菜单总览
— 优秀师资 —

李玉田

职位:

助理教授

教育背景:

博士(香港城市大学数学系)

学士(吉林大学数学与应用数学专业)

研究领域
分析及应用、偏微分方程、科学计算与数值分析,数理金融
Email

liyutian@cuhk.edu.cn

个人简介:


李玉田教授于2005年在吉林大学数学与应用数学专业取得学士学位,之后就读于香港城市大学数学系,分别于2007年和2010年取得硕士和博士学位。从2010年至2012年,他在香港城市大学刘璧如数学科学中心进行博士后研究;2012年至2017年于香港浸会大学数学系任职研究助理教授。他于2017年12月加入香港中文大学(深圳)理工学院担任助理教授。

李教授的研究兴趣包括:分析及应用、偏微分方程、科学计算与数值分析,数理金融等。他在国际主流期刊上发表文章20余篇论文,大部分发表于数学与应用数学领域的顶级期刊上,这些期刊包括: Studies in Applied Mathematics, Applied Mathematical Letters, Analysis and Applications, Constructive Approximations, Proceedings of the Royal Society London A, Discrete and Continuous Dynamical Systems, Journal of Scientific Computing, Optics Expresses, IEEE Transaction on Microwave Theory and Technologies, Quantitative Finance, etc.


学术著作:


分析及应用

Yutian Li, Saiyu Liu, Shuaixia Xu, and Yuqiu Zhao: Full asymptotic expansions of the Landau constants via a difference equation approach, Applied Mahtematics and Computation, 219 (2012), 988-995.

Yutian Li, Saiyu Liu, Shuaixia Xu, and Yuqiu Zhao: Asymptotics of Landau constants with optimal error bounds, Constructive Approximation, 40 (2014), 281-305.

Y. T. Li and R. Wong: Global asymptotics for Stieltjes-Wigert polynomials, Analysis and Applications, 11 (2013), article no.: 1350028, 12 pages.

L.-H. Cao and Y.-T. Li: Linear difference equations with a transition point at the origin, Analysis and Applications, 12 (2014), 75-106.

L.-W. Long, Y.-T. Li, S.-Y. Liu and Y.-Q. Zhao: Real solutions of the first Painlevé equation with large initial data, Studies in Applied Mathematics, 139 (2017), 505-532.

 

偏微分方程

6.       D.-C. Chang and Y. Li: SubRiemannian geodesics in Grushin plane, J. Geom. Anal., 22 (2012), 800–826.

7.       O. Calin, D.C. Chang, J. Hu, and Y. Li: On heat kernels of a class of degenerate elliptic operators, J. Nonlinear Convex Anal., 12 (2011), 309–340.

8.       D.-C. Chang and Y. Li: Small time asymptotics of the heat kernels for the Heisenberg subLaplacian and step two Grushin operator, Proceedings of the Royal Society A, 471 (2015), article no.: 20140943. 19 pages.

9.       Peter Greiner and Yutian Li: A fundamental solution for a nonelliptic partial differential operator, II, Analysis and Applications, to appear.

 

科学计算

10.   Y. Li and J. Zhu: Efficient approximations of dispersion relations in optical waveguides with varying refractive-index profiles, Optics Express, 23 (2015), 11952–11964.

11.   J. Zhu and Y. Li: A new approach of eigenmodes for varying refractive-index profile’s waveguides, IEEE Trans. Microw. Theory Tech., 64, no. 10 (2016), 3131–3138.

 

数理金融

12.   J. Han, M. Gao, Q. Zhang, and Y. Li: Option prices under stochastic volatility, Applied Mathematics Letters, 26 (2013), 1–4.

13.   X. Guo and Y. Li: Valuation of American options under the CGMY model, Quantitative Finance, 16 no. 10 (2016), 1529–1540.

14.   H. Song, K. Zhang, and Y. Li, Finite element and discontinuous Galerkin methods with perfect matched layers for American options, Numer. Math. Theory Methods Appl.,10 (2017), 829-851.