"Numerical Analysis" (in chinese): 《数值分析》(北京大学出版社). An errata is here.
Some publications
Chemical Reaction Kinetics: Currently we focus our research on the understanding of the
tauleaping algorithm and constructing more accurate and stabilized schemes based on solid mathematical analysis. I mainly collaborate with
Assyr Abdulle (EPFL), Fangting Li (PKU) and my students Yucheng Hu and Bin Min (PKU) in this research field.
 Analysis of explicit tauleaping schemes for simulating chemically
reacting systems, Multi. Mod. Simul. 6 (2007), 417436.
 SROCK methods for stiff Ito SDEs,
with Assyr Abdulle, Comm. Math. Sci. 6 (2008), 845868.
 Highly accurate tauleaping methods for simulating chemically
reacting systems, with Yucheng Hu, J. Chem. Phys 130 (2009), 124109.
 Chebyshev methods with discrete noise: the tauROCK methods,
with Assyr Abdulle and Yucheng Hu, J. Comp. Math. 28 (2010), 195217.
 The weak convergence analysis of tauleaping methods: revisited,
with Yucheng Hu and Bin Min, Comm. Math. Sci. 9 (2011), 965996.
 A weak second order tauleaping method for chemical kinetic systems, with Yucheng Hu and Bin Min, J. Chem. Phys. 135 (2011), 024113.
 Efficient simulation under a population genetics model of carcinogenesis, with Tianqi Zhu, Yucheng Hu, Zhiming Ma, Dexing Zhang, Ziheng Yang, Bioinformatics 27 (2011), 837843.
Rare events: We aim to develop the mathematical theory and numerical methods for the rare events in material sciences and systems biology. I mainly collaborate with Wei Zhang (PKU), Pingwen Zhang (PKU) and Xiang Zhou (CityU HK) in this field.
 Numerical study for the nucleation of onedimensional stochastic CahnHilliard dynamics, with Wei Zhang and Pingwen Zhang, Comm. Math. Sci. 10 (2012), 11051132.
 Nucleation rate calculations for the phase transition of diblock copolymers under stochastic CahnHilliard dynamics, with Wei Zhang and Pingwen Zhang, SIAM Multi. Model. Simul. 11 (2013), 385409.
 Constructing the energy landscape for genetic switching system driven by intrinsic noise, with Cheng Lv, Xiaoguang Li and Fangting Li, PLoS ONE 9 (2014), e88167. SI
 Energy landscape reveals that the budding yeast cell cycle is a robust and adaptive multistage process, with Cheng Lv, Xiaoguang Li and Fangting Li, PLoS Comp. Biol. 11 (2015), e1004156. SI
 Distinguishing the rates of gene activation from phenotypic variations, with Ye Chen, Cheng Lv and Fangting Li, BMC Syst. Biol. 9 (2015), 29.
 Finding transition pathways on manifolds, with Xiaoguang Li and Xiang Zhou, SIAM Multi. Model. Simul. 14 (2016), 173206.
 Large deviations for twoscale chemical kinetic processes, with Feng Lin, Submitted, 2014.
 Twoscale large deviations for chemical reaction kinetics through second quantization path integral, with Feng Lin, J. Phys. A: Math. Theor. 49 (2016), 135204.
 Construction of the landscape for multistable systems: Potential landscape, quasi potential, Atype integral and beyond, with Peijie Zhou, J. Chem. Phys. 144 (2016), 094109.
Anderson Localization: The theme is to understand the effect of the noise (timedependent for
linear Schrodinger equation and timeindependent for nonlinear Schrodinger equation) to the quantum system. I mainly collaborate with Weizhu Bao (NUS) and Bin Min (PKU) in this field.
Multiscale modeling of complex fluids: We have done some theoretical analysis for the
multiscale models of complex fluids, such as the wellposedness of the equations, convergence analysis of the BCF method, and HMM methods.
This is an exciting area. I mainly collaborate with Weinan E (Princeton), Eric VandenEijnden (Courant), Hui Zhang (BNU) and Pingwen Zhang (PKU)
in this field.
 Stochastic models of polymeric liquids at small Deborah number, with Eric VandenEijnden, Pingwen Zhang, and Weinan E, J. NonNewtonian Fluid Mech.
121 (2004), 117125.
 Analysis of 1+1 dimensional stochastic models
of liquid crystal polymer flows, with Pingwen Zhang and Xiang Zhou, Comm. Math. Sci. 2 (2004), 295316.
 Local existence for the dumbbell model of
polymeric fluids, with Hui Zhang and Pingwen Zhang, Comm. PDE, 29 (2004), 903923.
 Wellposedness for the dumbbell model of polymeric fluids, with Weinan E and Pingwen Zhang, Comm. Math. Phys. 248 (2004), 409427.
 Convergence analysis of BCF methods for Hookean dumbbell model, with Pingwen Zhang, Multi. Model. Simul. 5 (2006), 205234.
 Mathematical analysis of multiscale models of complex fluids, with Pingwen Zhang, Comm. Math. Sci. 5 (2007), 151.
Statistical data analysis: The data is emerging each second in our time. How to
extract the information from the data? We consider this problem from different interesting backgrounds such as the complex networks,
quantum optics, Netflix problems etc.
 Model reduction of complex networks: Complex networks usually have huge amount
of nodes and edges. How to optimally reduce this type of models to explore its essential behavior? This covers the problems from
Sociology, Biology and dynamical system theory. We try to do this rationally based on Markov chain theory.
 Optimal partition and effective dynamics of complex networks, with Weinan E and Eric VandenEijnden, Proc. Nat. Acad. Sci., 105 (2008), 79077912.
SI
 Probabilistic framework for network partition,
with Weinan E and Jian Liu, Phys. Rev. E 80 (2009), 026106.
 A validity index approach to network partitions, with Jian Liu, Phys. A, 390 (2011), 35793591.
 Real applications::
 Statistical method for resolving the photonphotoelectroncounting inversion problem, with Jinlong Wu, Xiang Peng and Hong Guo, J. Comp. Phys. 230 (2011) 726.
 A modified fuzzy Cmeans algorithm for collaborative filtering,
with Jinlong Wu, The 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2008), Las Vegas, 2008.
 Effect of exposure to trace elements in the soil on the prevalence of neural tube defects in a highrisk area of China, with Jing Huang et al, Biomed. Environ. Sci. 24 (2011), 94101.
Miscs:
 Marcus canonical integral for nonGaussian processes and its computation: Pathwise simulation and tauleaping algorithm, with Bin Min and Zhiming Wang, J. Chem. Phys. 138 (2013), 104118.
 Adiabatic elimination for systems with inertia driven by compound Poisson colored noise, with Bin Min and Zhiming Wang, Phys. Rev. E 89 (2014), 022144.
 Localized basis of eigensubspaces and operator compression, with Weinan E and Jianfeng Lu, Proc. Nat. Acad. Sci. 107 (2010), 1273.
 On the Poisson approximation for photon distribution for
faint lasers, with Yucheng Hu, Xiang Peng and Hong Guo, Phys. Lett. A, 367 (2007), 173176.
 Effectiveness of implicit methods for stiff stochastic
differential equations, with Assyr Abdulle and Weinan E, Comm. Comp. Phys. 3 (2008), 295307.

