PhD Advisors and Their Research Interests of Beijing International Center for Mathematical Research

No.

Research Fields

PhD Advisors of BICMR

Research Interests

Remarks

070101 Fundamental Mathematics

1

Algebra

Xiang Fu

1. The distribution of roots in the root systems of infinite reflection groups and Coxeter groups, and related geometric questions.
2. The rigidity question of Coxeter groups (the classification of Coxeter groups which can be uniquely determined by the associated Dynkin diagrams).
3. Topological questions on the Cayley graphs of infinite Coxeter groups. 
4. The classification of Infinite Coxeter groups.
5. The application of Coxeter group theory in physics and beyond.

Co-advise with Ruochuan Liu

2

Jun Yu

1. Lie group and its representation.
2. Langlands program.

 

3

Jiping Zhang

1. Finite Group and its applications.
2. Modular representation theory and fusion system.

 

4

Number Theory

Yiwen Ding

1.  Local-global compatibility in p-adic Langlands program.
2. Higher L-invariants and their relationship with  p-adic L functions.

 

5

Wenwei Li

1. Mathematical problems and methods related to Langlands program. 
2. Representation theory of p-adic reductive group and  real reductive group.
3. Trace Formula and its applications.

 

6

Ruochuan Liu

1. p-adic Hodge theory. 
2. p-adic automorphic forms.
3. p-adic Langlands program.

 

7

Liang Xiao

1. p-adic Hodge theory.
2. p-adic automorphic forms.
3. geometry of Shimura varieties.

 

8

Xinyi Yuan

1. Arakelov geometry.
2. Diophantine geometry and Algebraic dynamics.
3. Shimura varieties and L-functions.

 

9

Algebraic Geometry

Huayi Chen

1. Arakelov geometry.
2. Diophantine geometry.
3. Geometry of numbers.

Temporarily not accepting students

10

Zhiyu Tian

Rationally Connected Varieties.

 

11

Junyi Xie

Arithmetic Dynamics and Related Topics in Algebraic Geometry

 

12

Chenyang Xu

Birational Geometry:
1. Geometric and Arithmetic theory of Rationally Connected Varieties.
2. Minimal Model Program and Classification of varieties.
3. Stability.
4. Topology and Geometry of Singularities.

Temporarily not accepting students

13

Qizheng Yin

1. Moduli spaces and algebraic cycles.
2. Topology and algebraic geometry of hyper-Kähler varieties.
3. K3 categories.

 

14

Differential Geometry

Xiaobo Liu

His current research is focused on Differential Geometry and Mathematical Physics, including:
1. Gromov-Witten invariants.
2. Isoparametric submanifold.
3. Global minimal submanifold.

 

15

Jie Qing

1. Conformal Geometry and Differential Equation.
2. Differential Geometry in General Relativity.

Temporarily not accepting students

16

Gang Tian

His current research is focused on Geometric Analysis and Symplectic Geometry, including:
1. Geometric Equation and its analysis. 
2. Ricci Flow and its applications.
3. Complex geometry.
4. Symplectic geometry and symplectic topological invariants.

 

17

Mathematical Physics

Guochuan Thiang

K-theory, index theory, operator algebras, and differential geometry in: 
1.Topological phases of matter.
2. T-dualities in string condensed matter and string theory.
3. Applications of coarse geometry and index theory.

Co-advise with Xiaobo Liu

18

Bohan Fang

1. Sheaf-theoretic method in symplectic geometry, Fukaya categories and Mirror Symmetry.
2. Topological recursion and Gromov-Witten invariants.

 

19

Xiaobo Liu

His current research is focused on Differential Geometry and Mathematical Physics, including:
1. Gromov-Witten invariants.
2. Isoparametric submanifold.
3. Global minimal submanifold.

 

20

Emanuel Scheidegger

1. Mirror symmetry of Calabi-Yau manifolds, Gromow-Witten invariants.
2. Topological string theory and automorphic forms, BPS invariants.
3. D-brane categories of Calabi-Yau manifolds.

Co-advise with Xiaobo Liu

21

Gang Tian

His current research is focused on Geometric Analysis and Symplectic Geometry, including:
1. Geometric Equation and its analysis. 
2. Ricci Flow and its applications.
3. Complex geometry.
4. Symplectic geometry and symplectic topological invariants.

 

22

Xiaomeng Xu

1. Irregular singularities and representation theory.                                              2. Poisson geometry and quantization.

 

23

Topology

Yi Liu

1. Topology of 3-manifolds.
2. Hyperbolic geometry.

 

24

Yi Xie

1. Knots and links in 3-manifolds.                                                                                        2. Gauge theory.

 

25

Wenyuan Yang

1. Non-positively curved spaces and groups.
2. Random walk on groups.

 

26

PDE/Analysis

Yan Guo

1. Partial Differential Equations in kinetic theory.  
2. Stability in fluid.

Temporarily not accepting students

27

Zhiqiang Li

1. Dynamical systems.                                                                                                2. Metric geometry.                                                                                                    3. Complex analysis.

 

28

Baoping Liu

1. Low regularity solution for Chern-Simons-Schrodinger equation.
2. Long time dynamics and global center stable manifold.

 

29

Zhenfu Wang

1. The mean field limit for large systems of interacting particles. 
2. Analysis of kinetic equations.

 

30

Jiajun Tong

1. Free boundary problems in partial differential equations.
2. Equations of fluid dynamics.

 

31

Weijun Xu

1. Stochastic Analysis. 
2. Stochastic PDEs.

 

32

Shiwu Yang

1. Nonlinear wave equations. 
2. Einstein's equation.

 

070102 Computational Mathematics  

33

Computational Mathematics and Applied Mathematics

Bin Dong

1. Deep learning from applied mathematics perspective.
2. Inverse Problem in image processing.
3. Biomedical imaging analysis.

 

34

Zaiwen Wen

1. Algorithms and theories for non-convex, nonlinear and non-smooth optimization.
2. Algorithms and theories for optimization on manifold.
3. Machine learning: algorithms and theories for deep learning and reinforcement learning.

 

35

Lei Zhang

1. Numerical algorithms and applications of rare events and its saddle-point problems.
2. Computational materials science.
3. Computational systems biology.

 

36

Zhennan Zhou

1. Non-adiabatic phenomenon in quantum mechanics and theoretical chemistry.
2. Analysis and computation of semi-classical Schödinger equations.
3. Analysis and computation of Chemotaxis and tumor growth models, neuron network models, etc.

 

070103/071400 Probability and Statistics

37

Probability

Hao Ge

1. Stochastic theory of nonequilibrium thermodynamics and statistical mechanics;
2. Nonequilibrium landscape theory and rate formulas for single-molecule and single-cell biology;
3. Stochastic modeling in systems biology and biophysical chemistry;
4. Statistical analysis of single-cell big data.

 

38

Xinyi Li

Discrete stochastic models with significance in statistical physics, including:
1. Fractal Properties of Random walk and Brownian motion.
2. Percolation.
3. Random interlacements and related models.

 

39

Zhenfu Wang

1. Stochastic differential equations.
2. Large deviation estimates.

 

40

Weijun Xu

1. Stochastic Analysis. 
2. Stochastic PDEs.

 

41

Statistics

Xiaohua Zhou

1. Clinical experiment design and data statistics.
2. Causal inference.
3. Analysis and modeling of big data. 
4. Analysis of missing data. 
5. Evaluation of  artificial intelligence-based CAD sysytems. 
6. Machine learning and artificial intelligence.