PhD Advisors - 北京国际数学研究中心

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.	Co-advise 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		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	Zhiyu Tian	Rationally Connected Varieties.
10		Junyi Xie	Arithmetic Dynamics and Related Topics in Algebraic Geometry
11		Chenyang Xu	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		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.	Temporarily not accepting students
			2. Differential Geometry in General Relativity.
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:	Co-advise with Xiaobo Liu
			1.Topological phases of matter.
			2. T-dualities in string condensed matter and string theory.
			3. Applications of coarse geometry and index theory.
17		Bohan Fang	1. Sheaf-theoretic method in symplectic geometry, Fukaya categories and Mirror Symmetry.
			2. Topological recursion and Gromov-Witten invariants.
18		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.
19		Emanuel Scheidegger	1. Mirror symmetry of Calabi-Yau manifolds, Gromov-Witten invariants.	Co-advise with Xiaobo Liu
			2. Topological string theory and automorphic forms, BPS invariants.
			3. D-brane categories of Calabi-Yau manifolds.
20		Xin Sun	1. Random geometry.
			2. Statistical physics.
			3. Quantum field theory.
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 dimensional manifolds.
			2. Gauge theory.
25		Wenyuan Yang	1. Non-positively curved spaces and groups.
			2. Random walk on groups.
26	PDE/Analysis	Lingrui Ge	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		Zhiqiang Li	1. Dynamical systems.
			2. Metric geometry.
			3. Complex analysis.
29		Baoping Liu	1. Low regularity solution for Chern-Simons-Schrodinger equation.
			2. Long time dynamics and global center stable manifold.
30		Zhenfu Wang	1. The mean field limit for large systems of interacting particles.
			2. Analysis of kinetic equations.
31		Jiajun Tong	1. Free boundary problems in partial differential equations.
			2. Equations of fluid dynamics.
32		Weijun Xu	1. Stochastic Analysis.
			2. Stochastic PDEs.
33		Shiwu Yang	1. Nonlinear wave equations.
			2. Einstein's equation.
34	Combinatorics	Yibo Gao	1. Coxeter groups and Bruhat orders.
			2. Schubert varieties and related varieties.
			3. Polytopes and hyperplane arrangements.
			4. Enumerative combinatorics.
35	Mathematical Logic	Kyle Gannon	1. Model theory.	Co-advise with Wenyuan Yang
			2. Topological dynamics.
070102 Computational Mathematics
36	Computational Mathematics and Applied Mathematics	Bin Dong	1. Deep learning from applied mathematics perspective.
			2. Inverse Problem in image processing.
			3. Biomedical imaging analysis.
37		Zhengyu Huang	1. Bayesian inverse problems and uncertainty quantification.
			2. Scientific machine learning.
			3. Multiphysics simulation.
38		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.
39		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
40	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.
41		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.
42		Zhenfu Wang	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	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.
46		Xiang Zhan	1. Biostatistics and Bioinformatics.
			2. Statistical Genetics.
			3. High-dimensional omics data analysis and inference.