Applications
If you want to apply as my graduate student, ask me to supervise your undergraduate
study, or write recommendation letters for you, please read this at first.

Postdocs: Wanted!!!
We have enough funding for postdoc positions. If you have interests to do related research in stochastic modeling and computations, e.g. numerical methods for SDEs, applications in rare events, computational biology, etc. Please send your CV and application letter to me directly.

Grants
 NSFC, grant 10401004, 2005.12007.12
 NSFC, grant 20490222, 2005.12008.12
 MST, grant 2005CB321704, 2005.112010.11
 NSFC, grant 10871010, 2009.12011.12
 NSFC, grant 11171009, 2012.12015.12
 Major Program of NNSFC, grant 91130005, 2012.12015.12
 NSFC, grant 11222114, 2013.12015.12
 NSFC, grant 11421101, Creative group
 Major Program of NNSFC, grant 91530322, 2016.12018.12
Current students
 Ye Chen, Ph.D student
 Zhiming Wang, PhD student
 Feng Lin, PhD student
 Jifan Shi, PhD student
 Peijie Zhou, PhD student
 Tongkai Li, PhD student
 Fan Yao, Master candidate
 Chongning Liao, Master candidate
Former students
 Xiang Zhou, Master (cosupervise with Professor Pingwen Zhang), currently Assistant Professor in City University of Hongkong
 Yan Ding, Ph.D (cosupervise with Professor Pingwen Zhang), currently
in China Everbright Bank
 Yibiao Wu, Master (cosupervise with Professor Pingwen Zhang), currently
in Ping An Insurance Company of China
 Jing Huang, Master 2009 (cosupervise with Professor Pingwen Zhang), currently
in Baidu
 Dajiang Tao, Master 2009, currently in IBM
 Yucheng Hu, Ph.D 2010, currently Assistant Professor in Tsinghua University
 Jinlong Wu, Ph.D 2010 (cosupervise
with Professor Weinan E), currently in Shiji Jiayuan
 Rensheng Zhu, Master 2010
 Jian Liu, PhD 2011 (cosupervise with Professor Weinan E), currently in PICC
 Wei Zhang, PhD 2012 (cosupervise with Professor Pingwen Zhang), currently PostDoc in Freie University of Berlin
 Bin Min, Ph.D 2013, currently PostDoc in Courant Institute, NYU
 Ping Qin, Master 2013, currently in Douban
 Sisi Wang, Master 2015, currently in Renda Fuzhong
 Xiaoguang Li, Ph.D 2016, currently in CSRC
Last modified: Aug. 27th, 2015.
