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

Fumiaki Suzuki

1.  Algebraic cycles.

2.  Rationality questions.

Co-advise with Zhiyu Tian

10

Zhiyu Tian

1.  Rationally Connected Varieties.

11

Junyi Xie

1.  Arithmetic Dynamics and Related Topics in Algebraic Geometry.

12

Qizheng Yin

1.  Moduli spaces and algebraic cycles.

2.  Topology and algebraic geometry of hyper-Kähler varieties.

3.  K3 categories.

13

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.

14

Jie Qing

1.  Conformal Geometry and Differential Equation.

2.  Differential Geometry in General Relativity.

Temporarily not accepting students

15

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.

16

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

17

Bohan Fang

1.  Sheaf-theoretic method in symplectic geometry, Fukaya categories and Mirror Symmetry.

2.  Topological recursion and Gromov-Witten invariants.

18

Guillaume Baverez

1.  Random geometry.

2.  Conformal field theory.

3.  Harmonic analysis of infinite dimensional Lie groups.

4.  Moduli spaces.

Co-advise with Xin Sun

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, Gromov-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

Xin Sun

1.  Random geometry.

2.  Statistical physics.

3.  Quantum field theory.

22

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.

23

Xiaomeng Xu

1.  Irregular singularities and representation theory.       

2.  Poisson geometry and quantization.   

24

Topology

Yi Liu

1.  Topology of 3-manifolds.

2.  Hyperbolic geometry.

25

Yi Xie

1.  Knots and links in 3 dimensional manifolds. 

2.  Gauge theory.

26

Wenyuan Yang

1.  Non-positively curved spaces and groups.

2.  Random walk on groups.

27

PDE/Analysis

Albert Ai

1.  Low regularity well-posedness for quasilinear PDEs,.

2.  Water waves and fluid models.

3.  Strichartz estimates and harmonic analysis.

Co-advise with Baoping Liu

28

Lingrui Ge

1.  Dynamical systems.

2.  Mathematical Physics and Spectral Theory.

29

Zhiqiang Li

1.  Dynamical systems. 

2.  Metric geometry. 

3.  Complex analysis.

30

Baoping Liu

1.  Low regularity solution for Chern-Simons-Schrodinger equation.

2.  Long time dynamics and global center stable manifold.

31

Zhenfu Wang

1.  The mean field limit for large systems of interacting particles. 

2.  Analysis of kinetic equations.

32

Jiajun Tong

1.  Free boundary problems in partial differential equations.

2.  Equations of fluid dynamics.

33

Weijun Xu

1.  Stochastic Analysis. 

2.  Stochastic PDEs.

34

Shiwu Yang

1.  Nonlinear wave equations. 

2.  Einstein's equation.

35

Combinatorics

Yibo Gao

1.  Coxeter groups and Bruhat orders.

2.  Schubert varieties and related varieties.

3.  Polytopes and hyperplane arrangements.

4.  Enumerative combinatorics.

36

Mathematical Logic

Kyle Gannon

1.  Model theory.

2.  Topological dynamics.

Co-advise with Wenyuan Yang

070102 Computational Mathematics　　

37

Computational Mathematics and Applied Mathematics

Dong An

1.  Quantum algorithms and applications in scientific computing, including linear systems of equations and differential equations.

2.  Quantum simulation algorithms.

3.  Adiabatic quantum computing.

38

Bin Dong

1.  Deep learning from applied mathematics perspective.

2.  Inverse Problem in image processing.

3.  Biomedical imaging analysis.

39

Zhengyu Huang

1.  Bayesian inverse problems and uncertainty quantification.

2.  Scientific machine learning.

3.  Multiphysics simulation.

40

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.

41

Lei Zhang

1.  Numerical algorithms and applications of rare events and its saddle-point problems.

2.  Computational materials science.

3.  Computational systems biology.

070103/071400 Probability and Statistics

42

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.

43

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.

44

Zhenfu Wang

1.  Stochastic differential equations.

2.  Large deviation estimates.

45

Xin Sun

1.  Random geometry.

2.  Statistical physics.

3.  Quantum field theory.

46

Weijun Xu

1.  Stochastic Analysis. 

2.  Stochastic PDEs.

47

Statistics

Yijuan Hu

1.  Biostatistics.

2.  Bioinformatics.

3.  Microbiome statistics.

4.  Statistical genetics.

48

Molei Liu

1.  Data Fusion

2.  Semi-supervised and Transfer Learning

3.  Semi-parametric Theory

4.  Distributionally Robust Optimization

5.  Electronic Health Record Data

49

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 systems.

6. Machine learning and artificial intelligence.