程丽娟 

姓名： 程丽娟

职称： 副教授

邮箱： lijuan.cheng@hznu.edu.cn

教学与课程：

本科生课程：概率论、随机过程、概率论与数理统计

研究生课程：现代概率论基础、随机分析

研究方向：

黎曼流形上的随机分析，这是概率论与黎曼几何的交叉领域，致力于利用概率的方法来研究微分几何中所关心的问题，并逐步发展成一套完整的关于黎曼流形上扩散过程的概率理论。

学术研究：

1、论文代表著作

[1]     Cheng, Li-Juan, Thalmaier, Anton, Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows, Analysis&PDE, in press.

[2]     Cheng, Li-Juan, Thalmaier, Anton and Wang Feng-Yu, Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance,

Journal of Functional Analysis (2023), 285(5), 109997

[3]     Chen, Qin-Qian; Cheng, Li-Juan; Thalmaier, Anton, Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds, Stochastic Partial Differential Equations: Analysis and Computations (2023), 11(2), 685-713

[4]     Cheng, Li Juan, Grong, Erlend and Thalmaier, Anton, Funtional inequalities on path space of sub-Riemannian manifolds, Nonlinear Analysis: Theory, Methods and Applications (2021), 210(112387), 1-30

[5]     Cheng, Li Juan* and Thalmaier, Anton, Characterization of pinched Ricci curvature by functional inequalities, Journal of Geometric Analysis (2018), 28(3), 2312-2345

[6]     Cheng, Li Juan* and Thalmaier, Anton, Spectral gap on Riemannian path space over static and evolving manifolds, Journal of Functional Analysis (2018), 274(4), 959-984

[7]     Cheng, Li Juan, Thalmaier, Anton and Thompson, James, Functional inequalities on manifolds with non-convex boundary, Science China Mathematics (2018), 61(8), 1421-1436

[8]     Cheng, Li Juan, Thalmaier, Anton and Thompson, James, Quantitative C1-estimates by Bismut formulae, Journal of Mathematical Analysis and Applications (2018), 465(2), 803-813

[9]     Cheng, Li Juan, Thalmaier, Anton and Thompson, James, Uniform gradient estimates on manifolds with a boundary and applications, Analysis and Mathematical Physics (2018), 8(4), 571-588

[10] Cheng, Li Juan* and Thalmaier, Anton, Evolution systems of measures and semigroup properties on evolving manifolds, Electronic Journal of Probability (2018), 23(20), 1-27

[11] Cheng, Li Juan*, Diffusion semigroup on manifolds with time-dependent metrics, Forum Mathematicum (2017), 29(4), 751-1002

[12] Cheng, Li Juan* and Zhang, Kun, Reflecting diffusion semigroup on manifolds carrying geometric flow, Journal of Theoretical Probability (2017), 30(4), 1334-1368

[13] Cheng, Li Juan*, Transportation-cost inequalities on path spaces over manifolds carrying geometric flows, Bulletin des Sciences Mathématiques (2016), 140(5), 541-561

[14] Cheng, Li Juan* and Wang, Yingzhe, Algebraic convergence rate for reflecting diffusion processes on manifolds with boundary, Potential Analysis (2016), 44(1), 91-107

[15] Chen, Xin, Cheng, Li Juan and Mao, Jing*, A probabilistic method for gradient estimates of some geometric flows, Stochastic Process. Appl. (2015), 125(6), 2295-2315

[16] Cheng, Li Juan*, An integration by parts formula on path space over manifolds carrying geometric flow, Science China Mathematics (2015), 58(7), 1511-1522

[17] Cheng, Li Juan*, The radial part of Brownian motion with respect to L-distance under Ricci flow, Journal of Theoretical Probability (2015), 28(2), 449-466

[18] Cheng, Li Juan* and Mao, Yong-Hua, Eigentime identity for one-dimensional diffusion processes, J. Appl. Probab. (2015), 52(1), 224-237

2、教材著作

王颖喆 程丽娟 概率与数理统计习题精解 北京师范大学出版社

3、主持项目

1. 非时齐流形上扩散半群的性质及其应用, 国家自然科学基金青年项目 (基金号11501508), 2016.01-2018.12, 21.3 万 . 主持, 结题

2. 流形上非自适应扩散过程的渐近稳定性, 浙江省自然科学青年基金 (基金号LQ16A010009), 2016.01-2018.12, 5万. 主持, 结题

3. 黎曼流形上关于热半群二阶导数的Bismut型公式及其应用, 浙江省自然科学基金项目（基金号LGJ22A010001）, 2022.1.1-2024.12.31, 10万， 主持， 在研

4、学术交流

Sep.9 2015 –Feb. 1, 2019, 卢森堡大学，博士后、助理研究员。合作导师： Anton Thalmaier

June 1 2013- July 31,2013， 德国比勒菲尔德大学，交流博士生。访问导师：Michael Röckner

February 12-14, Young researchers between geometry and stochastic analysis, 卑尔根，挪威，邀请报告

June 14-19, 2019, The 8th International Congress of Chinese Mathematicians of 2019 (华人数学家大会)，北京，45分钟邀请组报告

June 25-29, 2018, Institut Henri Poincaré (Paris, France)-Summer School, Information Theory: Inequalities, Distances and Analysis, 巴黎，参加.

July 24-28, 2017, The 39th Conference on Stochastic Processes and their Applications (SPA2017), 莫斯科, 俄罗斯，邀请组报告.

July 10-14, 2017, The International Conference GeoProb 2017 in Luxembourg, 卢森堡，参加.

January 9-13, 2017, The Young Geometric Analysts’ Forum 2017 at TSIMF, 三亚, 参加.

July 11-15, 2016, Lake Como School of Advanced Studies: Geometric analysis on Riemannian and singular metric measure spaces, 意大利, 参加.