王楷植Kaizhi Wang
副教授Associate Professor

办公室??Office：
6 号楼 731
办公接待时间??Office Hour：
Monday 19:00-21:00
办公室电话??Office Phone：
**
E-mail：
kzwang at sjtu.edu.cn
教育背景??Education：
博士，2009，吉林大学
Ph.D., 2009, Jilin University

研究兴趣??Research Interests：
弱KAM理论；Hamilton-Jacobi方程；平均场博弈
Weak KAM theory; Hamilton-Jacobi equations; Mean field games

教育背景/经历　Education
2004-2009: Ph.D. in Mathematics, Jilin University, Changchun
2000-2004: B.Sc. in Mathematics, Jilin University, Changchun

工作经历　Work Experience
7/2015-present: Associate Professor, Department of Mathematics, Shanghai Jiao Tong University, Shanghai
9/2011-7/2015: Associate Professor, School of Mathematics, Jilin University, Changchun
2/2010-6/2012: Postdoctoral Researcher, School of Mathematical Sciences, Fudan University, Shanghai
7/2009-9/2011: Lecturer, School of Mathematics, Jilin University, Changchun
Academic Experiences
12/2017-12/2018:VisitingDipartimento di Matematica,Universita di Roma TorVergata, Rome, Italy

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9/12/2014: Visiting Institute of Mathematical Sciences, Chinese University ofHong Kong, Hong Kong

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9/2014-1/2015: Visiting Department of Mathematics, City University of Hong Kong, Hong Kong

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6/2013-7/2013: Visiting Shanghai Center for Mathematical Sciences, Shanghai

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2/2012-3/2012: Visiting Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan

Grants
2018.01-2021.12,Principal investigator,Contact Hamiltonian systems and propagation of singularities of viscosity solutions to a class of PDEs,National Natural Science Foundation of China (GeneralProgram).

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2014.01-2017.12,Principal investigator,Some problems in weak KAM theory,National Natural Science Foundation of China(GeneralProgram).

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2011.01-2013.12, Principal investigator,Some problems in Aubry-Mather theory for higher dimensional Hamiltonian systems,National Natural Science Foundation of China (Youth Foundation).

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2011.01- 2013.12,Principal investigator,Aubry-Mather theoryfor higher dimensional quasi-periodic Hamiltonian systems,Research Fund for the Doctoral Program of Higher Education.

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2011-2012, Principal investigator,New Lax-Oleinik type operators for time-periodic positive definite Lagrangian systems,China Postdoctoral Science Foundation (Special Foundation).

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2010-2012,Principal investigator,Minimal solutions of Monge-Ampère equations,China Postdoctoral Science Foundation(GeneralProgram).

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2010-2011,Principal investigator, Rate of convergence of Lax-Oleinik semigroups in weak KAM theory,Shanghai Postdoctoral Science Foundation(GeneralProgram).

A Partial List of Publications and Preprints

Mean field games
[1] Piermarco Cannarsa, Wei Cheng, Cristian Mendico, Kaizhi Wang, Long-time behavior of first-order discounted mean field games, preprint.
[2] Piermarco Cannarsa, Wei Cheng, Cristian Mendico, Kaizhi Wang,Weak KAM aspects of Hamilton-Jacobi equations with state constraints and applications to long-time behavior of constrained first-order mean field games, arXiv: 2004.06505.
[3]Piermarco Cannarsa, Wei Cheng, CristianMendico,KaizhiWang,Long time behaviour of first order mean field games on Euclidean space,Dynamic Games and Applications10 (2020) 361-390.

Weak KAM theory and Hamilton-Jacobi equations
[1] Kaizhi Wang, LinWang,Jun Yan, Aubry-Mather andweak KAM theories for contact Hamiltonian systems. Part 2: Strictly decreasing case, arXiv:1805.04738.
[2] Piermarco Cannarsa, Wei Cheng, Liang Jin, Kaizhi Wang, Jun Yan,Herglotz’ variational principle and Lax-Oleinik evolution,Journal de Mathématiques Pures et Appliquées141 (2020), 99-136.
[3] Kaizhi Wang, LinWang,Jun Yan, Aubry-Mather andweak KAM theories for contact Hamiltonian systems,Communications in Mathematical Physics366 (2019), 981-1023.
[4]Piermarco Cannarsa, Wei Cheng, Marco Mazzola, Kaizhi Wang, Global generalized characteristics for the Dirichlet problem for Hamilton-Jacobi equations at a supercritical energy level,SIAM Journal on Mathematical Analysis51 (2019), no. 5, 4213-4244.
[5] Piermarco Cannarsa, Wei Cheng, Kaizhi Wang, Jun Yan,Herglotz’ generalized variational principle and contact type Hamilton-Jacobi equations, Trends in Control Theory and Partial Differential Equations, 39–67. Springer INdAM Ser. 32, Springer, Cham, 2019.
[6] KaizhiWang,The asymptotic bounds of viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations, Pacific Journal of Mathematics298 (2019), 217-232.
[7] KaizhiWang, LinWang,Jun Yan,Variational principle for contact Hamiltonian systems and its applications, Journal de Mathématiques Pures et Appliquées123 (2019), 167-200.
[8] Kaizhi Wang,Exponential convergence to time-periodic viscosity solutions in time-periodic Hamilton-Jacobi equations,Chinese Annals of Mathematics, Series B39 (2018), 69-82.
[9] KaizhiWang, LinWang,Jun Yan,Implicit variational principle for contact Hamiltonian systems,Nonlinearity30 (2017), 492-515.
[10] Qihuai Liu, Kaizhi Wang, LinWang,Jun Yan,A necessary and sufficient condition for convergenceof the Lax-Oleinik semigroup for reversible Hamiltonians on R^n,Journal of Differential Equations261 (2016), 5289–5305.
[11] Kaizhi Wang,Jun Yan,Lipschitz dependence of viscosity solutions of Hamilton-Jacobi equations with respect to the parameter, Discrete and Continuous Dynamical Systems36 (2016), 1649-1659.
[12] Kaizhi Wang,Yong Li, Some results on weak KAM theory for time-periodic Tonelli Lagrangian systems, Advanced Nonlinear Studies13 (2013), 853-866.
[13] Kaizhi Wang,Jun Yan,Weak KAM theory in time-periodic Lagrangian systems, Proceedings on Sino-Japan Conference of Young Mathematicians on Emerging Topics on Differential Equations and their Applications, Nankai Series in Pure, Applied Mathematics and Theoretical Physics-Vol. 10, 227-238, 2013.
[14] Kaizhi Wang,Jun Yan,A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems, Communications in Mathematical Physics309 (2012), 663-691.
[15] Kaizhi Wang,Jun Yan,The rate of convergence of the new Lax-Oleinik type operator for time- periodic positive definite Lagrangian systems, Nonlinearity25 (2012), 2039-2057.
[16] Kaizhi Wang,Jun Yan,The rate of convergence of the Lax-Oleinik semigroup-degenerate fixed point case, Science China: Mathematics54 (2011), 545-554.


Teaching
2015年秋 数学分析 I（致远工科荣誉课程）
2016年春 高等数学 (A)
2016年秋 高等数学 (A)
2017年春 高等数学 (A)
2017年秋高等数学 (B)
2019年春 数学分析 II（致远工科荣誉课程）



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