives estimates for compact manifolds, Analysis & PDE, 5(2012), no. 4, 747-775. MR3006641


    (3) Li Yi. Harnack inequality for the negative power Gaussian curvature flow, Proc. Amer. Math. Soc., 139(2011), no. 10, 3707-3717. MR2813400 (2012g: 53137)


    (2) 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)


    (1) Li Yi. Some results of the Marino-Vafa formula, Math. Res. Lett., 13(2006), no. 6, 847-864. MR2280780 (2007g: 14071)



    Preprints


    (8) Li, Yi; Yuan, Yuan. On a new geometric flow over Kahler manifolds II: local curvatures estimates, preprint, 2020.


    (7) Li, Yi. Scalar curvature along the Ricci flow, preprint, 2019.


    (6) Li, Xiangdong; Li, Songzi; Li, Yi. Uniqueness and local curvature estimates for a class of generalized Ricci flow, preprint, 2019.


    (5) Li, Yi. Local curvature estimates for the Ricci-harmonic flow, preprint, arXiv: 1810.09760v1 (submitted)


    (4) Li, Yi. Local curvature estimates for Lapalcian G2-flow, preprint, arXiv: 1805.06231 (submitted)


    (3) Wu, Guoqiang; Li, Yi. Heat kernel estimates along the Ricci-harmonic flow, preprint, 2017 (submitted)


    (2) Li, Yi. Mabuchi and Aubin-Yau functionals over complex manifolds, arXiv: 1004.0553, preprint.


    (1) Li, Yi. Mabuchi and Aubin-Yau functionals over complex three-folds, arXiv: 1003.5307, preprint.



    In preparation



    (2) Li, Yi. Laplacian G2-flowII, in preparation, 2020.

    (1) Li, Yi; Yuan, Yuan. On a new geometric flow over Kahler manifolds III: long time behavior, in preparation, 2020.



  • 本科


    1.对数学感兴趣的并以后想从事数学的本科同学(是否数学专业不要紧),请直接给我发邮件。


    2.抓紧在本科多学点数学。


    3.东南大学丘成桐中心:

    https://yauc.seu.edu.cn/main.htm

    https://yauc.seu.edu.cn/yaucen/main.htm

     


    考研


    1.如果对我方向感兴趣想报考我的研究生,请直接给我发邮件。欢迎!


    2.努力和坚持并重,知行合一。


    3.已毕业学生:

    上海交通大学:文薇(非线性抛物方程的Li-Yau-Hamilton 估计,201512月,硕士),许宁(平移狄利克雷边界条件的平均曲率流研究,20161月,硕士),王倩云(转博)。



    项目


    1.流形上函数的频率及几何应用(11826031),国家自然科学基金天元基金,2019/1-2019/12,参与


    2.紧致流形上一类几何流和几何型方程的研究及应用(11401374)国家自然科学基金青年基金,2015/1-2017/12,主持


    3.流形上若干几何流的研究(14YF1401400)上海市科委杨帆计划,2014/7-2017/6,主持


    4.Geometry of random evolutionsGEOMREVO14/7628746,Fonds National de la Recherche Luxembourg (FNR) unde the OPEN scheme2015-2018,参与



    荣誉


    1.2016年上海交通大学校长教学奖以培养未来拔尖创新人才为目标的新型微积分教学模式的探索与实践),上海交通大学,特等奖,2016梁进、朱佐农、李伟民、李逸


    2.首届上海交通大学青年教师教学竞赛,上海交通大学,三等奖,2016


    3.已毕业2名硕士,1名硕博连读(海外联合培养)


    4.推荐多名优秀本科生出国留学攻读基础数学博士,比如德国波恩大学、美国威斯康辛大学麦迪逊分校、美国UIUC、纽约大学库朗研究所、美国加州大学圣地亚戈分校(UCSD)




    上课信息


    4.2020年春学期:微分流形,(单周)星期三(6-7节)、五(6-7节)九龙湖校区教二105(目前是上网课),教材为本人手写讲义。


    讲义

    Analysis on manifolds.pdf(第4版,初定稿,2020/5/20)


    讲义修改内容和时间:



