# 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, 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： **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, Wu Yunhui,Yang Xiaokui

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

**Assistant Professors：** Chen Weiyan, Gao Honghao, Huang Yi, Zhang Yingying

**Postdoctoral：**Deng Jialong, Shubham Gupta, Han Xiaolong, Monu Kadyan, Telpukhovskiy Ivan, Shang Shijie, Kamtue Supanat, Zhang Lei, 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

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

**Assistant Professors：**Chi-Ming Chang, Guo Hao, Robert McRae Harold, Liu Ziwen, Mauricio Romo, Wang Qingrui, Wei Zhaohui, Junya Yagi, Zhou Jie

**Postdoctoral：** Hamed Adami, Chen Yuewen, Holden Jack David, Arenas-Henriquez Gabriel, 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

**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, Shi Zuoqiang, Zhu Yi

**Associate Professors：** Zhou Yuan

**Assistant Professors：**Bao Chenglong, Li Hongjie, Liang Xin, Liu Shuang, Ni Angxiu, Pang Tongyao, Qiu Lingyun, Su Chunmei, Wang Jun

**Postdoctoral：** Chi Wenhao, Tahereh Eftekhari, 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：**Hu Jie, Huang Xiangyu, Peng Jingfu