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. 
Coadvise with Ruochuan Liu 
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. 

2 
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 
1. Localglobal compatibility in padic Langlands program. 


2. Higher Linvariants and their relationship with padic L functions. 

5 
1. Mathematical problems and methods related to Langlands program. 


2. Representation theory of padic reductive group and real reductive group. 

3. Trace Formula and its applications. 

6 
1. padic Hodge theory. 


2. padic automorphic forms. 

3. padic Langlands program. 

7 
1. padic Hodge theory. 


2. padic automorphic forms. 

3. geometry of Shimura varieties. 

8 
1. Arakelov geometry. 


2. Diophantine geometry and Algebraic dynamics. 

3. Shimura varieties and Lfunctions. 

9 
Algebraic Geometry 
Rationally Connected Varieties. 


10 
Arithmetic Dynamics and Related Topics in Algebraic Geometry 


11 
1. Geometric and Arithmetic theory of Rationally Connected Varieties. 
Temporarily not accepting students 

2. Minimal Model Program and Classification of varieties. 

3. Stability. 

4. Topology and Geometry of Singularities. 

12 
1. Moduli spaces and algebraic cycles. 


2. Topology and algebraic geometry of hyperKähler varieties. 

3. K3 categories. 

13 
Differential Geometry 
His current research is focused on Differential Geometry and Mathematical Physics, including: 


1. GromovWitten invariants. 

2. Isoparametric submanifold. 

3. Global minimal submanifold. 

14 
Jie Qing 
1. Conformal Geometry and Differential Equation. 
Temporarily not accepting students 

2. Differential Geometry in General Relativity. 

15 
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 
Ktheory, index theory, operator algebras, and differential geometry in: 
Coadvise with Xiaobo Liu 

1.Topological phases of matter. 

2. Tdualities in string condensed matter and string theory. 

3. Applications of coarse geometry and index theory. 

17 
1. Sheaftheoretic method in symplectic geometry, Fukaya categories and Mirror Symmetry. 


2. Topological recursion and GromovWitten invariants. 

18 
His current research is focused on Differential Geometry and Mathematical Physics, including: 


1. GromovWitten invariants. 

2. Isoparametric submanifold. 

3. Global minimal submanifold. 

19 
Emanuel Scheidegger 
1. Mirror symmetry of CalabiYau manifolds, GromovWitten invariants. 
Coadvise with Xiaobo Liu 

2. Topological string theory and automorphic forms, BPS invariants. 

3. Dbrane categories of CalabiYau manifolds. 

20 
Xin Sun 
1. Random geometry. 


2. Statistical physics. 

3. Quantum field theory. 

21 
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 
1. Topology of 3manifolds. 


2. Hyperbolic geometry. 

24 
Yi Xie 
1. Knots and links in 3 dimensional manifolds. 


2. Gauge theory. 

25 
1. Nonpositively curved spaces and groups. 


2. Random walk on groups. 

26 
PDE/Analysis 
1. Dynamical systems. 


2. Mathematical Physics and Spectral Theory. 

27 
Yan Guo 
1. Partial Differential Equations in kinetic theory. 
Temporarily not accepting students 

2. Stability in fluid. 

28 
1. Dynamical systems. 


2. Metric geometry. 

3. Complex analysis. 

29 
1. Low regularity solution for ChernSimonsSchrodinger equation. 


2. Long time dynamics and global center stable manifold. 

30 
1. The mean field limit for large systems of interacting particles. 


2. Analysis of kinetic equations. 

31 
1. Free boundary problems in partial differential equations. 


2. Equations of fluid dynamics. 

32 
Weijun Xu 
1. Stochastic Analysis. 


2. Stochastic PDEs. 

33 
1. Nonlinear wave equations. 


2. Einstein's equation. 

34 
Combinatorics 
1. Coxeter groups and Bruhat orders. 


2. Schubert varieties and related varieties. 

3. Polytopes and hyperplane arrangements. 

4. Enumerative combinatorics. 

35 
Mathematical Logic 
1. Model theory. 
Coadvise with Wenyuan Yang 

2. Topological dynamics. 

070102 Computational Mathematics 

36 
Computational Mathematics and Applied Mathematics 
1. Deep learning from applied mathematics perspective. 


2. Inverse Problem in image processing. 

3. Biomedical imaging analysis. 

37 
1. Bayesian inverse problems and uncertainty quantification. 


2. Scientific machine learning. 

3. Multiphysics simulation. 

38 
1. Algorithms and theories for nonconvex, nonlinear and nonsmooth optimization. 


2. Algorithms and theories for optimization on manifold. 

3. Machine learning: algorithms and theories for deep learning and reinforcement learning. 

39 
1. Numerical algorithms and applications of rare events and its saddlepoint problems. 


2. Computational materials science. 

3. Computational systems biology. 

070103/071400 Probability and Statistics 

40 
Probability 
1. Stochastic theory of nonequilibrium thermodynamics and statistical mechanics; 


2. Nonequilibrium landscape theory and rate formulas for singlemolecule and singlecell biology; 

3. Stochastic modeling in systems biology and biophysical chemistry; 

4. Statistical analysis of singlecell big data. 

41 
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. 

42 
1. Stochastic differential equations. 


2. Large deviation estimates. 

43 
Xin Sun 
1. Random geometry. 


2. Statistical physics. 

3. Quantum field theory. 

44 
Weijun Xu 
1. Stochastic Analysis. 


2. Stochastic PDEs. 

45 
Statistics 
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 intelligencebased CAD systems. 

6. Machine learning and artificial intelligence. 

46 
1. Biostatistics and Bioinformatics. 


2. Statistical Genetics. 

3. Highdimensional omics data analysis and inference. 