    (2)2020/5/20:1.5节之前习题答案补齐了。

    (1)2020/5/15:初步完成了讲稿



    习题参考答案(如有错误和纰漏请指正)


    1.5节之前的答案已经写在讲义上相应的习题之下。



    ==================================================================================


    3.2020年春学期:数学分析2,星期一(1-2节)、三(3-4节)、五(1-2节)九龙湖校区教二105(目前是上网课),教材为学院统编教材(张福保/薛金美编写)结合本人手写讲义


    理科实验班讲义

    基本分析讲义.pdf (第1版,初稿修订稿,2020/6/25,大一数分内容大约910页)


    讲义修改内容和时间:


    (10)2020/6/25:初稿修订稿第1版,全部完成修订。

    (9)2020/6/15:初稿修订稿第1版,完成了第1-5章的修订。

    (8)2020/5/28:补充了16.1.5小节,完成了16.2.8小节。

    (7)2020/5/19:增加了16.6节。

    (6)2020/5/16:增加了14.4.5小节。

    (5)2020/5/11:增加了14.3.4小节。

    (4)2020/5/3:完成剩下的 Fourier 级数部分,初定稿。

    (3)2020/5/1:只剩下 Fourier 级数章节未完成。

    (2)2020/4/26: 14.4.4小节给出了1-1+1-1+...=1/2 的合理解释,并给出级数求和的一般意义。

    (1)2020/4/22:P330,有限项级数乘积中 c_k 的定义P334,注6.3.10 (1),|c_n|极限为2。



    习题参考答案(如有错误和纰漏请指正)


    10.1.pdf 10.2.pdf 10.3.pdf 10.4.pdf


    11.1.pdf 11.2.pdf 11.3.pdf 11.4.pdf


    14.1.pdf 14.2.pdf 14.3.pdf


    15.1.pdf 15.2.pdf 15.3.pdf 


    16.1.pdf 16.2.pdf 16.3.pdf



    =====================================================================================


    2.2019年秋学期:拓扑学星期二(3-4节)、四(1-2节)(双周)九龙湖校区教三204,教材为本人手写讲义。


    作业HW1.pdf HW2.pdf HW3.pdf HW4.pdf HW5.pdf HW6.pdf 

    HW7.pdf HW8.pdf


    习题参考答案(如有错误和纰漏请指正)HW1.pdf HW2.pdf



    =====================================================================================


    1.2019年秋学期:数学分析1星期一(3-4节)、三(1-2节)、五(3-4节)九龙湖校区教三301,教材为学院统编教材(张福保/薛金美编写)结合本人手写讲义


    理科实验班讲义

    Basic_analysis.pdf(2019/10/14) 

    分析.pdf (2019/12/20)(中文版)

    基本分析.pdf (2020/5/4,完整版)


    习题参考答案(如有错误和纰漏请指正)

    2.1.pdf2.2.pdf2.3.pdf

    3.1.pdf3.2.pdf3.3.pdf

    4.1.pdf4.2.pdf4.3.pdf4.4.pdf

    5.1.pdf 5.2.pdf 5.3.pdf

    6.1.pdf 6.2.pdf 6.3.pdf

    7.1.pdf 7.2.pdf 7.3.pdf 7.4.pdf

    8.1.pdf 8.2.pdf





    ================================================================================================================================================================================================


    本科生讨论班



    1.2019年:拓扑学,每周日晚上6:00-8:00,数学学院第二报告厅

    2.2019年:数学分析提高(理科实验班导师制讨论班),每周一晚上6:00-8:00,数学学院523室



    ==================================================================================================================================================


    研究生讨论班


    时间和地点2019年4月3日,九龙湖校区李文正图书馆数学学院第一报告厅,下午2点-3点
    报告人李炯玥(清华大学) 
    题目

    Asymptotic properties of the spinor field and the application to nonlinear Dirac model

    摘要

    In this talk, we will first discuss the asymptotic behavior of the linear 

    solutions of massless Dirac equations in R1+3. It is proved that the 

    solutions decay in a sharp rate and enjoy the so-called peeling properties. 

    Based on this decay mechanism of the linear solutions and spinor null 

    condition we raised,we also discuss the small data global existence result 

    for a class of nonlinear Dirac models.


