# Research Teams

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, Sheng Mao, Zhu Yihang

**Associate Professors:** Diao Hansheng, William Donovan, Xu Bin

**Assistant Professors****:** Dylan Allegretti, Chen Lin, Du Heng, Fan Yu-Wei, He Xiang, Hu Yueke, Li Penghui, Li Yongxiong, Koji Shimizu, Su Changjian, Wang Chengxi, Yang Yilong, Yu Chenglong, Zhang Dingxin, Zheng Zhiwei, Zhou Yu

**Postdoctoral: **Chen Bingyi, Chen Fei, Chen Qingjing, Li Nianzi, Li Pengcheng, Lamarche Alicia Mae, Lukzen Elena, Jia Boming, Jia Jia, Jiao Junpeng, Meng Cheng, 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:** Kenji Fukaya, Akito Futaki, Lin Yong, Vladimir Markovic, Wu Yunhui, Yang Xiaokui

**Associate Professors:** Lin Jianfeng, Xiao Jian

**Assistant Professors:** Chen Weiyan, Gao Honghao, Yi Huang, Sun Weifeng, Zhang Yingying, Zhu Zhifei

**Postdoctoral： **Choudhury Diptaishik，Deng Jialong, Fan Shuanghe, He Xiang, Hu Jiahao, Hu Jinjin, Monu Kadyan, Qing Chenghao, Telpukhovskiy Ivan, Shang Shijie, Shubham Gupta, Sun Haotian, Wang Daxun, Zhang Lei

## 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, Jing Wenjia, Wang Xuecheng

**Assistant Professors： **Gui Bin, Lan Yang, Zhang Cheng

**Postdoctoral：** Carruth Nathan Thomas, Wang Gaoming, Zhang Jingxuan

## Mathematical Physics

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, Yan Wenbin, Zhou Jie

**Assistant Professors: **Chi-Ming Chang, Dawei Ding, Guo Hao, Liu Ziwen, Wang Qingrui, Wei Zhaohui, Junya Yagi

**Postdoctoral****:**** **Arenas-Henriquez Gabriel, Boujakhrout Youssra, Chen Liangyu, Chen Yuewen, Elmi Mohamed Abdulwahid Jama, Hao Pengxiang, Holden Jack David, Jin Anran, Kohli Ben Michael Miloud, Kolekar Kedar Shrikrishna, Li Huihui, Li Yong, Liu Han, Ma Guorui, Ruggeri Lorenzo, Santilli Leonardo, Shim Myungbo, Sugimoto Shoma, Wang Ce, Wang Hao, Wei Xingyue, Zhao Roy

**YMSC String Group**

## Applied Mathematics

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, Ma Jie, Shi Zuoqiang, Zhu Yi

**Associate Professors****:**** **Bao Chenglong, Zhou Yuan

**Assistant Professors****:**** **Angelica Aviles-Rivero, Li Hongjie, Li Li, Liu Jinpeng, Liu Shuang, Ni Angxiu, Pang Tongyao, Qiu Lingyun, Su Chunmei, Wang Jun

**Postdoctoral:** Chi Wenhao, Li Yueyao, Li Yun, Shi Qingxiang, Tahereh Eftekhari, Wen Jin, Zhang Zhen

## 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, Wu Hao, Yang Fan (F), Yang Yuhong

**Associate Professors: **Yang Fan (M)

**Assistant Professors: **Gu Chenlin, Jiang Jianping, Wu Yunan

**Postdoctoral: **Chen Yuanxing, Gao Ziwen, Hu Jie, Huang Xiangyu, Peng Jingfu