Mathematical research at YMSC spans a broad range in pure mathematics, applied mathematics, computational mathematics and related disciplines and engineering. The following are its six main research groups:
Representation Theory, Algebraic Geometry and Number Theory
This group focuses on research in algebraic and geometric representation theory, category theory, I-adic cohomology and applications, moduli spaces, Hodge theory, singularity theory, and arithmetic geometry.
Professors：Caucher Birkar, Fu Lei, Qiu Yu, Shan Peng, Zhu Yihang
Associate Professors： Diao Hansheng, Will Donovan, Emmanuel Lecouturier, Xu Bin,
Assistant Professors： Dylan Allegretti, Cao Jin, Chen Lin, Fan Yu-Wei, He Xiang, Hu Yueke, Li Penghui, Li yongxiong, Liu Yu, Koji Shimizu, Su Changjian, Yang Yilong, Yu Chenglong, Zhang Dingxin, Zheng Zhiwei, Zhou Yu
Postdoctoral： Amina Azzouz, Chen Bingyi, Chen Qingjing, Du Heng, Lukzen Elena, Jia Boming, Jia Jia, Jiao Junpeng, Li Pengcheng, Otani Takumi, Wang Jianping, Wang Qi, Zhang Xucheng, Zhao Qixian, Zou Yu
Geometry and Topology
Research of this group covers a broad range of research including differential geometry, geometric analysis, Teichmüller theory, low-dimensional topology, high-dimensional manifold topology, complex geometry, etc.
Professors： Akito Futaki, Lin Yong, Yang Xiaokui
Associate Professors： Lin Jianfeng, Wu Yunhui, Xiao Jian
Assistant Professors： Chen Weiyan, Gao Honghao, Huang Yi, Jiang Yi, Zhang Yingying
Postdoctoral：Deng Jialong, Han Xiaolong, Monu Kadyan, Telpukhovskiy Ivan, Shang Shijie, Kamtue Supanat, Zhu Zhifei
Analysis, Partial Differential Equation (PDE) and Dynamical Systems
This group studies the evolution of both finite dimensional and infinite dimensional phase spaces of ordinary or partial differential equations originating from dynamical systems, general relativity, hydrodynamics, etc.
Professors：Chen Zhijie, Yitwah Cheung
Associate Professors： Jin Long, Wang Xuecheng, Jing Wenjia
Assistant Professors： Gui Bin, Lan Yang, Zhang Cheng
Postdoctoral： Carruth Nathan Thomas, Wang Gaoming, Zhang Jingxuan
Mathematical Physics group are devoted to the interdisciplinary study between mathematics and physics, including superstring theory, gauge/gravity duality, supersymmetric theories and their applications in geometry, category theory and topological order in condensed matter physics, machine learning in mathematical physics, etc.
Professors： Ling-Yan Hung, Liu Zhengwei, Nicolai Reshetikhin, Song Wei, Zheng Hao
Associate Professors： Babak Haghighat
Assistant Professors： Chi-Ming Chang, Guo Hao, Robert McRae Harold, Liu Ziwen, Mauricio Romo, Wang Qingrui, Wei Zhaohui, Junya Yagi, Yan Wenbin, Zhou Jie
Postdoctoral： Hamed Adami, Chen Yuewen, Hao Pengxiang, Santilli Leonardo, Shim Myungbo, Sugimoto Shoma, Li Hao, Li Yong, Liu Han, Ruggeri Lorenzo, Ma Guorui, Wang Ce, Wang Hao, Nivesvivat Rongvoram, Kolekar Kedar Shrikrishna, Roby Simon,Thierry, Xu Fengjun, Zhang Bingnan
YMSC String Group
Computational and Applied Mathematics focus on utilizing mathematical theories and methods to solve practical problems, as well as on calculating and analyzing mathematical models through numerical methods. This field encompasses various subfields, such as mathematical modeling, numerical analysis, optimization, inverse problems, data science, and cryptography, and is widely applied in multiple disciplines, including engineering, physics, economics, finance, and biology. Computational and applied mathematics not only provide tools to approximate solutions to complex mathematical problems but also offer solid theoretical support for scientific research and engineering practice in various fields. The main research directions include Post-quantum cryptography, Mathematical modeling, Numerical analysis, Numerical solutions to partial differential equations, Computational dynamical systems, Numerical algebra, Inverse problems, Image processing, Large-scale optimization methods, Mathematical theories and computations in material science, Applied analysis, Machine learning theory, Operations and revenue management theory.
Professors： Ding Jintai, Shi Zuoqiang
Associate Professors： Zhou Yuan, Zhu Yi
Assistant Professors：Bao Chenglong, Du Jie, Li Hongjie, Liang Xin, Liu Shuang, Ni Angxiu, Qiu Lingyun, Su Chunmei, Wang Jun, Yu Hui
Postdoctoral： Chi Wenhao, Li Yun, Shi Qingxiang, Wen Jin, Xu Senzhe
Probability and Statistics
Probability studies the mathematical laws of random phenomena. At the end of 19th century, Kolmogorov and others established an axiomatic system of probability theory, setting up the mathematical foundation for probability theory. In recent years, probability theory has been widely used in many aspects such as fundamental mathematics, natural science and business management. The main research areas include: stochastic analysis, stochastic differential equations, limit theory and statistical physics.
Statistics is the foundation and an essential component data science. It studies data collection, data analysis, explanation and inference, and has been widely used in science, engineering, medicine, finance, government and many other areas. It is a tool to extract information from all kinds of data, quantify uncertainties of quantities of interest, and make accurate predictions for the future. The main research areas include: causal inference, missing data, model selection and model averaging, multi-armed bandits, high-dimensional data and machine learning.
Professors： Per Johansson, Donald Rubin, Wu Hao, Yang Fan (F), Yang Yuhong
Associate Professors： Yang Fan (M)
Assistant Professors： Gu Chenlin, Jiang Jianping
Postdoctoral：Huang Xiangyu, Peng Jingfu