    时间和地点2019年5月10日,四牌楼校区逸夫建筑馆15楼1511,下午2点-3点
    报告人毛井(湖北大学)
    题目Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold M^2*R
    摘要

    For the Lorentz manifold M^2*R, with M^2 a 2-dimensional complete surface with nonnegative Gaussian 

    curvature, we investigate its space-like graphs over compact strictly convex domains in M^2, which are 

    evolving by the non-parametric mean curvature flow with prescribed contact angle boundary condition, 

    and show thatsolutions converge to ones moving only by translation. This talk is based on a joint-work 

    with L. Chen, D.-D. Hu and N. Xiang.

    时间和地点2019年6月4日,四牌楼校区逸夫建筑馆15楼1502,下午2点-3点
    报告人王丽涵(University of Connecticut)
    题目

    Symplectic Laplacians, boundary conditions and cohomology

    摘要

    Symplectic Laplacians are introduced by Tseng and Yau in 2012, which are related to a system of 

    supersymmetric equations from physics. These Laplacians behave different from usual ones in Rimannian

     case and Complex case. They contain both 2nd and 4th order operators. In this talk, we will discuss these 

    operators and their relations with cohomologies on compact symplectic manifolds with boundary. For this

     purpose, we will introduce new boundary conditions for differential forms on symplectic manifolds. Their 

    properties and importance will be discussed.



    ======================================================= ============================================================================


    专题讨论班/会议


    1.2019/4/10:九龙湖校区数学学院,第一报告厅,东南大学几何分析高级研讨班


    时间报告人 题目
    9:00-9:45

    徐国义(清华大学)

    Xu Guoyi (Tsinghua University)

    The analysis and geometry of isometric embedding


    In 1950’s, Nash-Kuiper built up the C1 isometric embedding for any 

    surface into R3, this can be viewed as analysis side of isometric embedding. 

    On the other hand, there is obstruction for the existence of C2 isometric 

    embedding of surface into R3 known since Hilbert, which reflects the geometry 

    flavor of isometric embedding. Whats happening from C2 to C2 (from analysis 

    to geometry)? The talk will be accessible to general audience with basic 

    knowledge of analysis and geometry.   


    9:50-10:35

    王作勤(中国科学技术大学)

    Wang Zuoqin (USTC)

    On Weyl Asymptotic


    Weyl law, first discovered by H. Weyl in 1911 for the Dirichlet-Laplace 

    eigenvalues of bounded regions and then extended/strengthened by many 

    mathematicians to various general settings, relates the asymptotic 

    behavior of eigenvalues of certain operators with the background geometric/

    analytic/dynamic behavior. In this talk I will briefly describe 

    these connections and discuss some recent work.


    10:45-11:30

    华波波(复旦大学)

    Hua Bobo (Fudan University)

    图上的分析和应用


    我们研究图和离散Laplace算子用离散分析的技巧,研究图和Laplace算子的

    特征值问题、Schroendinger算子等。


    11:35-12:20

    来米加(上海交通大学)

    Lai Mijia (Shanghai Jiaotong University)

    The renormalized volume on 4-dimensional CCE manifolds


    The renormalized volume is a very important global invariant for 

    conformally compact Einstein (CCE) manifolds. In dimension 4, it is the 

    integral of sigma_2 of the Schouten tensor, which appears in the 

    Gauss-Bonnet-Chern formula. Based on Gurskys work on the Weyl functional 

    and the de Rham cohomology on closed 4-manifolds and Chang-Gursky-Yang

    conformal 4-sphere theorem, one can deduce interesting topological 

    consequences for 4-dim CCE manifolds under assumptions on the renormalized 

    volume. I will survey results in this direction and discuss some recent thoughts.


    2.2019年东南大学青年几何分析会议日程


    2019年东南大学青年几何分析会议.pdf












  • 社会兼职


    1. 美国《Math. Reviews》评论员

    2. 数学学术期刊审稿人

    3. 几何分析会议组织者

    4. 民进会员

    5. 南京市侨联青年委员会第三届委员大会常务委员(2020-2025)


    兴趣爱好


    1. 1840年之后的中国历史

    2. 明史

    3. 中共党史

    4. 篮球和跑步

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